THEO CHEM

ELSEVIER Journal of Molecular Structure (Theochem) 426 (1998) 53-58

Test study on the excitation spectra of the CO-H2 van der Waals molecule

Mary C. Salazar *, Jo& L. Paz, Antonio J. Hemhdez

Departmento de Quimica. Universidad Sir& Bolivar. Apdo. 89000, Caracas 108OA, Venezuela

Received 19 September 1996; accepted 28 October 1996

Abstract

In the present contribution we performed ab initio calculations within the supermolecule approach on the vertical excitation

spectra of the diatomic van der Waals CO-H2 molecule in its linear most stable 0-C,..H-H structure. They indicated the existence ofat least one vibrational state in the ground CO(X’C+)-H2(X’C,) state, and offive vibrational states in the electronic CO(A’II-HZ(X’Cg) excited configuration. Since ab initio correlation energy calculations for the excited electronic state are

extremely demanding on computational resources, we are forced in practice to use medium-size highly optimized basis sets, suggesting to investigate the use of less demanding ab initio methods to represents the complete interaction energy surface of the excited states of interest. 0 1998 Elsevier Science B.V.

Keywords: Ab initio; Van der Waals molecule; CO-H*; Excitation spectra

1. Introduction

The study of weak molecular interactions has

always been a very active research field. Nevertheless, in the last decade there has been a tremendous increase of interest, both by experimentalists and theoreticians, in van der Waals (vdW) molecular clus- ters. The development of laser techniques for state- selective chemistry and spectroscopy, and of highly sophisticated molecular beam techniques have con- tributed to the experimental progress [l-4]. The availability of powerful supercomputers and the development of efficient computational algorithms has made possible the quantum mechanical study of the properties of large molecular systems. In spite of the enormous experimental progress in recent years,

* Corresponding author.

there have been relatively few experimental studies aimed at investigating the electronic excitation spec- tra of the simplest diatomic vdW molecules.

The first spectroscopic evidence of CO-H2 is reported by Welsh et. al. in 1967 [5] using absorption spectroscopy in long path cells (LPGCAS) in the infrared region at 77°K. In this work, spectra of mix- tures of Nz-H2 and Ar-H2 are also collected and reported similar to the CO-H* spectra. In general, the observed spectra are of very low resolution because of the collisional broadening caused by the high pressure required to observe signal for this vdW dimer of low dipole moment. More recently, a well- resolved spectra of CO-H2 and N2-Hz has been recorded by McKellar [6,7], using LPGCAS com- bined with Fourier-transformation techniques and optical paths as long as 154 m to obtain spectral reso- lutions as low as 0.01 cm-‘. In this work, the N2-H2

0166- 1280/981$19.00 0 1998 Elsevier Science B.V. All rights reserved PII SO166-1280(97)00308-4

54 M.C. Salazar et d/Journal of Molecular Structure (Theochem) 426 (I 998) 53-58

and CO-H2 spectra are also reported as very similar, and although many lines could be assigned by assuming a T-shaped structure, its true conformation is still unknown. Indirect evidence of CO-H2 can be found in measurements of vibrational relaxation times [S] and collisional cross-sections of CO by H2 [9].

Recent developments in non-linear optics have pro- vided tunable and coherent vacuum ultraviolet radia- tion to obtain high-resolution fluorescence electronic excitation spectra. This technique, combined with supersonic beam expansion techniques to form cold vdW molecules, has shown to be a powerful tool for studying interatomic potentials of electronically excited rare gas vdW dimers. However, the applica- tion of these combined techniques for studying the intermolecular interaction between non- or weakly polar diatomic-diatomic vdW molecules has not yet been reported. In spite of the relative simplicity of diatomic-diatomic vdW complexes, relatively few excited-state studies have been reported so far, includ- ing studies of some of the excited states of CO-H2 and Nz-HZ [lo].

In the present contribution we are able to describe the vertical excitation electronic spectra of the dia- tomic van der Waals CO-H2 molecule, in its linear most stable 0-C...H-H structure, using standard ab initio methods of quantum chemistry. Despite many technical difficulties, ab initio methods offer a sound basis for the calculation of vdW potential energy sur- faces valid over the whole range of molecular dis- tances and orientations.

2. Theoretical method

Ab initio studies of vdW interaction energies have essentially followed two directions [ll]: the first, regards the interaction between the subsystems as a perturbation and partitions the energy into terms such as electrostatic, repulsion, polarization, induction and dispersion. The second approach considers the inter- acting subsystems as a supermolecule. The inter- molecular perturbation approach is far more suitable for calculations of weak interactions because the interaction energy is obtained directly, rather than as the difference between two numbers usually several orders of magnitude larger than the interaction energy itself. Nevertheless, since all the highly effective ab

initio methods developed for single-molecule calcula- tions are in principle applicable without change, the vast majority of calculations of the interaction energy of vdW complexes are carried out using the super- molecule approach.

In the present study, the interaction energy has been obtained in the framework of the supermolecule approach at the Hartree-Fock self-consistent-field (HF-SCF) and correlation levels of approximation for the total energy:

E = E~HF - SCF + pxxrelation (1)

The interaction energy (IE) is then defined as

Z&R) = E(CO-H,; R) - E(CO-X; R) - E(X-HI; R)

(2)

where E(CO-X, R) and &J-HZ; R) are used here to indicate that the monomer energies are derived in the total dimer centered basis set. This amounts to apply- ing the counterpoise procedure of Boys and Bernardi [ 121 to correct for the basis set superposition error (BSSE), at both the HF-SCF and the correlation levels of approximation at each molecular configuration R. Despite the long-lasting controversy on its credibility, the function counterpoise method of Boys and Bernardi proves to be the correct approach [13].

Previous calculations on the ground-state potential surface of CO-H2 have been performed by: (i) com- bining short-range interaction, calculated at the HF- SCF level of approximation, with long-range interac- tions represented by parametric dispersion energies [ 14,151; (ii) calculating free-parameter ab initio inter- action potentials, which combine HF-SCF calcula- tions with intermolecular second-order dispersion terms [ 16,171; (iii) using the MMC (molecular mechanics for clusters) method of Dykstra et. al. [ 181, which combines electrical interactions, calcu- lated from high-level ab initio calculations, with para- metric nonelectrical interactions; (iv) using model potentials in the framework of the electron gas model [19,20]. Some of these theoretical studies favour the 0-C...H-H [16,17], or the C-O...H-H [ 14,151 collinear structures, while the rest favour the parallel [ 19,201, or almost parallel [ 181 structures, as the most stable conformation for CO-H2. Of these, the potential energy surface of Schinke et al. [ 141 has been used to describe its experimental differential cross-sections and differential energy loss spectra

M.C. Salazar et al./Journal of Molecular Structure (Theochem) 426 (1998) 53-58 55

[21-231, the role of H2 rotation in the vibrational relaxation of CO [24,25], and the pressure broadening cross-section of CO-Hz [26].

Although a complete assignment of the CO-H2 spectra can be achieved by iterative fittings using parametric potential surfaces, which would permit successive refinements and assignments in order to determine an improved potential, we believe that pre- vious parametric potentials [ 14,15,18-201 may lack of general validity inasmuch as they may depend either on the functional forms chosen or on the proper- ties used in fitting the parameters, and consequently we make use in the present work of a free-parameter fully ab initio potential as an alternative. We also feel that previous ab initio calculations [ 16,171 are seriously hampered by the problem of basis set super- position error due to the use of basis sets of inadequate size, and as a consequence the ab initio potential energy surface of CO-H2 has to be recalculated.

3. Results and discussion

3.1. Ground CO(X’a’)-H$f’C,) electronic state

High-level ab initio calculations, in the framework of the supermolecule approach, were performed to determine the conformational structure of the CO- H2 vdW dimer in its ground electronic state at RHF- SCF and many-body perturbation theory (MBPT) levels of approximation [27-301 for the total energy

E = ERHF - SCF + EMBPT (3)

where the correlation energy is split into contributions that are due to different orders of MBPT:

EMBPT = EMBPT(2) + EMBPTO’ + ,yMBPTV) + . . (4)

Currently, going beyond the full fourth-order MBPT treatment does not seem feasible. It has also been shown that in order to obtain quantitatively meaning- ful results incomplete higher-order MBPT calcula- tions must be avoided [30], thus the complete fourth-order MBPT approximation has been adopted in the present study. With the linked cluster theorem automatically satisfied on each order of perturbation, this MBPT scheme is certainly size consistent [27,28], one of the best and more economical methods avail- able for a reliable calculation of interaction energies within the supermolecule approach.

Through fourth-order approximations in the corre-

lation perturbation, the interaction energy in Eq. (2) can be expressed in terms of the following com- ponents at any particular geometrical configuration R:

Ipirmd = &CF + z~MBPT(2) +z~MBPTW +lEMBPTW

(5)

The necessary MBPT correlation energies were cal- culated using the BRATISLAVA program [3 11, inter- face to the MUNICH molecular package [32] for the Gaussian integrals, RHF-SCF eigenvectors and ener- gies, molecular properties and four-index molecular integral transformation calculations, respectively. In all calculations reported in the present work we have employed the medium-size polarized POL 1 basis sets of the CGTO type devised by Sadlej [33,34], which comprises [ 10.6.4/5.3.2] GTOKGTO for C and 0 atoms, and [6.4/3.2] GTOKGTO for hydrogen. This basis set accounts for the diffuseness of the valence part of the wave function, leads to a correct calcula- tion of intermolecular electrostatic forces, and to a negligible secondary BSSE [35], which justifies the use of the standard counterpoise correction [ 121.

Here, the fourth-order MBPT counterpoise- corrected interaction energy of CO-H2 in its ground electronic state is computed according to Eq. (2) using the POLl basis set for all possible nuclear con- figurations having the CO or H2 molecular bonds along the X-, y- or z-axis. On the supermolecule cal- culations, these two units were kept rigid at their experimental equilibrium bond lengths of 1.40 and 2.132 a.u. for H2 and CO, respectively, so that only a rigid rotor potential surface resulted. The coordinate system used for the calculations is shown in Fig. 1, where R is the distance between the centre of masses of CO and HZ, 0, and p2 correspond to the polar angles of orientation of the vectors along the CO and Hz bonds, and 4 represents the torsional angle.

Fig. 1. Coordinate system for CO-H I,

56 M.C. Salazar et al./Journal of Molecular Structure (Theochem) 426 (1998) 53-58

Fig. 2. Interaction energy surface of CO-H2.

For each value of the pair (P’, /32), geometry optimi- zations were carried out only with respect to the inter- molecular parameter R, with the torsional angle fixed at 4 = 0. The calculated interaction energy surface is depicted in Fig. 2 [36,37], and shows that the collinear 0-C...H-H structure (with the carbon atom closest to H) corresponds to the most stable conformation on these calculations.

Equilibrium bond distance (R& the well depths (D,), and dissociation energy (D,), of the most stable 0-C...H-H conformation, is obtained by fitting the above fully ab initio MBPT interaction-energy points for this conformer to a eighth-order polynomial in the stretching coordinate R, analytically continued with a seventh-order polynomial on l/R (from l/R6 to l/R”) in the asymptotic R - ~0 region. The minimum of the interaction potential occurred at R, = 8.1 a.u. [36,37], with a well depth of D, = 9.2 meV. Vibrational energies were also calculated from the fitted potential curves using the numerical Numerov-Cooley pro- cedure [38], by treating 0-C...H-H as a diatomic system with only one degree of freedom R. The cal- culated dissociation energies corresponded to a D, of 4.9 meV with at least one vibrational state supported by this linear configuration, which agrees well with existing spectroscopic results [6,7].

3.2. Excited CO(A ’r)-H2(X1Cg) electronic state

We considered the CO(X’C+)-H2(X’C,) - CO(A ’II-H2(X’Cg) transitions as our first choice in this study, mainly for two reasons: (a) the A ‘II - X’C+ transitions in CO are well known experimentally as the fourth-positive system, and they represent the dominant features of its electronic spectra; (b)

although there exist spectroscopic results [6,7] for

the CO(X’C+)-H2(X’C,) ground state system, there is to date no direct experimental evidence of the formation of the excited CO(A’II)-H2(X’Cg) vdW dimer.

High-level ab initio calculation were performed in the framework of the supermolecule approach in order to determine the interaction of CO(A ‘II) and H2(X’C,) at the RHF-SCF and multireference config- uration-interaction (MR-CI) levels of approximation [39] for the total energy

E=ERHF-SCF+~MR-CI (6)

For any given excited electronic states of a molecule, there might be several electronic configurations of about the same energy, which must be combined pre- viously to use any known correlation method. Due to its efficiency and generality, we have used the follow- ing multireference scheme [40]: (a) we start from a RHF-SCF calculation for the ground state of CO-H2; (b) a configuration interaction calculation (for the excited state of interest) is performed including all single and double excitations out of the above refer- ence state; (c) a multiference state is chosen from (b) including all configurations with mixing coefficients larger than any given threshold (usually 0.06); (d) finally, a full singles and doubles CI is performed out of the multireference state generated in step (c).

This procedure has the advantage of including the most important single, double, triple and quadruple excitations contributing to the excited state of interest, and of recuperating a constant value of correlation energy for all points of the interaction potential sur- face (with a threshold of 0.06 we are able to recuper- ate about 86% of the total correlation energy with a multireference state consisting of six configurations). Additionally, it can be apply without any modification to CO-HZ; CO-X, andX-Hz [as prescribed by Eq. (2) above], in order to obtain the following interaction energy:

&XCited = &3CF + IEMR - Cl (7)

The necessary MR-CI correlation energies were all calculated for the linear 0-C...H-H structure by means of the SGGA-CI program [39] interface to the MUNICH molecular package [32], and using the medium-size polarized POLl basis sets [33,34] already described in Section 3.1. This linear structure

M.C. Salaznr et al./Journal of Molecular Structure (Theochem) 426 (1998) 53-58 57

t3.5eV

77 12 13 14 1s 10 I? II 19

R( u.a. )

Fig. 3. CO(A ‘II-H2(X’C,) -+ CO(X’E’)-H,(X’E,) vertical exci-

tation energies for the most stable 0-C..,H-H linear configuration

of COpH2.

was chosen to characterize the CO(A ‘II)-H&Y’C,) excited state because it corresponded to the most stable geometry found already in connection with the CO(X’C’)-H2(X’Cg) ground state system. Geo- metry optimizations were carried out with respect to the intermolecular parameter R only, so that vertical excitation energies result. Fig. 3 shows our final CO(X’C’)-H&C,) - CO(A ‘II-HQ’C,) vertical excitation spectra of the 0-C.. .H-H linear configura- tion. Calculations performed according to the fittings procedures described already in Section 3.1 above, show that the minimum of the excited state interaction potential (upper curve in Fig. 3) occurs at R, = 9.8 a.u. with a well depth ofD, = 33.4 meV. Vibrational ener- gies calculated from the fitted excited potential curve using the numerical Numerov-Cooley procedure [38], show that the CO(A ‘II-H&Y’C,) excited state in the linear 0-C...H-H configuration supports five vibrational states, corresponding to D, = 28.4 meV, D, = 13.6 meV, Dz = 8.0 meV, D3 = 4.7 meV and D4 = 2.1 meV, respectively.

4. Final remarks

Although all points on the calculated interaction energy curves are fully ab initio, the present results are to be taken only as a qualitative guide. In order to

increase the predictive value of Fig. 3, one is forced to improve the POLl basis to represent the dispersion energy more accurately, and to help represent the electric properties and correlation energy of the excited state involved more accurately. Nevertheless, extending the size of the POLl basis is very difficult to accomplish in practice, mainly because the present MR-CI correlation energy calculations are already extremely demanding on computational resources (CPU time and storage). Considering that the long- term goal of the present study is to represent a ‘complete interaction energy surface’ for several excited states of interest, it will be useless to increase the size of the basis sets and still use the MR-CI method described above. At present, it would be more advisable to investigate the use of less demand- ing ab initio methods in order to undertake such a challenging task.

Acknowledgements

The authors thank the Deutsche Forschungs- gemeinschaft (DFG), the Consejo National de Inves- tigaciones Cientificas CONICIT (Grant Sl-2238), the Decanato de Investigaciones de la Universidad Simon Bolivar (Grants Sl-CB-314, Sl-CB-816, and SlO- CB-852), the Alexander von Humboldt-Stiftung, and the Max-Planck Gesellschaft, for their continuous support to this research project.

References

[l] G.C. Maitl, M. Rigby, E.B. Smith, W.A. Wakeham, in: Inter-

molecular Forces, their Origin, Determination, Oxford Univer-

sity Press, Oxford, 198 1.

[2] C.E. Dykstra, S.-Y. Liu, in: A. Weber (Ed.), Structure,

Dynamics of Weakly Bound Molecular Complexes, Reidel, Dordrecht, 1987.

[3] P. Hobza, R. Zahradnik, in: The Role of van der Waals

Systems in Physical Chemistry. in the Biodisciplines, Elsevier,

New York, 1988. [4] A.C. Legon, D.J. Millen, Gas-phase spectroscopy of hydrogen

bond dimers Chemistry Review 86 (1986) 635.

[5] A. Kudian. H. Welsh, A. Watanabe, Journal of Chemistry and Physics 47 (1967) 1553.

[6] A.R. McKellar, Journal of Chemistry and Physics 93 (1990) 18.

[7] A.R. McKellar, Chemistry and Physics Letters 186 (1991) 58.

58 M.C. Salazar et al./Journal of Molecular Structure (Theochem) 426 (1998) 53-58

[8] D. Miller, R. Millikan, Journal of Chemistry and Physics 53 [25] Z. Bacic, R. Schinke, G.H.F. Diercksen, Journal of Chemistry (1970) 3384. and Physics 82 (1985) 245.

[9] S. Dimov, C.R. Vidal, Chemistry and Physics Letters 221

(1994) 307.

[lo] (a) R.F. Sperlin, M.F. Golde, Journal of Chemistry and Physics

89 (1988) 3113; (b) R.F Sperlin, M.F. Golde, D.J. Jordan,

Chemistry and Physics Letters 142 (1987) 359.

[ 1 l] P. Hobza, R. Zahradnik, Weak Intermolecular Interaction in

Chemistry, Biology, Elsevier, Amsterdam, 1980.

[12] S.F. Boys, F. Bemardi, Molecular Physics 19 (1970) 553.

[13] M. Gutowski, G. Chalasinski, Journal of Chemistry and

Physics 98 (1993) 5540.

[26] R. Schinke, V. Engel, U. Buck, H. Meyer, G.H.F. Diercksen, Astrophysics Journal 299 (1985) 939.

[27] J. Paldus, J. Cizek, Advances in Quantum Chemistry 9 (1975)

105.

[28] J. Bartlett, Annual Review of Physics and Chemistry 32 (198 1)

359.

[29] S. Wilson, Composite Physics Reports 2 (1985) 389. [30] G.H.F. Diercksen, V. Kello, A.J. Sadlej, Chemistry and

Physics 96 (1985) 59.

[14] R. Schinke, H. Meyer, U. Buck, G.H.F. Diercksen, Journal of

Chemistry and Physics 80 (1984) 5518.

[ 151 L. Paulsen, Chemistry and Physics 68 (1982) 29.

[16] J. Prisette, E. Kochanski, D.R. Flower, Chemistry and Physics

27 (1978) 373.

[3 l] J. Noga, Computers and Physics Communications 29 (1983)

117.

[32] G.H.F. Diercksen, W.P. Kraemer, Munich Molecular Program

System, Max-Planck-Institute fir Astrophysik, Garching b.

Miinchen, F.R.G., 1969.

[17] D.R. Flower, J.M. Launay, E. Kochanski, J. Prisette, Chemistry and Physics 37 (1979) 355.

[ 181 CA. Parish, J.D. Augspurger, C.E. Dykstra, Journal of Physics

and Chemistry 96 (1992) 2069.

[ 191 M.C. van Hemert, Journal of Chemistry and Physics 78 (1983)

2345.

[20] S. Green, P. Thadedeus, Astrophysics Journal 205 (1976) 766.

[21] A. Kupperman, R.J. Gordon, M.J. Coggiola, Discussions ofthe

Faraday Society 55 (1973) 145.

[33] A.J. Sadlej, Collection of the Czechoslovakian Chemical

Communications 53 (1988) 1995.

[34] A.J. Sadlej, Theoretica Chimica Acta 79 (1991) 123.

[35] G. Karlstrom, A.J. Sadlej, Theoretica Chimica Acta 61 (1982) 1. [36] M.C. Salazar, A.J. Hemandez, G.H.F Diercksen, Journal of

Molecular Structures 287 (1993) 139.

[37] M.C. Salazar, A. De Castro, J.L. Paz, G.H.F. Diercksen, A.J.

Hemlndez, International Journal of Quantum Chemistry 55 (1995) 251.

[22] H.P. Butz, R. Feltgen, H. Pauly, H. Vehmeyer, Zeitscrift

Physiks 247 (1971) 70.

[38] J.W. Cooley, Mathematical Composites 15 (1961) 363.

[39] W. Duch, J. Karwowski, Journal of Composite Physics Report

2 (1985) 93. [23] J. Andres, U. Buck, H. Meyer, J.M. Launay, Journal of

Chemistry and Physics 76 (1982) 1417.

[24] J. Tanner, M. Maricq, Chemistry and Physics 119 (1988) 307.

[40] P. Bruna, S. Peyerimhoff, in: K. Lawley (Ed.), Ab-Initio

Methods in Quantum Chemistry, Wiley, New York, 1987,

Chapter 1.