high performance computing at the army high performance...

Current Trends in Computational Chemistry 2001

101

High Performance Computing at the Army High Performance Computing Research Center

Frances C. Hill

AHPCRC-Network Computing Services, 1200 Washington Ave. S, Minneapolis MN 55415

The Army High Performance Computing Research Center (AHPCRC) is a consortium of

government, academic and industry partners dedicated to advancing the state of defense computational science through Army-university collaborative research. Center partners include Clark Atlanta University, Florida A&M University, Howard University, Jackson State University, University of Minnesota, University of North Dakota and Network Computing Services, Inc. The components of the AHPCRC are:

• Basic research in computational sciences • Development of new computational technologies in support of Army mission

requirements through the staff scientist program • Education and mentoring of students in high performance computing applications • Providing a high performance computing environment to provide software and hardware

resources for academic and government partners

Research emphasis at the Center is on electromagnetic signature modeling for the synthetic battlefield, projectile target interaction, virtual computing environments for future combat systems, chemical/biological defense and environmental modeling, and enabling technologies. Interactions among researchers at the partner institutions, as well as with staff scientists and with staff at Army research laboratories provides a strong framework for the rapid development of new ideas and technological advances.

Staff scientists work in support of Army laboratories to facilitate the application of new research methods in support of the Army warfighter. Staff scientists are working in areas such as solid mechanics, protein modeling, fluid dynamics for interior ballistics, groundwater modeling, attrition modeling, and electromagnetics.

The education programs include introductory and advanced summer institutes in HPC technology for undergraduates, ongoing training in HPC for researchers, and support for graduate students in computational science.

The computational systems available to researchers at AHPCRC include a Cray T3E-1200E with 1088 CPUs and four IBM RS/6000 SP2 systems. Together, they are capable of achieving peak performance of ~1.35 Tflops with 575 GB of distributed memory, 4.8 TB of disk available and 50 TB of tape storage. These resources are integrated into a single environment and are available to all AHPCRC researchers.


102

The Effects of Cis Me(NH3)22+, Me=Pd, Pt, and Ni on the Interaction

of Guanine and Cytosine in GC Base Pair

Glake Hill,a Robert. W. Gora,a,b Szczepan Roszak,a,b and Jerzy Leszczynskia

aThe Computational Center for Molecular Structure and Interactions, Department of Chemistry, Jackson State University,

P. O. Box 17910, 1400 J. R. Lynch Street, Jackson, Mississippi 39217 bInstitute of Physical and Theoretical Chemistry, Wroclaw University

of Technology, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland

Studies focused on the interaction of the guanine and cytosine in a canonical GC base pair were performed. These results were compared to the optimized structure the GC base pair when Cis Me(NH3)22+ (Me=Pd, Pt, and Ni) is complexed at the N7, O6 sites of guanine. Studies revealed two local minima (Fig 1 and 2). The interaction energy between the guanine and cytosine is greater when the base pair is complexed. Nickel, the smaller of the three metals, gave the strongest interaction. A detailed evaluation of the interaction energy reveals the individual energy terms that explain the differences in energy between the metals. Finally a population and charge analysis show small but significant electron density differences between the canonical and complexed base pairs.

Figure 1: Local Minima 1 Figure 2: Local Minima 2


103

Are Overlap-Induced Dipole Moments Pairwise Additive?

Robert J. Hinde

Department of Chemistry, University of Tennessee, Knoxville, TN 37996-1600

As two dissimilar atoms or molecules approach one another, their mutual interactions generate a pair dipole moment. This is true even for the approach of two dissimilar spherical (S-state) atoms, which lack electrostatic multipoles capable of inducing dipole moments at long range. These isotropic interaction-induced dipole moments arise from dispersion and exchange effects, and lead to collision-induced infrared absorption in dense mixtures of rare gases and in planetary atmospheres. Here we present ab initio calculations of the interaction-induced dipole moment of the Li–He pair and the Li–He2 triatomic complex. We investigate whether the dipole moment of the triatomic complex can be approximated as a pairwise sum of interaction-induced Li–He dipoles.


104

Recent Advances in Molecular Electronic Structure Theory

Kimihiko Hirao

Department of Applied Chemistry, School of Engineering, University of Tokyo, Tokyo, Japan 113-8656

Recently accurate ab initio quantum computational chemistry has evolved dramatically. The size of molecular systems, which can be studied accurately using ab initio methods is increasing very rapidly. Computational chemistry can treat real systems with predictive accuracy. It has opened a world of new possibilities and is becoming an integral part of chemistry research. Theory can now make very significant contribution to chemistry. Recent advances in molecular electronic structure theory achieved at the University of Tokyo will be reviewed. Emphasis will be put on the recent developments of (1) Multireference Based Perturbation Theory Multireference Møller-Plesset (MRMP) [1] has opened up a whole new area and has had a profound impact on the potential of theoretical chemistry. MRMP has been successfully applied to numerous chemical and spectroscopic problems and has established as an efficient method for treating nondynamical and dynamical correlation effects. The method has several attractive features for the study of chemical problems. It is almost size-consistent, it is capable of describing open-shell fragments with multiconfigurational electronic character, and it includes nondynamical and dynamical correlation effects in a balanced way in the electronic wave function of closed-shell and open-shell states. Recent advances in MRMP and its applications will be reviewed. (2) Relativistic Electronic Structure Theory It is now well known that relativistic effects are important in the study of heavy-element systems. Instead of the Schrödinger equation, one has to solve the Dirac equation, which involves a four-component Hamiltonian. Recently we have developed a very efficient algorithm of four-component Dirac-Fock, Dirac-Kohan-Sham formalisms [2]. The solution of the Dirac equation, however, still demands severe computational. Instead of explicitly solving the full four-component relativistic Dirac equation, several two-component treatments have been proposed. We have developed two-component RESC theory [3] and the higher order Douglas-Kroll approximation [4]. For accurate relativistic calculations the basis sets are also required, which are appropriate for the incorporation of the relativistic effects. Highly accurate relativistic Gaussian basis sets (Point nucleus and Finite nucleus Models) have been developed for the 103 elements from H (Z=1) to Lr (Z=103) [5]. References [1] K. Hirao, Chem.Phys.Lett., 190, 374 (1992), 196, 397 (1993), 201, 59 (1993); H. Nakano, J.

Nakatani, and K. Hirao, J.Chem.Phys., 114, 1133 (2001). [2] T. Yanai, T. Nakajima, Y. Ishikawa, and K. Hirao, J.Chem.Phys., 114, 6525 (2001). [3] T. Nakajima and K. Hirao, Chem.Phys.Lett., 302, 383 (1999). [4] T. Nakajima and K. Hirao, J.Chem.Phys., 113, 7786 (2000). [5] T. Tsuchiya, M. Abe, T. Nakajima, and K. Hirao, J.Chem.Phys., 115, 4463-4472 (2001).


105

Searches on the Potential Energy Surfaces of GaNH2 and GaPH2

Patricia L. Honea, Karen E. Hand, and David H. Magers

Department of Chemistry and Biochemistry Mississippi College, Clinton, MS 39058

Optimum equilibrium geometries are computed for several isomers on the potential

energy hypersurfaces of GaNH2 and GaPH2 using SCF theory, second-order perturbation theory, and density functional theory (DFT). The DFT functional employed is Becke=s three parameter hybrid functional using the LYP correlation functional. Nineteen initial geometries are investigated including linear, trans-bent, cis-bent, methylenecarbene-like structures, mono-bridged, and di-bridged structures. Harmonic vibrational frequencies are computed for the optimized structures to characterize them as local minima or transition states. Infrared intensities within the double harmonic approximation are also determined. Internal reaction coordinate calculations are used to determine what minima are connected by the transition states located in the initial computations. Two basis sets, both of triple-zeta quality on valence electrons, are employed: 6-311G(d,p) and 6-311G(2df,2pd). Finally, comparisons are made to the previously studied systems of AlNH2 and AlPH2. We gratefully acknowledge support from NSF EPSCoR (EPS-9874669).


106

Pronounced Structural Nonrigidity of the Canonical DNA Bases: A Post Hartree-Fock Quantum-Chemical Study

Dmytro M. Hovorun, Leonid Gorb and Jerzy Leszczynski

Computational Center for Molecular Structure and Interactions, Department of

Chemistry, Jackson, Mississippi, 39217 The idea that nonlinear-dynamical properties of DNA play an important role during all

steps of its functioning is generally accepted. However, traditional point of view considers the torsional flexibility of single chemical bonds, which belong to the sugar rings and (or) are attached to sugar rings as the source of such properties. Such a concept includes a presence of planar or non-planar nucleic acid bases as relatively rigid fragments. There the dynamic behavior is taken into account as small harmonic vibrations of corresponding atoms or atomic groups.

The presented investigation aims to validate the point of view described above. We will prove that the nucleotide bases are very important component of DNA nonlinear-dynamical behavior. Our statements will be based on the methodology that has been applied earlier to 2-aminoimidazole as a model molecule having all the most important structural components of modified DNA bases. As it follows from the results obtained in [1], the DNA bases having the amino-group should be considered as structurally nonrigid species where the interconversion of amino-fragment could occur through the three topologically and energetically non-equivalent pathways. The mentioned pathways are the plane inversion of C-NH2 fragment, and two possible anysotropic hindered rotations of amino-group around exocyclic C-N bond. The presented study is an example of an application of such methodology to the two DNA bases cytosine and thymine. It reveals:

1. For the first time it has been shown that the canonical structures of cytosine and thymine belong to the class of structural non-rigid molecules possessing strong non-linear dynamical behavior. The interconversion of cytosine amino-fragment could be realized by three topologically and energetically different pathways: the plane inversion of amino-group and its anysotropic hindered rotation around exo-cyclic C-N bond. The source of thymine structural nonrigidity is linked with hindered torsional rotation of CH3- group, which has the barrier of c.a. 1.2 kcal/mol.

2. Cytosine isolated at T = 0 K is effectively planar. This cause the plane inversion of amino-fragment as over-barrier large amplitude vibration with the frequency c.a. 200 cm-1.

3. The cytosine is a dipole non-conserving molecule. Its interconversion is accomplished by significant change of both the value and the direction of the dipole moment. We did not find the same phenomenon during the hindered rotation of CH3.group in thymine.

4. The analysis of a geometrical, electronic and spectral characteristics of conjugation suggests that the basic factor that controls the structural nonrigidity of cytosine is np-conjugation of lone electron pair of amino-nitrogen atom with π-electron system of the heterocyclic ring.

5. The DNA bases have soft (easily deformable in respect to the lowest out-of-plane vibrations) heterocyclic rings. This phenomenon is originated by low values of force constants which are in the range of 0.01 – 0.05 mdyn/Å. It results in atoms maximum orthogonal displacement of 0.1 Å even at T =0 K.


107

6. There is an important biological significance of obtained results. The structural nonrigidity (nonlinear dynamic behavior) of nucleotide bases should inevitably determine high conformational flexibility of Watson – Crick base pairs.

References

1. Dmytro M. Hovorun, Leonid Gorb, Jerzy Leszczynski. International J. Quantum. Chem. 75 (1999) 245 - 253.

2. Dmytro M. Hovorun. Doctor of Scinces Thesis. Kiev, 1999.


108

Theoretical Studies of Alkylation, Hydroxylalkylation, and Sulfobutyl Etheration of β-Cyclodextrins

Ming-Ju Huang and John D. Watts

Department of Chemistry, Jackson State University, P. O. Box 17910, 1400 J. R. Lynch Street,

Jackson, Mississippi, 39217

Nicholas Bodor

Center for Drug Discovery, College of Pharmacy, P. O. Box 100497, Health Science Center, Gainesville, FL 32610-0497

Semi-empirical AM1 molecular orbital calculations have been used to study β-cyclodextrins (β-CDs) in which (i) the 2-, 3- or 6-OH groups have been deprotonated; (ii) one of the 2-, 3- or 6-OH groups has been replaced by a hydroxypropyl ether group; (iii) the protons in all seven 2-, 3-, or 6-OH groups have been replaced by methyl, hydroxylpropyl or sulfobutyl groups. Some of the results are compared with α-D-glucopyranose, seven units of which make β-CD. In addition, the effect of substitution on cavity volume is studied. We found that (1) secondary hydroxyls are more acidic; (2) cavity volume is largest for the most stable hydroxypropylated and sulfobutylated isomers, but opposite is true for methylated isomers; (3) multiple substitution does not introduce significant steric hindrance.


109

Studies of Acetylcholinesterase and Model Nerve Agent Interactions: a QM/MM Approach

Margaret M. Hurley,§ J. B. Wright,† Gerald H. Lushington,‡ William E. White*

§Computational and Information Sciences Directorate, U.S. Army Research Laboratory, ATTN:

AMSRL-CI-HC, Aberdeen Proving Ground, MD 21005 †U.S. Army Natick Soldier Center, AMSSB-RSS-M, Kansas Street, Natick, MA 01760

‡University of Kansas, 1251 Wescoe Hall Rd., c/o Dept. of Medicinal Chemistry, Lawrence, KS 66045

*Edgewood Chemical and Biological Center, 5183 Blackhawk Road, Aberdeen Proving Ground, MD 21010

Calculations on reactions in large model biological systems are becoming more common

as mixed quantum/classical techniques gain in popularity. Here we present results comparing 2 QM/MM implementations (the SIMOMM technique of Gordon et al as implemented in GAMESS, and the ONIOM technique of Morokuma et al as implemented in Gaussian) as performed on the enzyme acetylcholinesterase and several model nerve agents. Details of the catalytic triad (an important feature of the efficacy of this enzyme) will be examined both in the native state, and in processes involving model agents with various structural features. This work represents part of the initial phase of a DoD HPCMO Challenge project.


110

Reconstruction of the Vbrational Hamiltonian from Qantum Chemical Data for the Malonaldehyde

I.S. Irgibaeva

Institute of Chemical Physics in Chernogolovka, Russian Academy of Sciences, 142432,

Moscow Region, Chernogolovka, Russian Federation

21-th dimensional potential energy surfaces (PES) and the tunneling coordinate dependent kinematic matrices of malonaldehyde (MA) are constructed in the low-energy region (< 3000 cm-1) using quantum-chemical data. MA is one of the simplest molecules with intramolecular hydrogen transfer. The two equivalent tautomers, -OH⋅⋅⋅O= and =O⋅⋅⋅HO-, are separated by a moderately high potential barrier. The ground state tunneling splitting ∆E0 = 647046.208 ± 0.019 MHz has been obtained from direct measurement [1]. This value is about two orders of magnitude larger than the value expected for a 1D barrier [2]. Indeed, it is well established that in MA the reaction path deviates strongly from the straight line connecting the equilibrium geometries of the two tautomers and involves substantial displacements along small-amplitude, non-tunneling coordinates. These displacements decrease the barrier and promote tunneling. MA has thus become a natural benchmark system for theoretical studies of multidimensional tunneling.

In the ground and transition states, planar MA belongs to the Cs and C2v symmetry point groups, respectively. The vibrational Hamiltonian is constructed in the reactive coordinates introduced in Ref. [3]. The rectilinear wide-amplitude coordinate X belongs to the A' and B2 irreducible representations in Cs and C2v. This tunneling coordinate is coupled with the set of twenty small-amplitude, transverse vibrations {Yk}. If the irreducible representations of X and Yk are the same in both symmetry groups, linear (L) XYk coupling exists. If the representations are the same in the Cs ground state only, the lowest order coupling is gated (G). For coordinates which do not belong to A' and B2 representations, the coupling is squeezed (Sq). For vibrations with L and G type coupling, Sq couplings exist also. The set of transverse modes in MA consists of six vibrations with L type coupling, eight with G coupling and six with Sq coupling. The potential energy corresponding to three types of coupling is expanded in a power series of reactive coordinates (X,{Yk}). If X-independent anharmonicities of transverse vibrations are neglected, the potential energy is given by the following expression:

{ }( ) ( )

∑∑

∑∑

∑ ∑

⊂⊂⊂

⊂⊂

⊂ ⊂

α+

ω−α+

+

ω−

ω−+

ω

α+

ω+

+−+

−

ω+=

Sq,G'k,k'kk'kk

G'k,Lk'k

k

kk'kk

L'k,k 'k

'k'k

k

kk'kk

Sq,G,Lkk

k

kkk

Lk Gkkkk

k

kkk

YYXYXC

YX

XC

YXC

YXaYX

YXCYXC

XC)X(VY,XV

22

22222

2

2

220

12

12

(1)

The double-well 1D potential is:


111

( )∑=

−=432

20 12

1

,,m

mm XV)X(V (2)

Using the eigenfrequency Ω0 in the minimum of the 1D potential the dimensionless transverse frequencies are given by:

0

2ΩΩ

= kkω (3)

The 2D XY terms for L, G, and Sq coupled vibrations and the YY' coupling terms are written in the form discussed in Refs. [3,4,5]. Apart from interactions of the tunneling coordinate with a harmonic bath, which are taken into account in the commonly used approximation of non-interacting transverse vibrations, Eq. (1) includes additionally X-dependent YY' interactions. This generalization is essential for MA, in which these interactions mix the normal modes of the transition state along the MEP. The PES of MA, defined by Eqs. (1) - (3), is characterized by a total of 143 parameters: (i) 3 parameters of the 1D potential m = 2, 3, 4 ; (ii) 14 L and G coupling constants, Ck ; (iii) 20 Sq coupling constants, αkk ; (iv) 106 YY' coupling constants, αkk'. The kinematic matrix is postulated to be the unit matrix in the transition state. The X-dependent elements of the kinematic matrix are uniquely determined by the symmetry of the potential couplings [6] and have the following form:

≠⊂

≠⊂⊂=

⊂⊂

=';,,',,

';',,,

,,

'

'' kkSqSqGGLLkkXg

kkGkLkXgG

GkXgLkXg

Gkk

kkkk

Xk

XkXk 2

2

22 11 XgGXgG kkkkXXXX +=+= , (4)

The evaluation of these parameters of the Hamiltonian is the inverse vibrational problem for small-amplitude classical vibrations. The general method of a solution is given in Ref. [4]. Near the stationary points, X0 = ±1 and X# = 0, the potential function, Eq. (1), is reduced to a quadratic form of the displacements, u0 = (X-X0,{Yk-Yk0}) and u# = (X-X#,{Yk-Yk#}), and these displacements are connected with the normal modes of the stationary points, Q0 and Q#, by the following linear transformations: 000 uPQuPQ == ,### (5) It follows from Eq. (1) that the matrix P# is the unit matrix for G and Sq type vibrations, because (X,{Yk})-coordinates coincide in this case with the corresponding eigenvectors of the transition state. For L vibrations this matrix becomes non-diagonal and can be defined using the fact that the geometry of the ground state is known in both reference frames, Q# and u#. The matrix S for the transformation of the normal coordinates is: 0QSQ =# (6) Once matrices P# and S are evaluated, matrix P0 is given by the expression:

( ) 10 −= PPS # (7) For L-, G-vibrations, the following relation connects the displacements, ∆Yk= Y#−Y0, with the coupling constants: k

2kk YC ∆ω= (8)

The YY' coupling constants are determined by elements of the force matrices of both the stationary states:


112

( ) ( )( ) ( ) 020020

220

kkkkkkkk

kkkk

'''' PP

#

ω+ω≈α

ω−ω≈α (9)

The equilibrium geometry of the hydrogen bonded fragment in the ground and transition states, calculated by HF/6-31G**, MP2/6-311G**, MP4SDQ/6-31G** and B3LYP/6-311+G (2dp) methods.

The L, G, and Sq coupling constants, listed in Table, show the following: (i) linear couplings are so weak that higher order squeezed couplings become dominant for all L vibrations; (ii) strong G coupling with the lowest frequency mode ν1 is partially compensated by the negative Sq coupling; (iii) the contributions that promote tunneling the strongest result from G couplings and positive Sq couplings with ν15 ; (iv) resonance effects occur for ν13 and ν14 vibrations; (v) all low-frequency Sq vibrations are inactive ; (vi) the strong couplings between the two L vibrations, ν7 and ν9, as well as between L vibations, ν7, ν9, ν10, ν12, and G vibrations, ν6, ν12, ν15, are ineffective due to the weakness of XY couplings for L vibrations. In contrast, mixing of G vibrations, ν1 and ν6, with ν8, ν15, and ν4, ν15, respectively, affects tunneling splittings.

Table. Potential L,G, and Sq couplings between tunneling and transverse coordinates in MA.

Modes of transition

state

Type of coupl.

Dimensionless frequency ωk

L,G-Coupling constant

Ck/ωk

Squeezed coupling constant αkk/ωk

δ(OH)/ν(OH) - ν8 T 2.0 - -

ring def. - ν2 L 0.365 -0.020 -0.108 δ(C-H3) - ν5 L 0.707 -0.038 0.285 δ(CH) - ν7 L 0.855 0.048 0.214 δ(C-H3)/ν(CC) - ν9 L 0.960 0.074 -0.138 ν(C=O)/δ(OH) - ν10 L 1.070 0.148 -0.185 ν(CH) - ν12 L 1.986 -0.007 -0.108

ring def. - ν1 G 0.399 0.602 -0.405 ring def. - ν3 G 0.600 0.210 -0.157 ν(C-C) - ν4 G 0.682 -0.197 0.048 δ(C-H2)/ν(C-O) - ν6 G 0.878 -0.211 0.182 ν(C=O)/ν(C=C) - ν11 G 1.058 -0.062 0.120 ν(OH)/δ(OH) - ν15 G 1.207 -0.447 0.421 ν(CH) - ν13 G 1.984 -0.172 -0.048 ν(C-H3) - ν14 G 2.078 0.137 -0.017

τ(C=C) - ν17 Sq 0.225 - 0.048 γ(CH) - ν18 Sq 0.483 - 0.024 γ(CH) - ν20 Sq 0.612 - -0.082 γ(OH) - ν19 Sq 0.835 - -0.122 τ(C=C) - ν16 Sq 0.237 - -0.077 γ(CH) - ν21 Sq 0.663 - -0.017

References 1. T. Baba, T. Tanaka, I. Morino, K.M.T. Yamada, K. Tanaka, J. Chem. Phys. 110 (1999) 4131. 2. J. R. de la Vega, Acc. Chem. Res. 15 (1982) 185.


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3. V.A. Benderskii, E.V. Vetoshkin, L. von Laue, H.P. Trommsdorff, Chem. Phys. 219 (1997) 143.

4. V.A. Benderskii, S.Yu. Grebenshchikov, E.V. Vetoshkin, L. von Laue, H.P. Trommsdorff, Chem. Phys. 219 (1997) 119.

5. V.A. Benderskii, E.V. Vetoshkin, H.P. Trommsdorff, Chem. Phys. 234 (1998) 153. 6. V.A. Benderskii, E.V. Vetoshkin, H.P. Trommsdorff, Chem. Phys. 244 (1999) 273.


114

Quantum Chemical Investigation of NMR Chemical Shifts in Bicyclic Amines

Alexander Isayev, Sergiy I. Okovytyy, Lilija I. Kasyan, Ludmila K. Umrikhina,

and Vladimir.V. Rossikhin

Department of Chemistry, Dnepropetrovsk National University Dnepropetrovsk, 49625, Ukraine

It is well known that NMR spectroscopy is widely used method for structure

investigation of chemical compounds. However, the relationships between the structure of molecules and NMR chemical shifts are mostly based on semiempirical rules that are determined for each group of substances. This is why developing and improving ab initio methods for calculation of NMR parameters is an important direction of theoretical chemistry.

In this work the results of theoretical investigation structure and magnetic properties of bicyclo[2.2.1]heptane, bicyclo[2.2.1]hept-2-ene amino-derivatives and azobrendane are presented.

The conformational analysis has been made with MM2 force field. Geometry of

stable conformers has been optimized at the Møller-Plesset second order perturbation theory level using the 6-31G* basis set. Constants of magnetic shielding were calculated at Hartree-Fock, Møller-Plesset, and density functional theory (DFT) levels with standard (6-311G**, 6-311++G**, AUG-cc-pVDZ) and magnetically consisted basis sets (6-31G##(I), 6-31G##(II)) [1]. The magnetically consisted basis sets are constructed by augmentation of the initial set of basis functions by specific types and numbers of components which are generated from the corresponding response functions. The response functions have been obtained by solution of the inhomogeneous Schrödinger equation for the model problem “a one-electron atom in an external uniform field”, by closed representation of the Green’s functions.

Finally, the comparison of the calculated NMR chemical shifts with the experimental data reveals the superiority of the magnetically consisted basis sets against standard ones [2].

References [1] Rossikhin, V.V.; Kuz’menko, V.V.; Voronkov, E.O.; Zaslavskaya, L.I.; J.Phys.Chem. 1996,

100, 19801 [2] Rossikhin V.V., Okovytyy S.I., Kasyan L.I. Voronkov E.O. Umrikhina L.K. and

Leszczynsky J., J. Phys. Chem. (in press).

(CH2)n NH2 (CH2)n NH2 HN

HO

n = 0, 1, 2.


115

DFT Investigation of Thermodynamics of the Reduction of TNT by Fe2+

Alexander Isayev,1 Leonid Gorb,1 Chris McGrath,2 Yevgeniy Podolyan,1

Danuta Leszczynska,3 Jerzy Leszczynski1

1Computational Center for Molecular Structure and Interactions, Department of Chemistry, Jackson, MS, 39217

2U.S. Army Engineer Research & Development Center, Vicksburg, MS, 39180-6199 3Department of Civil Engineering, Florida State University, Tallahassee, FL

The development of cleanup technologies for a disposal of explosives is a challenge for

environmental science. Such development involves the coordination of experimental and theoretical investigations to integrate both technological and fundamental aspects of key processes. Although the major processes affecting the natural and engineered treatment of explosives have been investigated qualitatively, many issues remain unsolved regarding reaction mechanisms and biogeochemical controls. To contribute to the understanding of the mechanism of explosive reduction in aqueous solution we applied the methods of computational chemistry.

We have performed theoretical investigation of thermodynamics of trinitrotoluene (TNT) stepwise reduction by Fe2+ in aqueous solution which includes the following progression: nitro (-NO2) → nitroso (-NO) → hydroxylamine (-NHOH) → amine (-NH2). The following methodological procedure has been applied.

1. The gas phase Gibbs free energies for all TNT derivatives, water molecule and OH- anion have been obtained at the DFT/B3LYP level of ab initio theory using 6-31G(d) basis set.

2. The solvent correction to gas phase Gibbs free energies has been evaluated from the single point DFT/B3LYP calculations in the framework of PCM model.

3. Due to impossibility to evaluate the value of Gibbs free energy for the process Fe2+ → Fe3+ at the DFT/B3LYP level with the same accuracy as for TNT derivatives , we have calculated this value from the expression ∆G0 = -nFE0,

where F is Faraday constant and E0 is the value of standard red-ox potential Based on the Gibbs free energy values and the values of corresponding equilibrium

constants we have discussed probability of these reactions in a gas phase and in water solution. We have also estimated the probability of the alternative paths leading to the condensation of amines and hydroxylamines.

Our results form a basis for fundamental understanding and quantification of the process of explosives reduction. The obtained results will have significant implication into remediation measures and for the choice of remediation schemes. For example, they will allow predicting the composition of the reaction mixture depending on the amount of reduction agent or depending on the chemical structure of explosives and its intermediate products.


116

Molecular Dynamics of Haemagglutinin Membrane Glycoprotein of Influenza Virus

Raúl Isea

Centro de Cálculo Científico de la Universidad de los Andes, CeCalCULA, Edif. Masini, Av. 4,

entre calles 18 y 19, Piso 3, Ofic. B-32, Mérida 5101, Venezuela

Haemagglutinin (HA) is responsible for influenza infection in humans [1]. It is known that HA is implicated in the binding process between the virus and receptors cells before the infection, which is necessary for the release of the viral genome into the cell. So in the light of the above facts, it is extremely important to understand the conformation of this glycoprotein. The crystal structure of Haemagglutinin has been determined by X-ray experiment [2]. Based on them, molecular dynamics (MD) simulations were performed using the Charmm software package [3]. We employed the release 27 force field provided by the Charmm package. The calculations were conducted with a cut-off distance for non-bonded van der Waals interaction at 15 Å. No explicit water molecules was employed, but we used a distance-dependent dielectric constant, ? = 1, 2 and 4, to simulate the solvent effects on the system. Periodic Boundary conditions were employed. The simulation was carried out with all atoms modeled in the described system at a temperature of 300 K. The starting structure was first minimized by the conjugate gradient method to a rms. Grd < 0.001 kcal mol-1 Å-2. The resulting structure was used in the molecular dynamics calculations until 1 ns. The simulation showed that HA is extremely mobile. This result could explain how the protein is able to find the sialic acid containing host cell receptor, and maybe, this is the main reason for the difficulty in producing an effective vaccine against influenza. Acknowledgments

I wish to thank the organizers of CCTCC-10 for your help in the presentation of this work. This work was supported in part by CONICIT of Venezuela, and by CAVEFACE (Cámara Venezolana de Fabricantes de Cerveza). Bibliography [1] R. M. Krug. "The influenza Viruses", Plenum Press, London (1989). [2] I. A. Wilson, J. J. Skehel, and D. C. Wiley. Nature (1981), vol. 289, 266. [3] CHARMM: A Program for Macromolecular Energy, Minimization, and Dynamics Calculations. J. Comp. Chem. (1983), vol. 4, 187.


117

Atoms in Molecules Theory Code Employing Python, a Real High-level Program

Raul Isea1 and Joaquín Brito2

(1) Centro de Cálculo Científico de la Universidad de los Andes, CeCalCULA, Edif. Masini, Av. 4, entre calles 18 y 19, Piso 3, Ofic. B-32, Mérida 5101, Venezuela; (2) Centro de Química del

IVIC, Apartado 21827, Caracas 1020A, Venezuela

The goal of this work is to show the easiness of the development and implementation of new algorithms in computing chemistry with high-level programming language, Python. Python is a dynamic, object-orient, high-level, and interpreter language [1]. It could be a first step to resolve problems in computational science. In addition, another advantage of employing Python is that this code could run on a lot of platforms such as Unix, Windows, Linux, OS/2, Mac, and so on. However, a disadvantage is the slower execution velocity [1]. Nevertheless, programs written in high-level languages are significantly shorter than programs using the common machine-oriented languages (Fortran, C, C++, etc). This means shorter development times, fewer mistakes, and code that is easy to understand.

Figure 1. Contour plots of the electron density distribution of metallic beryllium obtained with PyBader.

In this work, Python has been employed to determine the Critical Point (CP) according to the Atoms in Molecules theory (Bader's Theory) [2]. This code was called PyBader, has about 150 lines in Python code, approximately, and was tested in metallic beryllium. Figure 1 shows an example of the output of electron density distribution function obtained with PyBader. This simple code shows that the density distribution function of metallic beryllium presents non-nuclear attractors in agreement scientific literature [3]. Moreover, these results suggest bonds between non-nuclear attractors and beryllium atoms.

Finally, an important aspect of Python program is that it could be used interactively or as stand-alone scripts. And, of course, it could run on a lot of platforms. Therefore, Python is a tool of programming with several features: high flexible, highly modular, and extremely powerful to test algorithm challenges in computational chemistry.


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Acknowledgments We wish to thank the organizers of CCTCC-10 for your help in the presentation of this

work. We also thank the Conicit for the funds used in the present work. Bibliography [1] M. Lutz and D. Ascher. "Learning Python", O'Reilly & Associates, California (1999). [2] R. F. W. Bader. "Atoms in Molecules. A Quantum Theory", Clarendon Press, Oxford (1990). [3] B. B. Iversen, F. K. Larsen, M. Souhassou, and M. Takata. Acta Cryst. (1995), vol. B51, 580.


119

Relativistic Many-Body Perturbation Theory for Many-Electron Systems

Yasuyuki Ishikawa and Marius J. Vilkas

Department of Chemistry, University of Puerto Rico, POB 23346 San Juan, PR 00931

The majority of contemporary electronic structure calculations has been performed on light atoms and light-atom-containing molecules employing the Schroedinger equation. It ignores effects described by special theory of relativity but these effects are minor for light atoms and for molecules which contain only light atoms. The small relativistic effects may be incorporated with perturbation theory. This approach, however, becomes unsatisfactory as heavier atoms and heavy-atom-containing molecules come under consideration. For accurate calculations of heavy-atom systems, it is necessary to discard the Schroedinger equation in favor of the Dirac equation. Although the study of truly many-electron systems is increasing, accurate ab initio Dirac 4-spinor calculations on heavy atoms and on molecules that contain heavy atoms are still scarce. There are reasons for this scarcity. Heavy-atom species are many-electron systems with very complicated multiplet state structures that push computational techniques to their limits. And relativistic and correlation effects are so important that extant techniques are unsatisfactory; they must be approached with a relativistic many-body theory that simultaneously accounts for relativity and electron correlation. Because relativistic and correlation effects are intertwined and play an essential role in the electronic structure of many-electron systems, relativistic many-body perturbation theory (MBPT) and relativistic coupled cluster theory, have become the subject of active research interest in the last decade. Construction of an effective many-body theory that accurately accounts for both relativistic and electron correlation effects in many-electron systems is difficult. Theoretical methods developed to describe the structure of many-electron systems must yield wave functions which can be refined to account for relativistic, electron-correlation and quantum electrodynamic (QED) effects. At the same time they should be accurate, and whatever defects they may have should be consistent and well characterized. They must be computationally efficient because they will have to eventually describe electronic effects in systems which contain very large numbers of electrons. Finally, perhaps most important, an approximation should provide wavefunctions which are compact and easy to interpret chemically. These are properties which have caused the wide application of the matrix Dirac-Fock self-consistent field (DF SCF) method, and its many-body theoretical refinements. We survey such approaches, i.e. the solution of the matrix multiconfiguration DF SCF equations and its refinement by relativistic multireference MBPT.


120

ClOOCl: Theoretical Insights into its Torsional Potentials, Bond Dissociation Pathways, Atomization Energies, and Multiple

Isomerization Mechanics by Molecular Dynamics Simulations, High Level ab initio Approximation Methods, and Density Functional

Theory

Abraham F. Jalbout

Department of Chemistry, University of New Orleans, New Orleans, LA 70148-2820 USA

In order to further facilitate the physical understanding of ClOOCl and three of its isomers (ClOClO, ClClOO and Cl2OO) many high level Ab initio and density functional theory calculations were carried out. Among the methods employed were CBS-Q, CBS-QB3, G3, G3B3 and the B3LYP hybrid density functional theory (DFT) method. The calculations reveal very interesting information about the torsional potential, dissociation and isomerization mechanisms as well as evidence for new unexplored physical properties of ClOOCl from a theoretical perspective. To further support our arguments a simple molecular dynamics simulation (MDS) code was written to explore its time dependent behavior. Introduction

Among the most important applications of this work lie in the understanding of how the destruction of ozone occurs through a catalytic cycle of Cl2O2 in the Antarctic stratosphere, and also in the Arctic. However, many other applications and scientific studies have also attracted interest in this system Experimental studies into the thermodynamical properties of gaseous ClOOCl and its fragments have been performed in past whereby its dissociation energies, and heats of formation have been determined. Although many theoretical studies have attempted to understand these systems and their fragments, very little is available about the torsional behavior of ClOOCl from both a theoretical or from an experimental point of view.

Results and Discussion

From table 1 all the structural parameters of ClOOCl, cis-ClOOCl, and trans-ClOOCl, can be seen. Although it appears that none of the methods correlate well with the experimental values this concern will be completely addressed in subsequent sections. The molecular dynamics simulations seem to give good approximations of the geometry (at least qualitatively) but it a well know fact they are as reliable as quantum mechanical results. It is fairly obvious from the table that at the cis geometry (r3, r4, a2) the OO bond distances are larger due to the increased relative steric energy (figure 1) and at the trans geometry (r5, r6, a3) the value for the OO distance (“r6”) is smaller. There is a conflict between theory and experiment in relation to the Cl-O-O-Cl equilibrium dihedral angle. As can be seen, none of the methods approximate the dihedral angle accurately. At this point, we shall say that there are other factors that must be taken into consideration before solidification of this can be made.


121

Model r1(Å) r2(Å) a1(°) d1 (°) r3(å) r4(å) a2(°) d2 (°) r5(å) r6(å) a3(°) d3 (°) MDS 1.690 1.558 107.1 94.01 1.748 1.523 109.6 0.00 1.804 1.483 108.6 180.0 M2 1.677 1.362 109.8 90.61 1.659 1.414 118.1 0.00 1.660 1.408 105.2 180.0 M3 1.679 1.352 110.4 91.13 1.661 1.406 118.5 0.00 1.659 1.401 105.7 180.0 M4 1.742 1.419 109.0 85.01 1.685 1.573 114.8 0.00 1.701 1.524 102.0 180.0 M5 1.764 1.377 110.3 84.93 1.692 1.551 115.6 0.00 1.703 1.512 102.6 180.0 M6 1.809 1.331 111.9 85.79 1.690 1.534 116.1 0.00 1.705 1.501 103.4 180.0 M7 1.834 1.308 112.5 85.63 1.688 1.545 115.9 0.00 1.706 1.506 104.0 180.0 M8 1.748 1.361 111.4 84.60 1.647 1.573 115.1 0.00 1.672 1.506 104.5 180.0 Exper. [1]

1.704 1.426 110.1 81.00 - - - - - - - -

Table 1. Equilibrium geometry of the ClOOCl (C2v) species, the trans and cis isomers as well, r1 refers to

the Cl-O bond length, r2 refers to the O-O bond length, a1 Cl-O-O, d1 is the Cl-O-O-Cl angle for the equilibrium structure. Similarly, r3, r4, a2, and d2, refer to the Cl-O bond length, O-O length, Cl-O-O angle, and the Cl-O-O-Cl dihedral angle for the cis isomer respectively. And r5, r6, a3, and d3, refer to the Cl-O bond length, O-O length, Cl-O-O angle, and the Cl-O-O-Cl dihedral angle for the trans isomer respectively. MDS refers to Molecular Dynamics simulation optimization (described in text). M2 refers to the HF/6-31G(d) optimization; M3 is the HF/6-31G(d’) optimization, M4 refers to the MP2/6-31G(d) optimization, M5 refers to the MP2/6-31G(d’) method, M6, M7, and M8 are the B3LYP optimizations with the 6-31G(d), CBSB7, and 6-311++G (3df) basis set, and Exp is the experimental value.

The torsional barrier or potential of ClOOCl still remains a problem that has not been

completely solved both experimentally and theoretically. From figures 4-6 the torsional potential of ClOOCl is shown. If the geometry is optimized at 20.0-degree intervals, or even at 3.0 degree intervals (figure 1) it can be noticed that the correlations are better with available experimental data. Again, density functional theory (B3LYP/6-311++G (3df)) seems to approximate the cis barrier better than any other of the ab initio methods. The curve is normal even at 3.0-degree intervals it seems that the curve is very smooth and regular.

0 20 40 60 80 100 120 140 160 1800

2

4

6

8

10

12

14

Re

lati

ve E

ne

rgy

(kca

l mo

l-1)

D ihedral Angle (Degrees)

B3LYP/6-311+G(d) B3LYP/6-311+G(3df)//B3LYP/6-311G(d)

Figure 1. Relaxed plot of the variation of the relative energy with changes in the dihedral angle using density functional theory (methods shown in legend), calculations were carried out in 3.0-degree intervals and the energy is calculated relative to the equilibrium dihedral angle.


122

Another point to mention in regards to the torsional potential of ClOOCl is the trigonometric expansion coefficients. As can be seen from table 2 the coefficients after V4 are decreasing substantially to zero. To get very accurate results we have expanded the trigonometric series all the way from V0 à V10 until the series converges to as close to zero as possible. One major problem with the experimental studies of Birk et al (Birk, M.; Friedl, R. R.; Cohen, E. A.; Pickett, H. M.; Sander, S. P. J. Chem. Phys. 1989, 91, 6588) is the inability of considering enough terms in the expansion (only V0 à V2 were considered), which could lead to considerable deficiencies in the accuracy of the data. If we look at table 2 there is considerable changes in the coefficients from V2 to V4.We see that the coefficients of B3LYP/6-311++G (3df) are very similar to those obtained from the B3LYP/6-311+G (3df)//B3LYP/6-311+G (d) calculations.

Method V0 V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 M1 6.4060 1.6340 5.7410 1.2120 -0.639 -0.139 -0.025 -0.034 0.0260 0.0220 -0.004 M2 6.5540 0.9540 5.7710 1.1090 -0.782 -0.153 -0.008 -0.052 0.0620 0.0340 -0.037 M3 4.9350 1.8080 4.5280 1.2280 -0.434 -0.312 -0.386 -0.565 -0.446 -0.351 -0.225 M4 5.9590 1.7460 5.3080 1.0260 -0.679 -0.129 -0.034 -0.034 0.0380 0.0150 -0.001 M5 4.6790 1.3650 4.0100 0.8230 -0.586 -0.170 0.0120 -0.003 0.0090 0.0060 0.0020

Table 2. Expansion coefficients for the ∑=

=N

ii iVV

1

)cos()( ττ trigonometric expansion were of course V is the

coefficient and τ is the dihedral angle. M1=B3LYP/6-31G(d), M2=B3LYP/CBSB7, M3=B3LYP/6-311++G (3df), M4=B3LYP/6-311+G (d), M5=B3LYP/6-311+G (3df)//B3LYP/6-311+G (d). The units are in kcalories per mole. Conclusions

Many interesting conclusions can be drawn from the data provided. Among them is the deeper understanding of the torsional potential of ClOOCl. We have proven to a great degree that experimental uncertainness can occur with relative ease in certain cases due to the small rotational barriers around the equilibrium geometry.

Although density functional theory has been debated in the past as method for accurately calculating properties of these types of halogen containing systems we feel that through a careful analysis and consideration of many mechanisms (i.e. transition states, decomposition, atomization energies, etc) DFT provides for an excellent and computationally inexpensive method to evaluate the energetics of a process, given the use of a sufficiently large basis.


123

Efficient Space-Warping Method for the Simulation of Large-Scale Macromolecular Conformational Changes

Khuloud Jaqaman, Peter J. Ortoleva

Department of Chemistry, Indiana University, Bloomington, IN 47405

Mesoscopic objects, such as macromolecules and viruses, consist of a very large number of atoms. Modeling their conformational changes using all-atom simulations is not feasible in many cases due to computational limitations. They possess a large number of degrees of freedom, making their long-time dynamics complex and difficult to capture. The distances separating atoms in mesoscopic systems are much larger than the range of inter-atomic interactions. Thus many atoms cannot interact directly but rather interact through intervening atoms. For example, an atom on one end of an elongate macromolecule consisting of 10000 atoms needs a long time to experience the effect of the displacement of an atom at the other end of the molecule. In addition to slowing down simulations, the indirect interaction of atoms leads to the existence of a large number of minima and causes minimization algorithms to find a local rather than a global minimum. Another challenge in simulating mesoscopic systems is the multiple time scales characterizing their dynamics. While there are high frequency atomic oscillations, a macromolecule as a whole undergoes large-scale conformational changes. Such changes are difficult to capture because of the limitation on the time step imposed by the high frequency vibrations.

Here we present a methodology that addresses the above problems by accounting for large-scale conformational changes in macromolecules while retaining atomic scale detail. In our method, referred to as the space warping method, we introduce a new set of “global” coordinates, Γn{ }, through which atomic coordinates evolve in time via the mapping

v r i t( ) = Γn t( )

v f n

v r i

0( )n=1

N g

∑ , (1)

where v r i

0 is the initial position vector of atom i, v r i t( ) the position vector of atom i at time t and

Ng the number of global coordinates. All of the time dependence of the atomic positions is in the Γ ’s, which in turn evolve according to physical principles, such as free energy minimization or Newton’s equations of motion. While the flexibility of the transformation in Eq. (1) depends on the number and form of the transformation functions

v f n

v r ( ), the actual transformation that takes

place is determined by the values of the Γ ’s. Although the position of every atom is used in the evaluation of the forces on the global

coordinates, preserving some atomic scale detail, the evolution of atomic coordinates via Eq. (1) is nevertheless constrained. The form of the transformation functions used restricts the movement of the atoms, resulting in local stresses. For example, the bending of a cylindrical molecule causes a high density of atoms near the point where it bends, which creates a configuration that is not energetically favorable. To release such stresses, the space warping method iterates between global coordinate dynamics and atomic coordinate dynamics. Thus large-scale conformational changes are captured using global coordinates, but then local stresses are released by allowing for local redistribution of atoms. In the case of energy minimization, for example, the algorithm alternates between the two sets of coordinates until the solution is obtained.

Unlike other methods, such as constrained dynamics [1-3], our approach does not neglect any degrees of freedom of the system. Thus accuracy need not be compromised for speed.


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Moreover, our method does not require the system to stay close to a minimum, as limited by normal mode analysis. It accounts for overall conformational changes, and there is no need for a priori knowledge of the trajectory, as required by principal component analysis methods [4-7].

We have applied the space warping method to free energy minimization. The simulations for several test cases, where atoms interact via a central potential, show that the space warping method scales with system size better than atomic coordinate simulations. In addition to finding a solution faster, the minimum found in the case of multiple minima using the space warping method is always lower than that found by minimizing with respect to atomic coordinates only. With a smart choice of the transformation functions, a small number of global coordinates - much less than the number degrees of freedom of the system - is enough to capture large scale conformational changes.

The results of our simulation of [ ]+16Ala in vacuo are shown in Fig. (1). This system has been studied both experimentally [8] and using molecular dynamics [9], where it is found that the polypeptide, which has an extra proton at its C-terminus, prefers a globular conformation, possibly to “solvate” the extra proton. The atoms in our simulations interact via the CHARMM22 force field [10].

Starting with a linear configuration of the molecule, as shown in Fig. (1a), the system is evolved towards an energy minimizing structure. In one simulation only atomic coordinates are used, while in another the space warping method, with global coordinates corresponding to a cubic mapping, is used. While the molecule stays linear in the former, being trapped in a high-lying minimum, the space warping method finds a globular structure, as shown in Fig. (1b), with a much lower energy. This structure is at or very close to the global minimum of the potential energy surface. Notice that in order to overcome energy barriers and reach a low-lying minimum, the system has to be at a finite temperature. Thermal energy is introduced to the system using colored noise. In the spirit of simulated annealing, the temperature of the system is reduced with time. The exponentially decaying time course of the temperature is designed such that it is negligible in the last phase of both calculations.

In addition to finding a much lower minimum, the space warping method takes only three hours to reach the solution it finds. The simulation involving only atomic coordinates, on the other hand, needs more than one day to find its solution. Both simulations are performed on an IBM RS/6000 SP machine Given the scaling of the space warping method with system size, it is expected that its efficiency and superiority over direct local energy minimization will be even more pronounced for larger polypeptides and proteins.


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Figure 1: (a) Initial linear structure of [ ]+16Ala . (b) Final globular structure of [ ]+16Ala as found through energy minimization using the space warping method. References [1] Ryckaert, J. P.; Cicotti, G.; Berendsen, H. J. C. J Comp Phys 1977, 23, 327-341. [2] Rice, L. M.; Brünger, A. T. Proteins Struct Funct Genet 1994, 19, 277-290. [3] Chun, H. M.; Padilla, C. E.; Chin, D. N.; Watanabe, M.; Karlov, V. I.; Alper, H. E.; Soosaar, K.; Blair, K. B.; Becker, O. M.; Caves, L. S. D.; Nagle, R.; Haney, D. N.; Farmer, B. L. J Comp Chem 159, 21, 159-184. [4] Space, B.; Rabitz, H.; Askar, A. J Chem Phys 1993, 99, 9070-9079. [5] Askar, A.; Space, B.; Rabitz, H. J Phys Chem. 1995, 99, 7330-7338. [6] Elezgaray, J.; Sanejouand, Y. H. Biopolymers 1998, 46, 493-501. [7] Elezgaray, J.; Sanejouand, Y. H. J Comp Chem 2000, 21, 1274-1282. [8] Counterman, A. E.; Clemmer, D. E. J Am Chem Soc 2001, 123, 1490-1498. [9] Samuelson, S.; Martyna, G. J. J Phys Chem B 1999, 103, 1752-1766. [10] MacKerell, Jr., A. D.; Bashford, D.; Bellot, M.; Dunbrack, Jr., R. L.; Evanseck, J. D.; Field. M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; Joseph-McCarthy, D.; Kuchnir, L.; Kuczera, K.; Lau, F. T. K.; Mattos, C.; Michnick, S.; Ngo, T.; Nguyen, D. T.; Prodhom, B.; Reiher, III, W. E.; Roux, B.; Schlenkrich, M.; Smith, J. C.; Stote, R.; Straub, J.; Watanabe, M.; Wiorkiewics-Kuczera, J.; Yin, D.; Karplus, M. J Phys Chem B 1998, 101, 3586-3616.


126

Computer Simulations for Drug Lead Optimization

William L. Jorgensen

Department of Chemistry, Yale University, New Haven, CT 06520-8107

Protein-ligand binding is being studied via Monte Carlo and molecular dynamics simulations with statistical perturbation theory and linear response approaches. The OPLS-AA force field is used with explicit inclusion of water with the TIP4P model. Thermodynamic and structural results will be presented for HIV-RT, COX-1 and COX-2 with medicinally important inhibitors. Design of mutation-resistant inhibitors for HIV-RT and COX-2 selective ligands are principal goals. Accurate predictions are also made for pharmacologically important properties of drugs using descriptors from Monte Carlo simulations of the drugs in water. The availability of arrays of low-cost Pentium-based computers allows the computations to be executed in a high-throughput mode.


127

Is the Pauli Exclusive Principle an Independent Quantum-Mechanical Postulate ?

Ilya G. Kaplan

Instituto de Investigaciones en Materiales, UNAM, Apdo. Postal 70-360, 04510 México, D.F.,

MÉXICO

The Pauli exclusive principle and spin-statistics connection are discussed. For composite

particles, the spin-statistics connection in some cases is violated: the two-fermion particles (e.g. the Cooper pairs) are described by the symmetric wave functions but have the fermion occupation numbers of one-particle states. It is demonstrated that the indistinguishability principle is insensitive to the permutation symmetry of the wave function and cannot be used as a criterion for the verification of the Pauli exclusive principle. The heuristic arguments are given in favor that the existence in Nature only the non-degenerate permutation representations (symmetrical and antisymmetrical) is not occasional. As follows from our analysis of possible scenarios, the permission of degenerate permutation representations leads to contradictions with the concept of particle identity and their independence. So, from the point of the permutation symmetry, the Pauli exclusive principle follows from the general assumptions of quantum theory, but the problem of spin-statistics connection is still open. It is pointed out that the Pauli exclusive principle and the Jahn-Teller effect have some similar features.


128

C

C

CC

C

CC F

HH

H

H

H

H

π σ*- * HC

Theoretical Evidence for π*-σ* Hyperconjugation Effect on the Internal Methyl Rotation

Y. Kawamura, H. Nakai

Department of Chemistry School of Science and Engineering, Waseda Unversity,

Tokyo, 169-8555, Japan

We examined the theoretical evidence for the presence of the π*-σ* hyperconjugation effect on the internal methyl rotation we have found in our previous studies [1-5]. The bond order analysis and MO-basis population are applied to the methyl-substituted aromatic compounds. The orbital picture given by the MO-basis population analysis reveals the interaction between the benzene ring and the methyl group. The π*-σ* hyperconjugation has the similar but anti-bonding nature to the conventional hyperconjugation. The bond order analysis shows the important condition for the occurrence of π*-σ* hyperconjugation, where the π* orbital between methyl-bonded carbon and ortho-carbon have the same phase to methyl σ* orbital.

(a) (b)

Figure 1. Internal methyl rotation (a) and π*-σ* hyperconjugation (b) in ortho-fluorotoluene.

References [1] H. Nakai and M. Kawai, Chem. Phys. Lett. 307, 272 (1999). [2] H. Nakai and M. Kawai, J. Chem. Phys. 113, 2168 (2000). [3] H. Nakai and Y. Kawamura, Chem. Phys. Lett. 318, 298 (1999). [4] Y. Kawamura and H. Nakai, J. Chem. Phys., 114, 8357 (2001). [5] M. Kawai and H. Nakai, Chem. Phys., in press (2001).

X

Y


129

New Coupled-Cluster Methods for Excited States

Karol Kowalski and Piotr Piecuch

Department of Chemistry, Michigan State University, East Lansing, Michigan,48824

Equation-of-motion coupled-cluster theory (EOMCC) in its basic EOMCCSD (EOMCC singles and doubles) approximation has been very successful in describing the electronically excited states dominated by single excitations from reference configuration. Unfortunately, the EOMCCSD method fails to describe excited states that have significant doubly excited components and provides poor description of excited-state potential energy surfaces (PESs) that involve bond breaking. We have recently explored two new ideas to resolve these difficulties. In the first approach, the most important triply excited configurations are selected through the use of active orbitals, following the ideas developed earlier for the ground-state problem.1 As demonstrated in this, the resulting EOMCCSDt method leads to excellent description of excited states dominated by doubles and excited-state PESs.2 In the second approach, we combine the recently proposed method of moments of coupled-cluster equations (MMCC)3 with the EOMCC theory. The main idea of the EOMCC-based excited-state extension of the MMCC theory is that of the simple, noniterative energy corrections which, when added to the energies obtained in approximate EOMCC (e.g., EOMCCSD) calculations, recover the exact energies of the electronic states of interest.4 As in the ground-state MMCC theory,3 the excited-state MMCC approach leads to a hierarchy of approximations, including the CI-corrected MMCC approaches.4 It is demonstrated that these new single-reference theories provide the excited-state PESs that can compete with the EOMCCSDt and full EOMCCSDT results or results obtained with multireference approaches. References 1 N. Oliphant and L. Adamowicz, Int. Rev. Phys. Chem. 12, 339 (1993); P. Piecuch, N. Oliphant, and L. Adamowicz, J. Chem. Phys. 99, 1875 (1993); P. Piecuch, S. A. Kucharski, and R. J. Bartlett, J. Chem. Phys. 110, 6103 (1999); P. Piecuch, S. A. Kucharski, and V. Spirko, J. Chem. Phys. 111, 6679 (1999); K. Kowalski and P. Piecuch, Chem. Phys. Lett. 344, 165 (2001). 2 K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 8490 (2000); K. Kowalski and P. Piecuch, J. Chem. Phys. 115, 643 (2001); K. Kowalski and P. Piecuch, Chem. Phys. Lett., in press. 3 P. Piecuch and K. Kowalski, in Computational Chemistry: Reviews of Current Trends, edited by J. Leszczynski (World Scientific, Singapore, 2000), Vol. 5, pp. 1-104; K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000); K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 5644 (2000). 4 K. Kowalski and P. Piecuch, J. Chem. Phys. 115, 2966 (2001); P. Piecuch, K. Kowalski, I. S. O. Pimienta, and S. A. Kucharski, in Accurate Description of Low-lying Electronic States, edited by M. R. Hoffman and K. G. Dyall, in press (ACS, Washington, D.C.).


130

The New Generation of Visualization Systems in Quantum Chemistry

Mikhail Kozhin, Ilya Yanov and Jerzy Leszczynski

Computational Center for Molecular Structure and Interactions

Department of Chemistry, Jackson State University Jackson, Mississippi 39217-0510

Scientific visualization in the area of quantum chemistry includes the energy-minimized

structure of a molecule, reaction path trajectories, and 2D and 3D electronic properties. Due to the quick development of new and powerful computer systems, the possibility of larger and more complex calculations has arrived. In connection with that, the availability of new generation of software for analyzing and visualizing large data sets becomes crucial. To address these needs we have started development of new molecular visual analysis software.

Our program accepts the output files from the most popular ab-initio quantum chemical packages GAUSSIAN and GAMESS and provides geometrical reconstructions of molecular structures based on atom coordinates. The main differences between our approach and pre-existing programs are:

• multiplatform support due to built-in FTP and Telnet clients which allow for the processing of output from and the sending of input to different computer systems and operating systems;

• the possibility of working with output files in real time mode; • the possibility of animation from an output file during all steps of optimization; • the possibility of opening several files simultaneously at the one window for comparison

of molecular configurations; • the quick processing of huge volumes of data; • the development of custom interfaces. This presentation will provide the examples of the features and applications of the developed

software.


131

Numerical Aspects of the Calculation of Scaling Factors from Experimental Data

G.M. Kuramshina, A.G.Yagola, Yu.A.Pentin

Moscow State University, Moscow 119899, Russia

In the last two decades, the field of inverse problems has certainly been one of the

fastest growing areas in applied mathematics. This growth has largely been driven by the needs of applications in many branches of natural science and in industry. Inverse problems typically lead to mathematical models that are not well-posed in the sense of Hadamard, i.e., to ill-posed problems. This means especially that they might not have a solution in the strict sense, solutions might not be unique and/or might not depend continuously on the data. Mathematical problems having these properties are called ill-posed problems, mostly due to the non-stability of solutions to data perturbations. Numerical methods that can cope with this problem are the so-called regularization methods. The theory of ill-posed problems (A.N.Tikhonov and his scientific school) arose in 1960th investigates and develops the effective stable numerical methods for solution of the ill-posed problems. In the background of this theory lies an understanding of the underestimated character of the ill-posed problems and using a concept of the so-called regularizing operator (algorithm).

Inverse vibrational problem is a problem of finding the molecular force field parameters on a base of experimental data. In a general case, this problem is written in a form of nonlinear operator equation

δΛ=FAh (1) where F∈ Z ∈ Rn(n+1)/2 (Z is a set of possible solutions) is the unknown force constant matrix (real and symmetrical), Λ∈Rm represents the set of available experimental data (vibrational frequencies, etc.) determined within δ errorlevel: ||Λ-Λδ|| ≤ δ. A is a nonlinear operator which maps matrix F on the Λ, h is an error of operator A: ||A-Ah|| ≤ h .

This problem relates to the class of nonlinear ill-posed problems (it does not satisfy any of three the well-posedness conditions by Hadamard) and in the general case (except the diatomic molecules) could have non-unique solution or no solutions at all (non-compatible problem) and solutions are unstable in relation to the errors in operator A and set of experimental data Λ. The theory of regularization methods for nonlinear problems was developed in the last two decades [1] and applied to the inverse problems of vibrational spectroscopy [2].

We have proposed a principally new statement of a problem of searching the molecular force field parameters using all experimental data available and quantum mechanical calculation results taking into account the a priori known constraints for force constants. The essence of approach is that we proposed (using given experimental data and its accuracy) to find by means of stable numerical methods the approximations to the so-called normal pseudosolution, i.e. matrix F which is the nearest by chosen Euclidean norm to the given force constant matrix F0 and satisfies to the set of a priori constraints D and experimental data Λδ with regard for the possible incompatibility of a problem [2]. The including of some restriction on the searching matrix of force constants (in our case it is a requirement of the closeness of solution to the matrix F0) means the possibility to obtain the unique solution from the variety of possible ones.

There is a lot of publications described application of numerical methods to the solving inverse vibrational problem on a base of the least-square procedure. Very often as criteria of minimization, the authors choose the “best” agreement between experimental and fitted


132

vibrational frequencies. Not discussing a meaning of the “best” agreement criteria just note that it is non-sufficient from the ill-posed nature of the inverse vibrational problem. Even in the case of a single molecule consideration, it is well known the fact of existence of infinite number of solutions, which exactly satisfy to the given set of experimental frequencies. Inclusion of the expanded experimental information on isotopomers or related molecules frequencies might lead to the incompatibility of the mathematical problem and result in no solution at all. So, using any minimization procedure for solution of inverse vibrational problem it is necessary to include some additional criteria (that can be mathematically formulated) in the minimization procedure for the selecting the unique solution.

The wide use of quantum mechanical calculations of vibrational spectra and harmonic force fields of polyatomic molecules induced the necessity of empirical corrections of theoretical data for the comparison with experiment. The most popular approach is the so-called scaling procedure proposed by P.Pulay [3]. Though this scaling procedure (in reality it is rather strict limitations on the molecular force field [4,5]) often does not provide enough freedom to eliminate all discrepancies between calculated and observed data, it has certain advantages that follow from the comparatively small number of adjustable parameters and so moderate computational resources are necessary to perform force-field refinement. Indeed, it is very attractive to find a limited number of scaling factors for a series of model molecules and (assuming their transferability) to use them for the correction of quantum mechanical force constants of more complicated molecular systems. The most popular numerical procedure for the calculation (optimization) of scaling factors is the least square procedure but there is a few publications indicated to the nonconvergency and instability of this numerical procedure while solving an inverse scaling problem. It is explained by the impossibility of using the traditional numerical methods for solving the nonlinear ill-posed problems [1,2,6,7].

In our works the next strict mathematical formulation of the inverse scaling problem has been proposed [8]: the problem of finding scaling factors on a base of experimental data is considered through the solving an operator equation (1). Let introduce the following norms in the Euclidean space:

F f ijij

n=

∑

21 2

)

/

Λ =

=∑ λ ρkk

l

k2

1

1 2/

, where ρk > 0 are the positive weights; fij are the elements of matrix F; λk (k= 1,...m) are the components of Λ.

The inverse scaling problem can be formulated in the next way. Problem I. It is required to find

F F F

F F D F: F BF B AF

n = −

∈ ∈ − =

arg min 0

0

,

{ : F = { = }, }Λ µ

Here B is a diagonal matrix of scaling factors. µ is a measure of incompatibility of a problem. It may arise due to the possible anharmonicity of experimental frequencies or the crudeness of chosen model. The obtaining of such stable approximate solution may be provided by minimization of the Tikhonov functional

( ) [ ]M M F A F F Fhα α δβ α= = − + −Λ 2 02

(2)


133

where F=F(β). More complicated procedure was proposed for the solving the generalized inverse structural problem (GISP) [9] in a case of the joint treatment of the experimental data obtained by different physical methods (vibrational spectroscopy, electron diffraction data and microwave spectroscopy). The strict mathematical formulation of the inverse scaling problem could provide a possibility of comparison of results obtained by different investigators. Obviously, it is necessary to work within the same physical and mathematical models and use the stable numerical methods for the unification of different calculations. It is important that using the scaling scheme, as a rule it is impossible to obtain a solution that reproduces experimental data within given errorlevel. We could search for only the pseudosolution of the Problem I that satisfies to the input frequencies in the least square sense. In a case of solving GISP within the scaling approximation, it is necessary to include the cubic part of the force field [10]. Similarly, in order to get a set of more reliable cubic force constants it is undoubtedly beneficial to improve empirically the ab initio values, maybe by use of the Pulay harmonic scale factors. It has been our experience that two schemes of cubic constant scaling are generally feasible. Let the ab initio quadratic force constant 0ijf defined in natural internal coordinates be scaled as follows:

21210)scaled( jiijij ff γγ= , (3)

where γi and γj are the harmonic scale factors, (γI)2=βi. Then reasoning by analogy the cubic constants scaling mode can be formulated [10] as

2121210)scaled( kjiijkijk ff γγγ= (4) or, alternatively [11],

3131310)scaled( kjiijkijk ff γγγ= , (5)

where 0ijkf are the unscaled theoretical cubic constants. Both scaling schemes reduce the vibrational problem to the determination of a much smaller number of parameters. The examples of the applying the last procedure are given in Refs. [12,13]. As examples of solving the inverse scaling problem we perform the calculations of force fields of the halogenated methylsilanes. Quantum mechanical DFT (B3LYP) calculations of optimized structures and harmonic force fields for a series of ethane-like silanes (CH3SiH3, CH2ClSiH3, CHCl2SiH3 and CCl3SiH3) have been done using different standard basis sets (varying from 6-31G* to AUG-cc-pVDZ). Corresponding ab initio calculations were also performed at the HF/6-31G*, HF/ AUG-cc-pVDZ and MP2/6-31G* and MP2/6-311++G** levels of theory. Quantum mechanical results serve as the very informative guide for describing the vibrational spectra and molecular force fields. Acknowledgement This work was partially supported by the RFBR grant 01-03-32412. References

1. A.N.Tikhonov, A.S.Leonov, A.G.Yagola. Nonlinear Ill-posed Problems. Chapman&Hall, London, 1998 (Original Russian language edition: Nonlinear Ill-posed Problems. Nauka, Moscow, 1993).

2. A.G. Yagola, I.V. Kochikov, G.M. Kuramshina, Yu.A. Pentin. Inverse Problems of Vibrational Spectroscopy. VSP, Zeist, The Netherlands, 1999.


134

3. P. Pulay, et al. J. Am. Chem. Soc., 105 (1983) 7037. 4. G. M. Kuramshina, A. G. Yagola, J. Struct. Chem., 38 (1997) 181. 5. G. M. Kuramshina, F. Weinhold, J. Mol. Struct., 410 (1997) 457. 6. T.I. Seidman, C.R.Vogel, Inverse Problems , vol. 5 (1989) 227-238 7. H.W.Engl et al. Regularization of Inverse Problems. Kluwer Academic Publishers,

Dordrecht, 1996. 8. A.V.Stepanova, I.V.Kochikov, G.M.Kuramshina, A.G.Yagola. Regularizing scale factor

method for molecular force field calculations. Computer Assistance for Chemical Research. International Symposium CACR-96). Moscow, 1996, p. 52.

9. I.V. Kochikov, Yu.I. Tarasov, V.P. Spiridonov, G.M. Kuramshina, et al. J. Mol. Struct., 485-486 (1999) 421.

10. S. Kondo, J. Chem. Phys., 81 (1984) 5945. 11. I. V. Kochikov, Yu. I. Tarasov, V. P. Spiridonov, G. M. Kuramshina, et al. Russian

Journal of Physical Chemistry, 75(3) (2001) 395. 12. I.V. Kochikov, Y.I. Tarasov, V.P. Spiridonov, G.M. Kuramshina, et al., J. Mol. Struct.,

550-551 (2000) 429. 13. I.V. Kochikov, Yu. I. Tarasov, V. P. Spiridonov, G. M. Kuramshina, et al. J. Mol. Struct.,

567-568 (2001) 29.


135

Quantum Mechanical Investigations of the Low Temperature Reactions of AlCl3 and Simplest 1-Nitroalkanes

G.M. Kuramshina, M.I.Shilina, V.V.Smirnov

Faculty of Chemistry, Moscow State University, Moscow 119899, Russia

During the last decade the formation of weak molecular complexes formed at low

temperatures by the aluminium chloride monomer and dimer with nitrosubstituted compounds have been confirmed by means of spectral investigations and quantum mechanical calculations. The interest to these complexes is explained by their specific catalytic properties performed e.g. in some alkylation and isomerization reactions of aromatic carbons. For the AlCl3-CH3NO2 system the 1:1 associate was identified and the possibility of forming the 1:2 and 2:1 molecular complexes was predicted [1]. The structure and vibrational spectra of AlCl3-(CH3NO2)2 [1] as well as for (AlCl3)2-CH3NO2 [2] were studied recently and supported by ab initio molecular orbital calculations. In this presentation the theoretical structures and infrared spectra of the complexes formed by AlCl3 and 1-nitropropane are investigated with a goal to identify the more stable conformations taking into account the possible rotational isomerism of the 1-nitropropane molecule.

Ab initio (HF/6-31G*) and DFT calculations (with the B3LYP hybrid functional) were carried out with a help of GAUSSIAN 94. The optimized geometries of the 1:1 and 2:1 complexes were obtained and the harmonic force fields were calculated using analytical derivatives. Corresponding calculations were also carried out for the free reagent molecules.

The optimized (B3LYP/6-31G*) geometrical structures of investigated complexes are presented in Table 1 in comparison with results of similar calculations for the AlCl3-CH3NO2 1:1 and 2:1 complexes [1,2]. As well as for the Al2Cl6-CH3NO2 systems [2], the theoretical results predict the preferable formation of the AlCl3 dimer complex in comparison with the monomer complex of the same stoichiochemistry. The analysis of theoretical results and experimental low temperature infrared spectra of complexes allowed us to define some characteristic vibrational frequencies which can be used for the identification of the complex structures. There is the NO-stretching region (assigned to the symmetrical and asymmetrical stretching vibrations of the NO2 group) that could be considered as the “analytic” and it demonstrates the characteristic frequency shifts depending on the stoichiochemistry and structure of the complex. Theoretical ν(NO) frequencies of AlCl3-CH3CH2CH2NO2 and Al2Cl6- CH3CH2CH2NO2 complexes are presented in Table 1 in comparison with similar data for CH3NO2 [2], 1-nitropropane [3] and AlCl3-CH3NO2 and Al2Cl6-CH3NO2 [2].

Joint consideration of the theoretical and experimental data allows us to conclude that the complexes where the association is realized through the participating only one oxygen atom from NO2 group are more stable and preferable in comparison with systems where both oxygen atoms participate in the complexation. The RFBR grant No 01-03-32412 is gratefully acknowledged for the partial financial support. References 1. M.I.Shilina, T.N.Rostovshchikova, O.V.Zagorskaya, V.V.Smirnov. J. Mol. Cat., A, 1999, vol. 146, No 1-2, pp. 337-343.


136

2. M.I.Shilina, G.M.Kuramshina, V.V.Smirnov, T.N.Rostovshchikova. Russian Chemical Bulletin, No 7, 2001, pp. 1106-1111 (in Russian). 3. M.I.Shilina, G.M.Kuramshina, V.V.Smirnov, Yu.A.Pentin. Structure and vibrational spectra of 1-nitropropane rotational isomers: theoretical and experimental studies. Eightteenth Austin Symposium on Molecular Structure, March 6-8, 2000,Austin, p.98. Table 1. Theoretical (B3LYP/6-31G*) and observed vibrational frequencies (in cm-1) of investigated molecular systems.

B3LYP/6-31G* Observed (IR) No Structure ν(NO)asym ν(NO)sym ν(NO)asym ν(NO)sym

I

1679

1444

1560

1403

IIa

1671

1442

IIb

1672

1436

1557

1378

III

1695

1387

1610

1325

IVa

1692

1402

1617

1317

IVb

1607

1406

-

-


137

Table 1 (continued).

B3LYP/6-31G* Observed (IR) No Structure ν(NO)asym ν(NO)sym ν(NO)asym ν(NO)sym

Va

1685

1368

Vb

1684

1357

1604

1322

VIa

1699

1357

VIb

1680

1353

1610

1316

Notes. I – CH3NO2; IIa, IIb – trans- and gauche- CH3CH2CH2NO2 ; III – AlCl3 - CH3NO2; IVa, IVb – Al2Cl6-CH3NO2; Va, Vb - AlCl3 - CH3CH2CH2NO2 (a – trans-, b – gauche-1-nitropropane); VIa, VIb – Al2Cl6- CH3CH2CH2NO2 (a – trans-, b–gauche-1-nitropropane).


138

Overview of Quantum Monte Carlo Developments for the Past Decade

William A. Lester, Jr.

Chemical Sciences Division, Lawrence Berkeley National Laboratory, and Department of

Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, CA 94720-1460

The quantum Monte Carlo method has developed from an approach only applicable to small atoms and molecules to one that can be applied to molecular systems addressed by other ab initio methods. This talk will comment on advances that have enabled this development and present representative findings.


139

Extrapolating Finite Basis Electronic Structure Calculations to the Complete Basis Set Limit: Does it Work for Potential Energy

Curves?

Tim C. Lillestolen and Robert J. Hinde

Department of Chemistry, University of Tennessee, Knoxville, TN 37996-1600

In recent years, a number of schemes have been proposed for extrapolating finite basis ab initio calculations to the complete basis set (CBS) limit. Here we assess the performance of these extrapolation schemes by applying them to the H2 molecule, a traditional benchmark system for theoretical and computational studies of the covalent bond.

The H2 molecule is an ideal testing ground for basis set extrapolation schemes because numerically exact ab initio energies are available for H2 over a wide range of bond lengths. In addition, recent developments in numerical methods for computing diatomic Hartree–Fock (HF) energies allow us to obtain the exact HF energy of H2 at these bond lengths. Consequently, the exact correlation energy of the H2 system at each bond length can be determined by subtraction. This makes it possible for us to assess, over a range of bond lengths, the performance of schemes that extrapolate the HF and correlation energies independently to the CBS limit, and to compare these schemes with those that extrapolate only the total energy to the CBS limit. Consequently we can determine whether proposed extrapolation schemes can generate reliable potential energy surfaces for molecular systems.


140

Entropy of Mixing Quantum States and the Mathematical Foundation of Quantum Mechanics

Shu-Kun Lin

Molecular Diversity Preservation International (MDPI) Saengergasse 25, CH-4054 Basel,

Switzerland In his book "Mathematical Foundations of Quantum Mechanics", John von Neumann used entropy of mixing to characterize process irreversibility. Applying the Gibbs inequality, I proved the relation of higher similarity-higher entropy of mixing and disproved von Neumann's higher similarity-lower entropy of mixing relation. This entropy-similarity relation can sertainly serve as the very foundation of quantum mechanics for consideration of the structural stability and process irreversibility. More generally, information theory is introduced with revision by three laws of information theory: The function L (the sum of entropy and information, L=S+I or L=lnw, w is the number of microstates) of the universe (universe = system + surroundings) is a constant (the first law of information theory). The entropy S of the universe tends toward a maximum (the second law of information theory). For a perfect symmetric static structure, the information is zero and the static entropy is the maximum (the third law of information theory). Symmetry and stability will be considered and any symmetry will define an entropy (see recent papers listed at the http://www.mdpi.org/lin/lin-rpu.htm website, particularly Lin, S. -K. The Nature of the Chemical Process. 1. Symmetry Evolution -Revised Information Theory, Similarity Principle and Ugly Symmetry. Int. J. Mol. Sci. 2001, 2, 10-39.


141

Exact Exchange Energy Functionals for Atoms: Failure of the Generalized Gradient Approximation.

Sergey N. Maximoff, Gustavo E. Scuseria

Department of Chemistry, Rice University, Houston, TX, 77005-1892

The exchange energy in the generalized gradient approximation (GGA) is written as

∫= r,)(3/4GGAx x dxFCE ρ where F(x) is an enhancement factor that is a function of the reduced density gradient

.||

3/4ρρ∇

=x

We constructed exact exchange energy functionals for several atomic systems using the exact Hartree-Fock exchange energy density. The exact enhancement factor is found a multivalued function. This implies that the exchange energy of atoms cannot be expressed in terms of the electron density and its gradient only. We demonstrate that introducing an additional to the reduced gradient x variable such as the non-interacting kinetic energy density or Laplacian of the electron density makes the enhancement factor a single-valued function.


142

The Effect of Symmetry on the Molecular Geometry of C9H9B Using Gaussian 98

James L. Meeksa, Harry B. Fanninb

aPaducah Community College Department of Physics PO Box 7380 Paducah,

Kentucky 42002-738; bDepartment of Chemistry Murray State University Murray KY 42071

The insertion of a Boron atom into tetracyclo (6.1.0.02,4.05,7) nonane gives a “caged” molecule with the Boron atom in the center of the molecule, s-C9H9B. The s-C9H9B molecule with the use of the symmetry option keeps the starting geometry of the model. When the symmetry function is not used, the s-C9H9B (D3h) molecule undergoes a molecular rearrangement into a non-symmetrical molecule, n-C9H9B of C2v symmetry with the ab initio computations of Gaussian 98. The 6-31g** basis set was used for final optimizations. The geometries of both molecules, s-C9H9B and n-C9H9B, will be discussed. The changes of the molecular energies, bond distances and angles are compared.


143

The Semiclassical Initial Value Representation: A Way to Include Quantum Effects into Molecular Dynamics

Simulations

William H. Miller

Department of Chemistry, University of California Berkeley, CA 94720 USA

It has been known* since the early 1970's that semiclassical approximation

high performance computing at the army high performance...

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