Computational and Theoretical Chemistry 1001 (2012) 20–25

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Computational and Theoretical Chemistry

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Atomic partial charges for mixed chloroammine chromium(III) complexes fittedto the molecular electrostatic potential

Ivana Djordjevic ⇑, S.R. Niketic ⇑Chemistry Centre, IHTM, University of Belgrade, Njegoseva 12, PAK 125213, 11001 Belgrade, Serbia

a r t i c l e i n f o

Article history:Received 15 September 2012Received in revised form 30 September2012Accepted 2 October 2012Available online 3 November 2012

Keywords:Partial atomic chargesChromium(III)Quantum mechanical calculationsRestrained atomic chargesRESP

2210-271X/$ - see front matter � 2012 Elsevier B.V.http://dx.doi.org/10.1016/j.comptc.2012.10.013

⇑ Corresponding authors. Tel.: +381 63 8904508 (SE-mail addresses: ivana.djordjevic@chem.bg.ac.rs

com (S.R. Niketic).

a b s t r a c t

Using the RESP procedure partial atomic charges for six isomers of a series of octahedral complexes[Cr(NH3)6�x(Cl)x](3�x)+ (x = 0, 1, 2, 3) were least-square fitted to the molecular electrostatic potential(MEP) derived from quantum mechanical (QM) calculations with different HF basis sets. The resultingcharges are self-consistent, they match MEPs, QM dipole and quadrupole moments, and they reflect fineelectronic effects in the coordination sphere (viz. trans and cis influence) offering a possibility to explicitlyincorporate some of these electronic features in a molecular mechanics (MM) treatment. RESP derivedpartial atomic charges (together with other nonobservable quantities, such as atomic dipole moments,and atomic polarizabilities) could thus be parametrized on the basis of a multibody model, which is a pre-requisite for any nonadditive MM approach.

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1. Introduction

For quantitative atomistic computer simulation of complexchemical systems molecular mechanical (MM) force fields oftenrepresent the only practically feasible alternative. With availableefficient algorithms and computer resources most of the earlierrestrictions (size, sampling ability, time scales, etc.) have beeneliminated so that efforts have increasingly developed into asearch for more exact models of potential energy surfaces, i.e.,more accurate and physically more realistic force fields. One ofthe major aspects of this quest are partial atomic charges, in a forcefield based on monopole approximation, which are recognized aspivotal MM parameters that regulate conformations and particu-larly the intermolecular interactions.

With the force field for coordination compounds containing theCoulomb term [1] we were able, over an extended period, toachieve satisfactory parametrization to account for energeticsand structures of a number of Co(III) and Cr(III) complexes withdiamine metal chelate rings [2–5], various (poly)amino(poly)carboxylate complexes [6–10], as well as metalloporphyrins withNi(II) and Tb(III) [11–13].

In these studies partial atomic charges were obtained fromatom type specific input parameters using a CFF intrinsic algorithm[1], which assigns a value to each atom (except the central metal

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.R. Niketic).(I. Djordjevic), niketic@gmx.-

atom) on the basis of its type, input parameter, position in a chain,and number and types of neighboring atoms, with the requirementthat the sum of all partial atomic charges matches the total formalcharge of the species.

However, in a recent attempt to build a force field that will ac-count also for vibrational frequencies (VOFF) [14] it was realizedthat partial atomic charges defined in the indicated way are notaccurate enough to reproduce vibrational intensities. Similar prob-lems are encountered in ongoing conformational studies [15] of aseries of mixed Cr(III) complexes with diamine chelate rings andvarious halogeno ligands and, according to our experience, in manycases where the Coulomb term appears to be dominant among theterms making up the total conformational energy in MM.

1.1. Partial atomic charges

Many ways to obtain partial atomic charges for a molecule ofinterest are known. Some are defined in Hilbert space, and othersin Euclidean space. Of the former, the earliest methods based di-rectly on the wave function were Mulliken population analysis[16] and later refinements: Löwdin [17] and natural populationanalysis [18] (NPA). Bader’s atoms in molecule (AIM) theory [19]may also be classified as a Hilbert space method. More recently,widely used methods became those based on a least-squares fitto the molecular electrostatic potential (MEP) calculated on a num-ber of points in Euclidean space surrounding the molecule. The lat-ter methods comprise CHELP [20], CHELPG [21], Merz–Kollman(MK) [22], ESP [23] and RESP [24], among others, which differ from

Table 1Calculated RESP atomic charges (a.u.) for [Cr(NH3)6]3+.

No. Basis set q(Cr) q(N) q(H)

1 6-31G 1.3667 �0.9581 0.41012 6-31G(d) 1.6903 �1.0712 0.42983 6-31G(d,p) 1.6618 �1.0694 0.43084 TZV/DZV 1.4323 �0.9648 0.40875 TZV 1.3273 �0.9419 0.40696 TZV/6-31G(d) 1.6911 �1.0605 0.42627 TZVP 1.6179 �1.0402 0.42358 SBKJC/6-31G(d) 1.7081 �1.0722 0.42929 cc-pVTZ/6-31G(d) 1.6240 �1.0425 0.4239

10 cc-pVTZ/cc-pVDZ 1.5973 �1.0311 0.421611 aug-cc-pVTZ/6-31G(d) 1.3991 �0.9274 0.398112 aug-cc-pVTZ/aug-cc-pVDZ 1.3748 �0.9167 0.3959

I. Djordjevic, S.R. Niketic / Computational and Theoretical Chemistry 1001 (2012) 20–25 21

each other mainly in the choice of points. Unfortunately, neither ofthe methods could yield ‘‘correct’’ partial atomic charges, whichare not quantum mechanical observables and cannot be measuredexperimentally.

1.2. RESP approach

In this work we considered RESP [25] as an attractive choice dueto its versatility to control the fitting, to its ability to consistently fitcharges on multiple structures, to the fact that it is used in deriva-tion of some popular and widely used biomolecular force fields(like, e.g., AMBER), and finally, to the availability of the stand-aloneFortran code [26], which can be operated in batch mode that iscompatible with old computational habits of one of us.

In RESP [25] (standing for Restrained Electrostatic Potential)partial atomic charges are obtained by iterative optimization(using the technique of Lagrangian multipliers) of the fit, v2

esp, as:

v2esp ¼

Xpoints

i

VQM �Xatoms

j

qj

Rij

!2

between QM derived electrostatic potential, VQM, and the Coulombmonopole approximation model, with a possibility to moderateatomic charges by means of a hyperbolic restraint function, v2

rstr:

v2resp ¼ v2

esp þ v2rstr ¼ v2

esp þ krstr

Xatoms

j

q2j þ b2

� �12 � b

� �

where the weight krstr controls the strength of the restraint. In thisway it is possible to attenuate the charge difference between polaratoms. However, the effect of krstr in deriving partial atomic chargesfor chromium(III) complexes studied in this work diverged from theone that is common for organic molecules [24], as will be shown be-low. The tightness of the hyperbola, b, was kept at its originally setvalue of 0.1 electrons [24].

1.3. Choice of the structures

For the present comparative assessment of the basis set depen-dence of MEP for the RESP derivation of partial atomic charges wehave chosen the series of octahedral [Cr(NH3)6�x(Cl)x](3�x)+ (x = 0, 1,2, 3) complexes. The choice was influenced by the fact that thestructures are simple enough (eliminating or minimizing any sec-ondary effects) and yet multifaceted: providing a range of coordi-nation patterns with ammine and chloro ligands, of overallcharges of the species (from +3 to 0), of geometrical isomerism(cis/trans and fac/mer), and a possibility to evaluate anticipated dif-ferences between stereochemically nonequivalent ligands of thesame type. A further incentive for the choice of structures is aremarkable deficiency of any experimental data on these as wellas any other complexes of chromium(III), which could be directlyrelated to their electrostatics.

2. Computational methods

All calculations reported here were carried out using the GA-MESS electronic structure program [27]. To gain insight into theinfluence of basis set on the RESP derived partial atomic chargesfrom the quantum mechanically computed MEP, which to ourknowledge was not systematically investigated hitherto for transi-tion metal complexes, we have chosen the following twelve basissets that approximately represent an increase of the level of theircomplexity. For historical reasons we started with the Pople basisset 6-31G and its polarized variants 6-31G(d) and 6-31G(d,p)[28]. Those and larger Gaussian-type split valence basis sets wereoften proved successful in describing small organic molecules

[29–31] as well as ligands of inorganic complexes [32]. Since a reli-able description of transition metal atoms calls for extended basissets, we next chose Dunning’s full double-f [33] and triple-f [34]valence basis sets viz. TZV/DZV (for metal and ligands atoms,respectively), TZV (for all atoms), TZV/6-31G(d) (for metal and li-gands atoms, respectively), and TZVP (polarized TZV for all atoms).Triple-f basis sets are better than double-f ones, but do not per-form well without polarization functions. We next chose the effec-tive core potential valence basis (SBKJC) [35,36] due to Stevens,Basch, Krauss, Jasien and Cundari, which so far yielded good resultsin calculations on transition metal complexes [37,38]. We nextused Dunning-type correlation consistent basis sets with polariza-tion functions: cc-pVTZ/6-31G(d), cc-pVTZ/cc-pVDZ, and with dif-fuse functions aug-cc-pVTZ/6-31G(d) and aug-cc-pVTZ/aug-cc-pVDZ (for Cr, N, and Cl atoms) [39–41]. Hydrogen atoms of ammineligands were treated with non-polarized 6-31G basis set in all cal-culations. Throught, the self-consistent field theory and the re-stricted open Hartree–Fock (ROHF) method was employed,except in a few calculations on [Cr(NH3)5Cl]2+ with cc-pVTZ andaug-cc-pVTZ basis sets that required the UHF regime in order toachieve the convergence. In addition, we performed a limited num-ber of calculations with representative DFT functionals. They weresubstantially more computationally intensive, but the results failedto produce any new insight apart from the fact that partial atomiccharges on chromium turned out to be almost halved in compari-son to the values from analogous HF calculations.

A fit of atomic charges to MEP with the RESP program was carr-ried out by a usual two-stage procedure [30]: first by fittingcharges on all atoms independently, followed by assigning stereo-chemically equivalent atoms of the same kind the same averagevalues for partial atomic charges. The second step could be reiter-ated if necessary, with different atom assignment, to ascertainphysically (and stereochemically) meaningful partial charge valuesfor all atoms.

MEP maps were generated and graphically rendered in Mac-MolPlt program [42], directly from the eigenvectors produced byGAMESS, in an attempt to present them alongside the correspond-ing RESP generated maps, but due to technical limitations of theavailable contouring programs, this effort was given up. Neverthe-less, a satisfactory convergence was confirmed in all cases: theresidual sum of squares (v2 < 0.007) and the standard error of esti-mate (v2/n < 0.003) were well below the margins for this type offitting.

3. Results

3.1. General considerations

Final RESP charges for the six structures of the [Cr(NH3)6�x(-Cl)x](3�x)+ (x = 0, 1, 2, 3) series are presented in Tables 1–6. Before

Table 2Calculated RESP atomic charges (a.u.) for [Cr(NH3)5Cl]2+.

No. Basis set q(Cr) q(Cl) q(N) q(H)

1 6-31G 1.2668 �0.5741 �0.8246c 0.3666c

�1.0426t 0.4163t

2 6-31G(d) 1.3054 �0.5012 �0.9123c 0.3825c

�0.7802t 0.3451t

3 6-31G(d,p) 1.3051 �0.5003 �0.9174c 0.3844c

�0.8021t 0.3513t

4 TZV/DZV 1.1360 �0.4831 �0.8508c 0.3723c

�0.7227t 0.3352t

5 TZV 1.0771 �0.4840 �0.8163c 0.3661c

�0.7735t 0.3509t

6 TZV/6-31G(d) 1.1801 �0.4400 �0.9087c 0.3819c

�0.5673t 0.2929t

7 TZVP 1.1425 �0.4337 �0.8917c 0.3788c

�0.5764t 0.2961t

8 SBKJC/6-31G(d) 1.1805 �0.4386 �0.9135c 0.3834c

�0.5702t 0.2936t

9 cc-pVTZ/6-31G(d) 1.1333 �0.4365 �0.8827c 0.3770c

�0.5899t 0.2999t

10 cc-pVTZ/cc-pVDZ 1.0859 �0.4243 �0.8731c 0.3756c

�0.5471t 0.2902t

11 aug-cc-pVTZ/6-31G(d) 1.1034 �0.4183 �0.8790c 0.3761c

�0.5599t 0.2926t

12 aug-cc-pVTZ/aug-cc-pVDZ 1.0719 �0.4122 �0.8700c 0.3745c

�0.5369t 0.2876t

c = cis(Cl,NH3); t = trans(Cl,NH3).

Table 3Calculated RESP atomic charges (a.u.) for cis-[Cr(NH3)4Cl2]+.

No. Basis set q(Cr) q(Cl) q(N) q(H)

1 6-31G 1.4512 �0.6358 �0.6915c 0.3189c

�1.1215t 0.4221t

2 6-31G(d) 1.2503 �0.5595 �0.7198c 0.3222c

�0.9066t 0.3647t

3 6-31G(d,p) 1.2596 �0.5593 �0.7290c 0.3247c

�0.9212t 0.3686t

4 TZV/DZV 1.1200 �0.5423 �0.6966c 0.3218c

�0.8615t 0.3584t

5 TZV 1.1836 �0.5582 �0.6663c 0.3137c

�0.9491t 0.3802t

6 TZV/6-31G(d) 1.0530 �0.5063 �0.7091c 0.3204c

�0.7665t 0.3314t

7 TZVP 1.0656 �0.5050 �0.6940c 0.3161c

�0.7927t 0.3369t

8 SBKJC/6-31G(d) 1.0491 �0.5051 �0.7028c 0.3192c

�0.7735t 0.3331t

9 cc-pVTZ/6-31G(d) 1.0402 �0.5047 �0.6793c 0.3135c

�0.7855t 0.3363t

10 cc-pVTZ/cc-pVDZ 0.9669 �0.4895 �0.6670c 0.3121c

�0.7502t 0.3290t

11 aug-cc-pVTZ/6-31G(d) 1.0084 �0.4904 �0.6706c 0.3106c

�0.7723t 0.3325t

12 aug-cc-pVTZ/aug-cc-pVDZ 0.9672 �0.4822 �0.6629c 0.3096c

�0.7546t 0.3290t

c = cis(Cl,NH3); t = trans(Cl,NH3).

Table 4Calculated RESP atomic charges (a.u.) for trans-[Cr(NH3)4Cl2]+.

No. Basis set q(Cr) q(Cl) q(N) q(H)

1 6-31G 1.2494 �0.6588 �0.7504 0.33912 6-31G(d) 1.2475 �0.5849 �0.8090 0.34653 6-31G(d,p) 1.2582 �0.5850 �0.8210 0.34974 TZV/DZV 1.1359 �0.5688 �0.7890 0.34655 TZV 1.1095 �0.5806 �0.7525 0.33856 TZV/6-31G(d) 1.1411 �0.5284 �0.8062 0.34507 TZVP 1.1371 �0.5276 �0.8012 0.34368 SBKJC/6-31G(d) 1.1393 �0.5300 �0.8083 0.34619 cc-pVTZ/6-31G(d) 1.1024 �0.5280 �0.7811 0.3398

10 cc-pVTZ/cc-pVDZ 1.0470 �0.5131 �0.7703 0.338411 aug-cc-pVTZ/6-31G(d) 1.0829 �0.5145 �0.7784 0.338312 aug-cc-pVTZ/aug-cc-pVDZ 1.0485 �0.5061 �0.7705 0.3371

Table 5Calculated RESP atomic charges (a.u.) for fac-[Cr(NH3)3Cl3].

No. Basis set q(Cr) q(Cl) q(N) q(H)

1 6-31G 1.7850 �0.6915 �1.1212 0.40592 6-31G(d) 1.4248 �0.6123 �0.9232 0.35353 6-31G(d,p) 1.4320 �0.6124 �0.9308 0.35534 TZV/DZV 1.2594 �0.5935 �0.8604 0.34475 TZV 1.5263 �0.5263 �1.0137 0.37856 TZV/6-31G(d) 1.1982 �0.5677 �0.8253 0.33127 TZVP 1.2986 �0.5754 �0.8817 0.34148 SBKJC/6-31G(d) 1.2046 �0.5662 �0.8323 0.33239 cc-pVTZ/6-31G(d) 1.2368 �0.5659 �0.8597 0.3378

10 cc-pVTZ/cc-pVDZ 1.1138 �0.5447 �0.8108 0.328111 aug-cc-pVTZ/6-31G(d) 1.2458 �0.5593 �0.8727 0.338912 aug-cc-pVTZ/aug-cc-pVDZ 1.1721 �0.5467 �0.8443 0.3334

22 I. Djordjevic, S.R. Niketic / Computational and Theoretical Chemistry 1001 (2012) 20–25

delineating the contents of these tables it is appropriate to com-ment on overall charge reproducibility in the present work andin particular on the conformational and rotational dependence ofour RESP derived charges in the light of other published reportstouching upon the same issues [25].

Stereochemically, the present chromium(III) complexes aresimple octahedral structures with six unidentate ligands, thereforeof a very limited conformational flexibility. In gas-phase structuresall valence angles on Cr are practically p/2 (or p), and in a few crys-tallographically determined structures they do not deviate fromthe ideal values [43–49] (except in cases[50–52] where thecharged species are associated with larger and structurally morecomplex counterions). Therefore it was valid to treat all structures

as regular octahedral. Rotations of NH3 groups about the metal–li-gand bonds are practically free and give rise to a number of rota-mers, some of which bear high symmetries (as shown inTable 7). It was found that RESP charges are not significantly per-turbed by orientations of NH3 groups: they were always withinthe range of values obtained by averaging the charges on stereo-chemically equivalent NH3 groups within the RESP procedure.

Rotational dependence of RESP derived charges was likewise aninsignificant matter. For octahedral structures there are two intrin-sic and conventional orientations with the central metal atom inorigo: either the so called orthoaxial (with all ligator atoms layingon Cartesian axes), or the one with the coordinate system definedby the principal moments of inertia. Values presented in Tables 1–6 were obtained with orthoaxial orientation of the structures. Afterany random Eulerian rotation of a structure changes in RESP de-rived charges were 61% for Cl, N, and H, and 65% for Cr, but theirrelative values change with the choice of basis set in practically thesame pattern.

Much has been said in other published reports on RESP about‘‘buried’’ atoms [53,54]. In this work it is the central metal atom(chromium), which is at the same time of principal concern inour quest for partial atomic charges of chromium(III) complexes.Following the common practice we started with default valuesfor the restraint parameters, which systematically yielded toolow values for q(Cr). Furthermore, even a slight increase of the re-straint weight sharply lowered the q(Cr) down to physically unre-alistic negative values (Fig. 1). For that reason it was necessary todecrease or eventually to remove the restraining weight. Valuespresented in Tables 1–6 were obtained with zero restraint.

3.2. Dipole and quadrupole moments

Dipole moments calculated from RESP derived partial atomiccharges are qualitatively anticipated and acceptably independent

Table 6Calculated RESP atomic charges (a.u.) for mer-[Cr(NH3)3Cl3].

No. Basis set q(Cr) q(Cl) q(N) q(H)

1 6-31G 1.4749 �0.7128t �0.6932c 0.3122c

�0.6697c �1.0343t 0.3894t

2 6-31G(d) 1.2291 �0.6351t �0.6934c 0.3078c

�0.5950c �0.7963t 0.3241t

3 6-31G(d,p) 1.2427 �0.6355t �0.7078c 0.3112c

�0.5957c �0.8070t 0.3265t

4 TZV/DZV 1.1313 �0.6197t �0.6922c 0.3128c

�0.5837c �0.7768t 0.3254t

5 TZV 1.2915 �0.6535t �0.6732c 0.3047c

�0.6157c �0.9437t 0.3644t

6 TZV/6-31G(d) 1.0671 �0.5880t �0.6914c 0.3073c

�0.5545c �0.6981t 0.3002t

7 TZVP 1.1330 �0.5969t �0.6792c 0.3011c

�0.5620c �0.7700t 0.3149t

8 SBKJC/6-31G(d) 1.0667 �0.5908t �0.6807c 0.3051c

�0.5523c �0.7112t 0.3031t

9 cc-pVTZ/6-31G(d) 1.0565 �0.5872t �0.6630c 0.3000c

�0.5504c �0.7190t 0.3043t

10 cc-pVTZ/cc-pVDZ 0.9534 �0.5673t �0.6479c 0.2988c

�0.5296c �0.6613t 0.2916t

11 aug-cc-pVTZ/6-31G(d) 1.0609 �0.5810t �0.6538c 0.2951c

�0.5431c �0.7462t 0.3091t

12 aug-cc-pVTZ/aug-cc-pVDZ 1.0009 �0.5692t �0.6464c 0.2948c

�0.5309c �0.7139t 0.3021t

For Cl ligand: c = cis(Cl,Cl); t = trans(Cl, Cl). For NH3 ligand: c = cis(Cl, NH3); t = trans(Cl, NH3).

Table 7Symmetries and dipole moments.

Species Symmetrya l/Db

[Cr(NH3)6]3+ S6 0[Cr(NH3)5Cl]2+ Cs 12.2cis-[Cr(NH3)4Cl2]+ C2v 15.2trans-[Cr(NH3)4Cl2]+ C2h, C4h, D2d, D2h 0fac-[Cr(NH3)3Cl3] C3 17.7mer-[Cr(NH3)3Cl3] Cs 9.7

a Rotamers with nontrivial symmetries; all others are C1.b Calcd. from RESP derived charges for basis sets 6, 7, 8, and 9.

Fig. 1. Effect of restraint weight, krstr, on RESP charges for [Cr(NH3)6]3+ (number ofatoms: 25; total ionic charge: +3).

I. Djordjevic, S.R. Niketic / Computational and Theoretical Chemistry 1001 (2012) 20–25 23

of basis set used to generate MEP (Fig. 2). The values shown in Ta-ble 7 correspond to basis sets 6, 7, 8, and 9 (cf. Conclusions). Paren-thetically, the structures comprise rotamers of eight nontrivialsymmetries (Table 7) and nicely illustrate the elementary textbookstatement about point groups of polar molecules. Since the exper-imental dipole moments of [Cr(NH3)6�x(Cl)x](3�x)+ (x = 0, 1, 2, 3) are,to our knowledge, unavailable it was only possible to compare the

RESP values to those coming out of ab initio calculations (Fig. 2)and to confirm excellent correlation. For the same reason the quad-rupole moment calculated from RESP derived atomic charges couldonly be compared with QM results (not shown) and predictably agood agreement was obtained for its diagonal components for allthe structures.

3.3. Individual structures

[Cr(NH3)6]3+ appears like a positively charged sphere at suffi-cient distances from its vdW volume of enclosure. Only one centro-symmetric rotamer (point group S6) with zero dipole moment isdiscerned. RESP fitted charges vary in intervals of 0.34, 0.15, and0.03 a.u. for Cr, N, and H, respectively. The charge on NH3 groupsis slightly positive (0.24 ± 0.03 electrons).

[Cr(NH3)5Cl]2+ behaves like a dipole (l � 12 D). One rotamerhas a plane of symmetry (Cs); others are C1. Charges on Cr areslightly lower than in hexaammine complex but their variationfor different basis sets retains the same pattern. There are twokinds of ammine ligands: the apical NH3 trans to Cl is expectedto differ from the four in-plane NH3 groups as a result of transinfluence [55]. In RESP fitting this is reflected in a slight decreaseof partial charge on N trans to Cl together with a slight increaseof the total charge of the same ammine.

[Cr(NH3)4Cl2]+ has two diastereoisomeric forms (cis and trans),both of which comprise four rotamers of nontrivial symmetry.Rotamers of the cis isomer belong to C2v point group (l � 15 D).Those of trans isomer are either centrosymmetric (C2h, C4h, andD2h) or dihedral (D2d), all of which having zero dipole moment.The cis isomer has two nonequivalent pairs of ammine ligands. Dif-ference in RESP derived charges is opposite to that in [Cr(NH3)5-

Cl]2+ (slight increase of the charge on N atoms trans to Cl, andslight decrease of the total charge on these NH3 groups).

[Cr(NH3)3Cl3] also has two diastereoisomeric forms: fac (C3, l �17 D) and mer (Cs, l � 10 D). Ligands of the same type are equiva-lent in fac. For mer isomer RESP analysis distinguishes not only thetwo nonequivalent ammine ligands (as in previous examples), butalso the two different Cl ligands: one trans to NH3 and the othertrans to Cl. In the case of NH3 RESP derived charges are slightly de-

Fig. 2. Comparison between dipole moments calculated from RESP derived partial atomic charges and the QM values.

24 I. Djordjevic, S.R. Niketic / Computational and Theoretical Chemistry 1001 (2012) 20–25

creased for ammines trans to Cl both with respect to the charge onthe N atom and on the whole NH3 group. This outcome, togetherwith the preceding ones (in [Cr(NH3)5Cl]2+ and cis-[Cr(NH3)4Cl2]+)strongly suggests that charge assignment to stereochemically non-equivalent ligands of the same kind is the resultant of several fac-tors, among which both cis and trans influences [55] should beconsidered with equal measure.

4. Conclusions

When it comes to the choice of the ‘‘advisable’’ basis set theproblem of extreme scarcity of the published data, which couldserve as a , keeps recurring. Nevertheless, on the basis of self-con-sistency of the present RESP derivation of atomic charges andagreement of the results with e.g., atomic charges of ammine in[Co(NH3)6]3+ complex,[32] those of coordinated Cl� in [ZrCl6]2�

[37], charges on Cr in [CrF6]3+ [38] and in [Cr(H2O)6]3+ [56], as wellas those of the free or coordinated NH3 [57], it appears that mutu-ally convergent TZV, TZVP, SBKJC, and cc-pVTZ basis sets (in com-bination with 6-31G(d), that is, our basis sets 6, 7, 8, and 9)produce most reasonable results.

On average, for recommended basis sets (6, 7, 8, and 9), q(Cr)was +1.6 for hexaammine or +1.2 ± 0.2 for all chloro complexes,q(Cl) was �0.5 ± 0.1, and the total charge for coordinated ammineligand was +0.2 ± 0.1. In addition, due to the trans and various cisinfluences in chloro complexes, the charge on ammine ligand

was increased by up to 20% (in monochloro species) or decreasedby about 10% (in cis-dichloro and mer-trichloro species).

These partial atomic charges would constitute a reliable choicefor the optimization of a new generation force field for chro-mium(III) complexes, based on nonadditive MM approach, thattakes into account trans and cis influences in the octahedral coor-dination sphere.

Acknowledgment

Financial support from the Serbian Ministry for Science throughGrant No. 172035 is gratefully acknowledged.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.comptc.2012.10.013.

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