Geometry and electronic structure studies using computational quantum chemistry

Journal of Molecular Structure (Theochem), 234 (1991) 185-200 Elsevier Science Publishers B.V., Amsterdam

185

Geometry and electronic structure studies using computational quantum chemistry Harold Basch Department of Chemistry, Bar Ilan University, 52100 Ramat Can (Israel) (Received 18 September 1990)

Abstract Some very recent applications in ab initio computational quantum chemistry are reviewed and mainly previewed. A large number of sulphone, sulphoxide and sulphide geometric structures have been gradient optimized at the single electronic configuration self-consistent field (SCF) level using a 6-31G* (or 6-31+G+ for anions) basis set. This collection allows a comparison and understanding of trends and effects in their electronic and geometric structural properties. The degree of intra- and inter-molecular hydrogen bonding involving the methyl group with the S=O bond in hypervalent sulphur compounds has been characterized. A comparison of calculated dimer and 1: 1 monomer-water complex structures allows a consideration of the relative importance of different hydrogen bonding situations (C-H, S-H and O-H with the S-O bond) in these types of compound. A number of other hydrogen-bonded adducts involving (C-)H. *-0 (=C) and (HO-)H- --0(=P) interactions, which shed light on recent experimental results, have also been studied. The homonuclear and mixed triple-bonded diatomic molecules (XY”+ ) with X,Y =nitrogen and oxygen form a ten-valent electron isoelectronic series (N,, NO+ and 0:’ ) for comparison of calculated properties with experiment. The O$+ energy interaction curve shows an interesting avoided curve crossing and a metastable energy minimum, a barrier to dissociation and an exothermic bond energy. For these systems, the complete active space multi-configuration SCF method is needed for even a qualitatively correct electronic structure description of the whole curve. Relativistic effective core potentials, which replace the inert core electrons in the heavier elements, allow this study to be extended to, for example, Pg’ , Au;+ and H&+ , as well as the whole XY2+ series with X,Y = 0, S, Se and Te.

INTRODUCTION

It is a privilege and a pleasure to contribute a paper to this special issue marking 40 years of computational quantum chemistry, measured from the variational basis set expansion formulation of the closed shell Hartree-Fock (HF) equations presented by Roothaan [l] and Hall [ 21 in 1951. There have been many advances in theory and methodology since then which have allowed ever-widening use of computational quantum chemistry as a useful and practical tool for problem solving in the field of molecular electronic structure. We

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0 1991 Elsevier Science Publishers B.V. All rights reserved.

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would like to review and preview here a selected combination of very recent applications biased towards the author’s research interest and activities. All the computationalwork is based on the use of Gaussian-typefunctions introduced by Boys [ 31 for use in ab initio electronic structurestudies. Of course, it is not possible to ponder in wonderment on the progress and achievementsin computationalquantumchemistryof the past 40 years without notingthe dramaticadvancesin computertechnologyand algorithms.Here we will concentrate on the quantum chemical aspects with emphasis on ab initio methods and applications, and only note in dry understatementthat computer resourcesare still a factor to be considered. STRUCTURE

Moleculargeometricstructurede~r~nation can be a difficultexperimental task. Histo~cally, and even today, a greatdeal of our empiricalunderstanding of electronic structure and bonding is based on the knowledge of molecular geometry.The recent developmentof analyticalenergy gradientmethods [ 41 and efficient solution of the perturbedHF equations [ 51 have opened the way for computationalquantumchemistryto provide calculatedequilibriumstructures on an almost routine basis, within computer resource limitations. The Browse QuantumChemistryData Base [6] of calculatedmolecularstructures has over 25 066 entries and, if only in sheer numbers, is rapidly approaching the largest corresponding experimental compilation [of X-ray and neutron diffraction results (geometriesobtained from microwave,electron diffraction, optical, photoelectron,etc. Spectroscopiesand methods are not covered) 1, the CambridgeStructuralDatabase [ 71. The accuracy of the single electronic configuration (SEC) self-consistent field (SCF) method in geometric structuredeterminationhas been reviewed [8]. The generalconsensus is that an unconstrainedgradientoptimizedstructure at the SCF level in a valence double-zetaplus polarizationbasis set (i.e. 6-31G*) for neutralmoleculescontainingonly singlebonded atoms of the first two rows of the Periodic Table should give bond lengths of 0.01-0.02 A and bond angles of 1-3” within experimentalgas-phase structures.On the other hand, for example, formally unsaturatedsystems and molecules composed of combinations of only fluorine, nitrogen and oxygen atoms with homonuclear bonds are inadequately described in the SEC approximation even with extended basis sets. The difficulty with this second set of molecules is, apparently, also due to some intrinsic double bond character in the homonuciear bond [ 9,101,which demandsa higherleveltreatmentfor comparableaccuracy. We have recently computationallysurveyedthe electronic structureproperties of a substantial number of small sulphinic (XSOOH) and sulphonic (XSO,OH ) acids, and their sulphoxide (XSOY) and s&phone (XS02Y) derivatives [ 11,121,with substituentsX,Y = H, CH3,NH2, OH, SH, 0CH3, F, Cl

187

and C6H5 (not in all combinations). Comparison with experiment, where available, indicates that SCF/6-31G* [ 131 optimized geometries are in very good agreement with experiment, comparable with the single bonded category of molecules mentioned above. This accuracy is obtained even though the sulphur- (terminal)oxygen bonds are commonly written in double bond form, S=O, implying that the SEC approximation should give poor geometry results. Thus, from the good geometric structure results obtained for these types of compounds, the alternative combined o bond+ ionic configuration, S+-O-, is indicated as the more correct electronic structure description of this bond type in sulphoxides and sulphones [ 141. Together with a series of sulphenic acids (XSOH) and sulphide derivatives (XSY), over 70 neutral sulphoxide, sulphone and sulphide structures have been SCF/6-31G* gradient optimized [ 11,12,15]. This collection represents a substantial data base of simple sulphur-containing compounds that allows a comparison and understanding of many trends and effects in their geometric and electronic structure description; all at a given level of theory. These computational experiments have been extended to include radical species, anions

q(S) Fig. 1. Plot of orbital energy tzs(S ) vs. Mulliken charge q (S ) . 1, F,SO,; 2, FSO,OH; 3, Cl&SO,; 4, ClSO,OH; 5, HOSO,OH; 6, HSO,F; 7, HSSO,OH; 8, HSO,Cl; 9, H,NSO,OH; 10, CH,SO,OF; 11, HSO,OH, 12, CH,SO,OCI; 13, HSO,OCH,; 14, CH,SO,OH; 15, ClSO,F; 16, CsH,SO,OH; 17, HSO,SH; 18, HSONHOH; 19, HSO,NH,; 20, FSOOH; 21, HSO,H; 22, CH,SO,NH,; 23, CGHSSOZNH,;24, ClSOOH; 25, HSO,CH,; 26, CsH,SO,H; 27, CH,SO,CH,; 28, HOSOOH; 29, HSOF; 30, HOSOSH; 31, HSOC1; 32, NHsSOOH; 33, HSOOH, 34, F2SH2; 35, HSOOCH,; 36, C,H,SOOH; 37, CH,SOOH, 38, HSOSH; 39, CHsSOOCH,; 40, HSHNOH; 41, HSONH,; 42, CsH,SONH,; 43, H2S (OH),; 44, H,SO; 45, FSOH; 46, C,H,SHO; 47, HSOCH,; 48, ClSOH; 49, H,SNH; 50, CH,HSNH; 51, HOSOH; 52, HSF; 53, HOSOCH,; 54, HSSOH; 55, CH,OSOCH,; 56, CH,SF; 57, HSCI; 58, NH,SOH; 59, CH,SCI; 60, HSOH; 61, C,H,SOH; 62, HSOCH,; 63, CH,SOH, 64, HSSH, 65, HSSH; 66, CH,SSH; 67, NH,SH; 68, C$H,SNH,; 69, H,S; 70, CH,SNH,; 71, C,H,SH; 72, CH,SH; 73, CH3SCH3. The compounds are arranged in decreasing (absolute) value of ezs.

188

(using the 6-31+ G* basis which includes diffuse functions) and cations, allowing even wider comparisons, especially of the connection between electronic and geometric structural effects [ 11,12,15]. A relatively trivial example of the use of this data for the neutral molecules is shown in Fig. 1. Here, the Koopmans’ theorem [ 161 ionization energy of an atomic 2s electron in the sulphur atom, represented by the SCF orbital energy of the easily identified molecular orbital (MO) [ e2a(S ) 1, is plotted against the calculated Mulliken [ 171 gross atomic charge on that sulphur atom in that molecule, q (S ), for the whole series. A least squares fit of the data to a straight line equation

gives m = 4.17 eV per unit charge, b = 244.0 eV, an average absolute error of 0.76 eV and a linear correlation coefficient of 0.930. The approximately linear fit obtained is an expression of the environmental dependence of core electron binding energies [ 18,191. This particular correlation neglects the relaxation energy needed to reach the final cation state from the initial frozen MO Koopmans’s state, as well as assuming that the Mulliken atomic charge is a sufficiently good reflection of the chemical environment surrounding that atom. The linear correlation is seen to be reasonable. Deviations from linearity can be analyzed [ 151 in terms of the assumptions described above, as reviewed by Carlson [ 201. HYDROGEN BONDING

The hydrogen bond (H-bond) is of great interest and importance, both as a special type of chemical bond occurring in a wide variety of molecular complexes and because of its pervasive presence in biochemical systems. It is generally accepted that the mechanisms of enzyme reactions usually depend on H-bonding as the precursor to proton transfer (see, for example, ref. 21). Direct phosphate-amine and nucleotide carbonyl-amine hydrogen bonding also help stabilize the binding of cis-Pt (II) -diamines to DNA [ 221. Almost all known H-bonding situations involve oxygen or nitrogen atoms as the donor/acceptors. However, a recent ab initio study of the formic acid-formate anion system has shown the existence of a C-H. - -0 interaction which is estimated to contribute at least 2.4 kcal mol-l (SCF) to the biformate anion dimer binding energy [ 231. This additional H-bond, at least partially, explains the unusually high stability of the biformate anion measured experimentally in the gas phase w41. Actually, evidence of intramolecular C-H ***0 (=S ) hydrogen bonding has been noted in the ab initio study of a series of methyl-substituted sulphonic acids ( XS020H ) and sulphones (XSO,Y) referred to above [ 12,251. This interaction is detected by noting, for example, consistently larger methyl C-H

189

and S=O bond lengths for bonds involvingthose atoms that participatein the H-bond, compared with those not involved. The Mulliken gross atomic populations also show the involved hydrogen atom to be more ionic (positively charged) than the other methyl hydrogen atoms. The relevant bond angles (usually H-C-S and O=S-C) are also affected in the expected way. The optimal dihedral alignment of H-C-S=0 is found to be such as to give eclipsed C-H and S=O bonds with (C-)H* l O(=S)distances that are typically = 2.5 A. These somewhatlong H-bond distances are reminiscentof the intermolecularH-bond distancesfound recentlyfor water-sulphinicacid complexes [ 111. Experimental evidence for intramolecular (C-)H* m*O(=S) bonding from experimentalmoleculargeometricstructureshasbeen notedpreviously[ 26,271. Intermolecularassociation involvingthe methyl C-H bond in hydrogenbonding and its influenceon the chemicaland physicalpropertiesof sulphonylcompounds havebeen discussedby Robinson and Aroca [ 28,291.In orderto obtain a quantitativeestimateof the energy of this association, dimer structuresand energies were calculated for a number of simple sulphoxides and sulphones containing at least one methyl group. Optimum structures were also determined for the 1: 1 addition complexes of each monomer with a water molecule, and the correspondingdimer and adduct systemswith -H replacing-CH3 were also characterizedfor comparison purposes.The geometrieswere gradientoptimized in the 3-21G* basis set [ 13 1 and the final binding energies were corrected for basis set supe~osition error (BSSE) using the full ~mer/complex basis set for each monomer (counterpoise method) f 301. The results [ 251, which arepartiallysummarizedin Table 1, showthat there are two dimer structures (H,SO and H,SO,) that have only (S-)H***O(=S) andno (C-)H***O(=S) bonding,threedimerswithonly (C-)H*--O(=S) interactions [ ( CHB)ZSOZ,( CH3)FS02 and (CH,)HSO,-I] and three structures with both types of H-bonding simultaneously [ (CHB)HSO-I,11 and (CH~)HSO~-II]. Generally, from a comparison of these dimer binding energies, the H-bonding capability of the C-H bond with the S-O group is similar to that of the S-H bond in these hypervalentcompounds, and, as shown by the monomer-water complex binding energies, is in the same energy range as O-H. The complexity of the structurescomplicatesa more detailedresolution of the different type of H-bond energies.Encouragingly,the more accurate631G* optimized dimer binding energies,where they are listed in Table 1, are similarto the 3-21G* results. The calculated intermolecularH -0 (=S ) hydrogen bond distances, however, are generallyin the order, S-H > C-H > O-H, which can be taken as a measure of the inverse order of H-bond strength. The intermolecular (C-)H. *-0 (=S) distances in Table 1 are generally smaller than the correspondingmonomer intramoleculardistances (not listed here), presumablybecause of the greater conformational flexibility in the dimer/complex structures. The dimer/complex structures found here, which are all cyclic with l

l

l

190 TABLE 1 Binding energies and H-bond lengths for dimers and complexes* Monomer

(CH,),SO,

Binding energyb (kcal mol-’ )

H-bond lengths’ (A)

Dimer

(C-)H..

Water

6.5”

(S-)H...

2.09 2.24 2.46

2.32* 2.32

3.9 CH,HSO, I II

2.17 2.17 2.34 2.34

4.7d 6.5d 5.6

CH,FSO*

5.7d

CH,HSO I

4.6”

2.03k

2.22 2.25 2.21

4.8” 7.1

H,SO

4.5”

2.46 2.46

2.25 2.25

4.8

II

2.11h 2.44 2.45 2.47 1.76’ 2.41 2.43

6.0’ 5.8 6.6’ HzSOz

6.3”

CH,CHO

1.4 2.4’

1.80’ 2.32 2.46 2.48

6.7

Hz0

6.0 4.7’

(0-)H...

2.25’

5.0 4.2f 6.0 4.7f

“3-21G* basis set optimized. See ref. 25. bIncludes BSSE as described in text. “H-bonded to 0 (=S). dSymmetric structure. “Asymmetric structure. ‘6-3lG* basis set optimized. gBicyclic structure with (C-)H*..O(H,) bond of length 2.3zA. “Cyclic structure with (C-)H***O(H,) bondof length 2.12-A. ‘Cyclic structure with (S- )H * *-0 (H, ) bond of length 2.46 A._ ‘Bicyclic structure with (S-)H** *O(H,) bond of length 2.43 A._ kBicyclic structure with (S-)H.**O(H,) bond of length 2.55 A and (C-)H***O(H,) 2.27 A. ‘Cyclic structure with (C-)H* *-0(H,) bond of length 2.17 A.

of length

191

multiple H-bonds [ 11,311, may not be optimum in the neat liquid phase or aqueous solution where a given monomer interacts with many other molecules. However, the importance of methyl C-H hydrogen bonding in hypervalent sulphur compounds is established. The optimized monomer/dimer/complex structures and energies, and a detailed analysis of the results will be presented elsewhere [ 251. In general, the interaction of solvent molecules with substrates is of fundamental importance to understanding solvent effects on the thermodynamics and kinetics of chemical reactions. The spectroscopic study of these weakly bound complexes in the gas phase has been greatly facilitated by the use of supersonic expansions to obtain low-temperature molecular beams [ 32 1. Charged species, anions and cations, can also be studied by techniques that take advantage of the charge, such as ion cyclotron resonance and high-pressure mass spectrometry [ 331. Ab initio studies of the structure and binding energies of anion-water complexes [ 341 have accompanied these experimental advances. There is particular interest in the hydration energies of phosphate systems [35] due to their relevance to hydrolysis reactions, solvation and as reaction intermediates in biological systems. We have, therefore, carried out ab initio SCF and post-SCF (MP2 = MsllerPlesset perturbation theory to the second order) [ 361 calculations on a series of phosphates with the general formula H,PO;, and monochloro (H,PO,&l- ) - and dichloro ( H2P03 Cl, ) -substituted adducts or intermediates [ 371. The structures (including HzO, Cl- and OH- adducts of these general formulae) were SCF gradient optimized in a valence double-zeta basis set [ 38]+ diffuse p-type Gaussians on oxygen and chlorine + d-type functions on the P, 0 and Cl atoms. Compact effective potentials (CEP) [ 381 were used in place of the atomic core electrons. Table 2 presents the calculated water binding energies for both the linear (single H-bond to P=O ) and cyclic (double H-bond to two P=O groups) conTABLE 2 Binding energies for phosphate-water adducts” S&&rate

Binding energy (kcal mol- ’ ) Linear

PO, HzPOc HPO&lPOzClz

Cyclic

SCF

MP2

SCF

MP2

12.4 12.0 11.2

14.2 14.5 12.9

14.5 14.3 13.4 12.0

15.9 16.2 15.2 13.9

BEEP-31( + )G* basis set as described in text. See ref. 37. Structures optimized at the SCF level.

192

formations. The former is probably more appropriate to solution while the cyclic structure, more stable by l-2 kcal mol-‘, is probably the preferred gasphase structure under experimental conditions that allow only 1:1 complex formation. BSSE corrections and energy terms necessary to convert the binding energies in Table 2 to enthalpy changes have not been included. BSSE is expected to be small due to the use of the CEP. The major thermodynamic correction is the zero-point energy which is not expected to differ much between the weakly bound adduct and the component species. Thus, the enthalpy of hydration to form the PO; -water complex is reported experimentally at 12.9 kcal mol-’ [35], which is close to the calculated energies of hydration shown in Table 2. A detailed analysis of these and other adducts is given elsewhere [ 371. DIATOMIC DICATIONS, MAIN GROUP ELEMENTS

A major defect of the single electronic configuration description of closedshell molecules was realized at a very early stage of quantum mechanics because of the incorrect dissociation of the hydrogen molecule to a mixture of covalent (homolytic dissociation) and ionic (heterolytic dissociation) atom states [ 391. The hydrogen molecule problem also pointed the way to the general solution of bond dissociation to the wrong asymptotic state limits in the SEC approximation; the need to include additional electronic configurations in the wave function expansion which occupies valence antibonding molecular orbitals. This multi-configuration (MC) formulation was generalized by Wahl and Das [40] for diatomic molecules to construct a configuration selection procedure which was intended to give only the (geometric) structure-sensitive part of the electron correlation energy. Difficulties in its implementation for diatomic molecules and in its extension to polyatomic molecules [ 411 led to the complete active space (CAS) MCSCF method with its automatic configuration selection procedure [42] once the active orbital set is chosen. When the active MO set is chosen as the complete set of valence atomic orbitals (AO), the full optimized reaction space (FORS) version of the MCSCF method is obtained [ 431. The CAS-MCSCF method in the valence atomic orbital space is a well-defined model which gives a good account of the molecular correlation energy and always dissociates correctly unless correlation energy errors cause gross errors in, or even an incorrect ordering of, the asymptotic fragment or atom electronic states. This latter possibility does not seem to be a serious threat to accuracy in molecules made up of main group elements. Thus, the electronic ground states of Al, [ 441 and Ala [ 45 1, for example, are both correctly predicted by a FORS-MCSCF calculation in a large basis set, even though there are other electronic states that are calculated to lie very close in energy (within several hundred cm- ’ ) to the respective ground states near equilibrium.

193

The abilities of‘the FORS form of the CAS-MCSCF method can be demonstrated by calculations on the triple-bonded isoelectronic series, Na, NO+ andO;+, shown in Table 3 [46,47]. Here a CEP-211G (2d) basis set (valence triple-zeta sp [ 38]+ double-zeta d) was used, and the full energy interaction curves for the ground ‘C state and the excited 3(x,n*), 3(c7,n*) and ’ (c,,n*) electronic states were calculated using the GAMESS [ 48 ] set of computer programs. A core effective potential (CEP) replaced the chemically inert K shell electrons on the nitrogen and oxygen atoms. The number of confi~rations (defined by the GUGA method [49] is, for example, 176 (D& or 328 (Cz,) for the ‘C,+ ( NP, Oi+ ) or ‘C + (NO+ ) ground states, respectively. The comparison with experimental results [ 501 for Nz and NO+ in Table 3 is for properties very near the equilibrium bond distance (R,). Thus, R, itself TABLE 3 FORS-MCSCF results for Nx, NO+ and O$+ e Configuration state

Ground

Y%, x:1

%rx,

1-b 2,

3

-Exptl. E, (eWd Exptl. w, (cm-‘)’ Exptl.

1.112 1.098 0. 0. 2309 2359

1.312 1.287 6.34 6.22 1407 1460

7.95 7.41 1451 1501

NO+ R, (A;,” Exptl. F, (eWd Exptl. 0. (cm-‘)e Exptl.

1.075 1.063 0. 0.0 2334 2376

1.310 1.264 6.64 6.47 1252 1293

1.307 1.280 8.18 7.67 1294 1313

1.060 0 2146

g

1.419 6.87 575

N3 R

&lb

Of” R, (8,” E, (eWd w, (cm-‘)e

x:1

St&k? + Ll

3C;f

342

1.303

1.304 1.276 8.62 8.22 1517 1.314 1.290 8.75 8.40 1284 1.387 7.82

34

'4

1.235 1.213 7.92 7.39 1667 1733

1.242 1.220 9.12 8.59 1649 1694

1.185 1.175 7.65 7.43 1665 1710

1.215 1.193 9.54 9.11 1522 1602

1.227 7.89 1205

1.227 9.45 1297

‘~EP-211~(2d) basis set as described in text (see ref. 47). The g and u symbols refer to the homkrclear diatomics. bEquilibrium bond distance. “Experimental results from ref. 50. dAdiabatic excitation energy from the ground state. ‘Harmonic stretch frequency. ‘Configuration interaction based on CAS “A,, MOs. PDissociative.

194

is calculated to be within 0.010-0.025 A of experiment and consistently on the high side. This is the usual result for this type of CAS-MCSCF. The basis set would also be improved by the addition of f-type basis functions which have been shown to be of particular importance in such multiple bonding situations [51]. Analogously, the calculated harmonic stretch frequencies (me) are uniformly lower than experiment and the adiabatic excitation energy (E,) from the ground to excited electronic states is generally overestimated by 0.2-0.5 eV. All in all, the comparison results for a wide range of electronic states give a uniform and encouraging picture of equilibrium geometry properties as calculated by the FORS model. The FORS-MCSCF model also does reasonably well for non-equilibrium geometry properties. Thus the ground (‘1: ) state dissociation energy (Do) of Nz from the zero point vibrational level is calculated to be 8.94 eV compared with Q, (experimental) = 9.76 eV [ 501. For NO+, the corresponding numbers are 9.97 and 10.85 eV [50], respectively. Thus binding energies are consistently underestimated by this method. The actual interest in these studies (see also ref. 47) involves the 0;’ system as a prototypical molecular dication with a high exothermic dissociation energy (D,) from R,. Because of simple electrostatic repulsion, gas-phase dications would be expected to dissociate spontaneously to pairs of monocations. In fact, many dications, such as O$+,are observed experimentally [ 52-541. Already, in 1933, Pauling [ 551 predicted the kinetic stability of Hei+ and identified the major factors that seem to determine the energy interaction curve in this type of system. Thus, an avoided crossing between a rising coulomb repulsion curve (0+-O+) and a falling ion-induced dipole interaction curve ( 02’-0) with decreasing internuclear distance (R) produces a trapped dication with a typically short R,, a barrier to dissociation and an exothermic bond dissociation energy [ 561. These thermodynamically unstable systems could be interesting for energy-storage purposes. Computational chemistry can be used to characterize their energy interaction curves and, by indicating the proper choice of systems and conditions, allows optimization of the desirable properties and processes. The calculated FORS-MCSCF energy interaction curve for the ground ‘I,+ state of O$+ is shown in Fig. 2. Tht barrier which determines the lifetime for dissociation is located at Rt= 1.605 A at a height (E,) of 3.49 eV relative to the minimum at R,. D, is calculated at - 4.51 eV (exothermic ) from R, relative to the asymptotic monocations. This latter value is expected to be an overestimation (in absolute value) for the same reasons that the values of D, for N2 and NO+ are calculated too small by FORS-MCSCF; i.e. incomplete basis set and electron correlation at R, relative to the dissociation limits. However, the qualitative shape of the curve, including the barrier, is correct. The FORS-MCSCF model, being conceptually simple and qualitatively correct, can be used to compare trends in similar dication systems. The valence isoelectronic XY2 + series, with X,Y = oxygen, sulphur, selenium and tellur-

195

-30.3 -

-30.4 0.05

1 1.85

2.85

3.85

o+Ps)+o+Ps) I

4.85

5.85

Bond Distance (A) Fig. 2. Energy interaction curve of the ‘1:

of OS+.

ium, comprises ten different diatomic &cations with a wide range of constituent atomic properties, such as ionization/excitation energies and polarizabilities. These properties are important determinants for the overall energy interactioncurves and the molecularelectronic structuredescription [ 47,561. Calculationson these systems are made simpler by the use of accurate CEPs [ 381, and in the case of Se and Te relativisticCEPs (RCEP) [ 571 alreadyused in other contexts [58,59] . A more detailed analysis of these ten systems will be presentedelsewhere 1471. DIATOMIC DICATIONS-THE

TRANSITION

METALS

The CEPs generatedfor the first two rows of the Periodic Table from Li to Ar and their basis sets [ 381 have been incorporatedinto the latest versions of the standard ab initio electronic structure packages [13,48]. Analogously, E-dependentrelativisticCEPs and basis sets have been generatedfor K to Rn [ 571 by a similar method based on relativisticatomic orbitals [60]. Some applications involvingthe transitionmetal atoms havebeen reported [ 22,61-631. Besides reducingthe number of expansion basis functions needed in the electronic structurecalculation, replacing the chemically inactive core electrons by an RECP (see also ref. 64) eliminatesthat part of the BSSE that is due to the high-energycore electrons j65 ] . However, the correlation energy problem for transition metal atoms/ions can be seriousfor severalreasons.All experienceindicatesthat a qualitatively correct electronic structure description of a transition metal-ligand system can be stronglydependenton an accuratereproductionof the asymptoticmetal atomic state splittings (between and among d”, dn--lsl and dnm2s2 state configurations) because of their high density at low energy.This objective is usually beyond the capabilitiesof the SEC SCF method, even with very largebasis sets

196

[661. Accuracy is needed in the asymptotic energies because different types of bonding situations (covalent-homolytic vs. charge transfer-heterolytic, for example), derived from different asymptotic state configurations, can have very different-looking corresponding molecular orbitals, especially with regard to relative valence d- and s-type composition and metal-ligand mixing. These circumstances make it difficult to describe different electronic states with the same set of MOs. Avoided crossings between two diabatic energy interaction curves, arising from different state-configuration asymptotes, can then be particularly difficult to describe accurately because of initial errors in the asymptotic energies and because the optimal molecular orbitals can be very different in the intersecting states (see, for example ref. 67). The degree of correlation of the metal d electrons can also affect the degree of covalent-type bonding and be (geometry) structure dependent [68,691. Thus, it is necessary to use at least a CAS-MCSCF level theory in describing low-formal valent, low-coordination number transition metal compounds, although defining the valence orbital set to be used in an FORS treatment is not completely unambiguous [ 701. As is implied by the previous discussion, transition metal dimers are expected to be particularly complicated [ 711 (see also survey in ref. 72). However, highly charged species, where coulomb effects could be dominant and the spacing of atomic or ion states with different combinations of d and s orbital occupancies is expected to be larger, may be more amenable to computational treatment without the need for exhaustive electron correlation treatment. Therefore, the diatomic dications of certain transition metals, which could have interesting energy storage properties as described previously, have been studied [ 731. It should be noted, however, that the characteristic avoided curve crossing in these type systems (Fig. 2) involves the neutral atom in the (charge transfer) configuration, which is presumably important at R,. Besides the MC treatment, the additional necessity of using a relativistic CEP in these systems has been clearly shown [ 741. Ab initio RCEP [ 571 calculations have, therefore, been carried out on Ptz+, Au:+ and H&+, where the semi-core 5s and 5p electrons are explicitly considered in the valence (and not in the RCEP) space. The Gaussian function basis set on each metal atom is 7s%5d(the sp set are shared-exponent) contracted to 4”p3dto describe the metal 59, 5p, 5d, 6s and 6p atomic orbitals [ 571. The CAS-MCSCF method was used to generate the complete potential interaction curves for the lowest energy ‘C,+ states, where the occupancies of the eight atomic 5s and 5p-character molecular orbitals were kept fixed at their atomic values but variationally determined. The variably occupied MO space was defined as 18electrons distributed among 12MOs for Ptz’ + , 20 electrons among 13 MOs for Au;+ and 22 electrons distributed among 14MOs for H&+ . The maximum excitation level was then six in all cases. The calculated properties are shown in Table 4. Pti’ is calculated to have a

197 TABLE 4 FORS-MCSCF

Confjgurationsb R, (4)’ R, (A)d Et (kcal mol-‘)” D, (kcal mol-‘)’

results for P%’ , A@

and H&+ a

PG’

Au;+

H$+

2078 2.84 2.92 -0 -96.6

3419 8

5416 2.85 (2.70) 3.60 5.3 (10.4) -71.0 (-68.3)

‘Lowest energy ‘X: state. For H&+ the numbers in parentheses are from ref. 75. See also ref. 76. bNumber of GUGA [ 491 configurations. “Equilibrium bond length. dBarrier height internuclear distance. “Barrier height from the energy minimum (R,) . %ssociation energy (from R. to asymptotes). Wssociative.

very shallow well and barrier, constituting almost an inflection point. Configuration mixing is strong and the natural orbital occupancies [ 481 at the energy minimum are [ d~gg Skw a;” x:87 r~i.~Oat521 oy crto7. The bracketed molecular orbitals are 5d orbital based and those outside the brackets have mainly 6s character. The Hartree-Fock configuration [s~8qlr~n”,r$] has a coefficient of only 0.80. The calculated exothermicity is high but will probably be substantially reduced by a bigger basis set and more correlation, as the binding and asymptote regions are better described. From Table 4 we see that the lowest energy ‘1: state of Au:+ is calculated to be dissociative, as might be expected from the closed-shell-closed-shell, d”-d” configurations, and in spite of favourable o,, ( 5d)2+o, (6~)~ mixing. However, triplet excited states are calculated to be bound [ 731. H&+ has also been studied by Durand et al. [ 751 using a multi-reference perturbation theory treatment. Their calculated equilibrium bond length, barrier distance and height, and bond dissociation energy agree qualitatively with the CAS-MCSCF results in Table 4. Ignoring the asymptotic energy problem, a single reference configuration approach would also be valid here at R, since the Hartree-Fock configuration at equilibrium has a coefficient of 0.977. It is interesting to note that the calculated equilibrium bond distances in Pt?j’ and H&+ are essentially the same even though the primary bonding molecular orbitals [ ap(5d) and op(6s)) respectively] are very different for the two cases. More extensive calculations and analysis, including excited states and the corresponding diatomic dication electronic states of the corresponding first row transition metals (Ni, Cu and Zn) are given elsewhere [ 731.

198 ACKNOWLEDGEMENT

The contribution of Dr. Tova Hoz to the preparation of this paper is gratefully acknowledged.

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