CEPA calculations on open-shell molecules. V. The vibration frequencies of SF and SCl

Ab initio calculations for the ² ground states of SF and SCl have been performed on Hartree-Fock level and with inclusion of valence shell correlation effects by means of the CI and CEPA approaches. The calculated properties are: Equilibrium distances, vibration frequencies, and dipole moment curves in the vicinity of the respective equilibrium geometries. Our best estimates for the 0 1 infrared absorption frequencies _o for SF and SCl are 786 cm^–1 and 520 cm^–1, respectively, both with an uncertainty of about 10 cm^–1. This confirms a recent experimental value obtained by Willner for SF (791 cm^–1), but indicates that for SCl both experimental values reported previously in the literature (617 cm^–1 and 574 cm^–1) are wrong. The S—F and S—Cl bonds in SF and SCl are very similar to the ones in SF₂ and SCl₂, being essentially single p-bonds in either case. In the analogous oxygen-halogen molecules the situation is different, the O—F and O—Cl bonds in the diatomic radicals OF and OCl have partial double bond character and are much stronger than those in OF₂ and OCl₂ or in HOF and HOCl.     

Conjugated-molecule dipole polarizability in the spin-Hamiltonian method

A simple technique is proposed for calculating the dipole polarizabilities of -electron shells in covalent molecules within the framework of the spin-Hamiltonian method. This gives results for polyenes more accurate than those from the restricted and unrestricted Hartree-Fock methods. A major advantage of the technique is that, in some cases, it is possible to perform an analytical treatment.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 4, pp. 469–472, July–August, 1986.     

Effect of configurational composition of the wave function on calculated dipole polarizability of molecules

On the basis of the -electron approximation we have investigated the dependence of the calculated dipole polarizability of molecules on the configurational composition of the variational wave function. The values which were closest to the results of complex configurational interaction were obtained for sets including the single-determinant Hartree-Fock function and all the bonding doubly excited configurations constructed from the localized MO, and also from the complete set of singly and doubly excited configurations.Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 26, No. 1, pp. 70–73, January–February, 1990.     

On the asymptotic behavior of Hartree-Fock orbitals

Summary Handy et al. have shown that the asymptotic behavior of Hartree-Fock orbitals is controlled by the energy of highest occupied molecular orbital, except for the atomic case in which onlys-orbitals are occupied. However, their proof is not complete at one point. This point is clarified, and a more unified derivation is given. Further, we discuss the preexponential factorr of the leading asymptotic termr exp[–r], where =(–2_HOMO)^1/2 and _HOMO is the orbital energy of HOMO. New results are obtained for linear molecules, and the results of several authors for atoms and non-linear molecules are reproduced.     

Ab initio calculations ofp-Cl2C6H4 molecule and its35Cl NQR parameters

Ab initio calculations ofp-dichlorobenzene molecule were carried out using the Hartree-Fock method in the 6–31 G* valence-split basis set. The molecule was also calculated by the MNDO method in the valence sp-basis set for comparison. The populations of the valent p-orbitals of the C and CI atoms were analyzed. The optimized geometry of the molecule as well as its³⁵Cl NQR frequency and the asymmetry parameter of the electric field gradient at the³⁵CI nuclei calculated using the populations of the less diffuse components of the valent p-orbitals of the Cl atoms are in agreement with the corresponding experimental values for the -modification of 1,4-Cl₂C₆H₄.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 2177–2179, September, 1996.     

Toward the Experimental Structure Determination of Larger Molecular Clusters: Application and Limitations of the Weak Interaction Model to the (C6H6)13B2u ← A1g00 0 Spectrum

The experimental B_2u A_1g0⁰ ₀ spectrum of (C₆H₆)₁₃ was analyzed within the weak-interaction model using minimum energy structures calculated from six different potential energy surfaces. The coexistence of two isomers—both of C₃ symmetry and with nearly equal populations—is supported. Structures predicted by two of the six potential energy surfaces are strongly favored. The transition dipole of benzene moieties within the cluster has a magnitude of 0.23 Debye. Weak transition dipole–dipole interactions fall between –1.95 and +2.24cm^–1 and site shifts of ligand molecules range from –160.3 to –153.8cm^–1. Although the weak-interaction transition dipole–dipole model falls short of unambiguously determining isomeric structures of benzene-13, it establishes a solid foundation on which modeling can be based for determining structures of larger, high-symmetry, molecular clusters.     

Stark mixing by ion-Rydberg atom (molecule) collisions

Classical molecular dynamics simulations are performed to cover Stark mixing transitions (nℓ→nℓ^′) in Rydberg atoms by collision with slow ions. Accuracy is tested by comparison with the exact analytical classical probabilities previously obtained when the ion–atom potential is taken as the long-range ion–dipole interaction. The results are provided not only for the ion–dipole interaction but also for the full electrostatic interaction. It is shown, by comparison, that the ion–dipole potential alone provides reliable probabilities. The method is highly accurate and is very amenable to ready inclusion of other processes competing with Stark mixing.     

Roothaan–Hartree–Fock wave functions for cations and anions in Slater-type basis sets with doubly even tempered exponents

Summary Roothaan-Hartree-Fock wave functions in Slater-type basis sets are reported for the cations Li⁺-Cs⁺ and anions H^–-I^– using the double even tempering (DET) method of selecting orbital exponents. The DET total energies do not differ from the corresponding numerical Hartree-Fock values by more than 0.2 millihartrees for the cations and anions. The present results together with the previous ones for neutral atoms [Theor Chim Acta 88:273 (1994)] provide a compilation of DET wave functions of near Hartree-Fock quality for all the neutral and singly-charged atoms with the number of electronsN54.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The first-order polarized basis sets for the use in high-level-correlated investigations of molecular electric properties have been generated for Pb, Bi, Po, and At. The performance of the standard [10.17.14.5/13.11.8.2] and extended [20.17.14.9/13.11.8.4] basis sets has been examined in nonrelativistic and quasirelativistic calculations for atoms and simple closed-shell hydrides. The relativistic contributions to electric dipole properties of those systems have been evaluated by using the recently developed quasirelativistic scheme. The predicted dipole polarizability of At is in good agreement with the results of other relativistic calculations. The calculated quasirelativistic dipole moments of BiH₃ (–0.499 a.u.), PoH₂ (–0.207 a.u.), and AtH (+0.036 a.u.) involve a significant relativistic contribution which amounts to —0.230 a.u., –0.177 a.u., and –0.097 a.u., respectively. The basis set details append this paper. They are also available as a part of the basis set library of the MOLCAS system.     

Comparative studies of static dipole polarizabilities of ionic crystals on the basis of different self-consistent potentials

The static dipole polarizabilities, ^D , have been studied for the ions O^2–, F^–, Na⁺, Mg²⁺, Cl^–, K⁺ and Ca²⁺ in the crystals NaF, KF, NaCl, KC1, MgO and CaO. The starting zero-order wave functions have been generated using various exchange- and exchange-correlation potentials in order to study the effect of these potentials on ^D . The direct contribution to the dipole polarizability, _o ^D , has been determined by the uncoupled Hartree-Fock method. Self-consistency effects have been included by the geometric approximation. The crystal potential is incorporated using the Watson sphere model. Good agreement between theoretical and experimental results are found for those self-consistent potentials which exclude self-interaction.     

Calculation of molar Kerr and Cotton-Mouton constants of azines as aza-substituted benzenoid hydrocarbons

For the case of aza substitution within coupled Hartree-Fock -electron perturbation theory, we consider the effect of substituents on double refraction of alternant hydrocarbons in transverse electric and magnetic fields. The calculated values of the Kerr and Cotton-Mouton constants in the azine series agree well with experimental data.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 2, pp. 124–130, March–April, 1992.     

Influence of electron correlation on the character of the splitting of degenerate states in metalloporphyrin dianions

The lowest singlet and triplet energy levels of metalloporphyrin dianions have been calculated according to the extended Hartree-Fock method in the -electronic approximation with consideration of electron correlation. The calculations confirm the deviation from Hund's rule observed for these compounds. The possibility of the application of the method indicated to the construction of many-electron functions with the correct symmetry in the case of orbital degeneracy has been discussed.Translated from Teoreticheskava i Éksperimental'naya Khimiya, Vol. 24, No. 2, pp. 208–211, March–April, 1988.     

Collective electron excitations in long molecules with conjugated bonds (cyclic and linear polyenes)

Conclusions The technique used above for calculating electronic excitations is equivalent to the random phase approximation, but permits a clearer understanding of the approximations made. The linearization with respect to Ø in the derivation of the equations for the excited states means that the approximation made is valid only for small changes in the spin (or electron) density in the atoms in the excited states from that in the ground state. This is always the case for fairly small excitation energies. The proposed calculation technique may be used to calculate excitations both in long conjugated molecules and in ordinary molecules just as well as the Pariser-Parr-Pople and random phase approximations [14, 17, 18].We note that another approach was used in [6] to find the energy of the first triplet level in polyenes. In that paper the wave function of the generalized Hartree-Fock approximation was projected onto a singlet (ground) and a triplet state. The latter was treated as a very low triplet excited state. However, as shown in [1, 2], the energies of these (the singlet and triplet) states differ by a quantity that decreases like N^–2 or even faster as N. On the other hand, as shown in [7], the energy of the first triplet excitation should decrease like ₁ 1/N as N. This implies that the interaction between electrons above the generalized Hartree-Fock approximation must be taken into account in order to obtain the first triplet state.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 10, No. 6, pp. 723–731, November–December, 1974.     

Nitrogen-containing bisheterocyclic systems

A method has been developed for the synthesis of the previously undescribed hydroxy- and amino-1-benzazolyl-2-pyrazoles. Examination of the IR spectra and determination of the dipole moments has shown that these derivatives exist in the crystalline form and in solution as the hydroxy and amino forms, which are stabilized by intramolecular hydrogen bonding.For part III, see [12]Translated from Khimiya Geterotsiklicheskikh Soedinenii, Vol. 6, No. 5, pp. 660–663, May, 1970.     

Theoretical study of PO and PO−

The diatomic systems, PO and PO^– are studied, using numerical Hartree-Fock (NHF) and coupled-cluster calculations. The latter employs a hybrid NHF and Slater orbital basis set. Highly accurate CCSD methods predict bond lengths accurate to <0.004 Å and frequencies to 60 cm^–1. In addition the electron affinity of PO is computed to be 0.89 eV compared to an experimental value of 1.09±0.01. Comparisons are made with SCF and MBPT(2) results for PO⁺ using conventional basis sets.Dedicated to Professor J. Koutecký on the occasion of his 65th birthdayGuggenheim Fellow     

Hamiltonian and overlap matrix elements between half-projected Slater determinants

We obtain expressions for the Hamiltonian and overlap matrix elements between half-projected Slater determinants of the type different orbitals for different spins and differing by one or two orbitals. We consider the use of these expressions in the construction of direct orbital optimization schemes in the half-projected Hartree-Fock method (HPHF), in the study of the instability of the Hartree-Fock solution, in the study of the singly-excited configuration interaction and random phase methods and in the interpretation of the static response function in the HPHF method.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 5, pp. 525–536, September–October, 1990.     

Low-spin excitations of quasi-one-dimensional polyacetylene chains in Hartree-Fock models

In the -electron approximation taking into account Coulomb repulsion and electron correlation, we have calculated the excitation energy _s of the state with spin s=1, 2, 3 in long polyacetylene chains. From numerical calculations, we have established the dependence _s=(2s–1)₁, which is satisfactorily satisfied for the different wave functions used (from the unrestricted and two variants of the extended Hartree-Fock method). For some of the solutions, localization of the excitation in 2s–1 fragments of the chain is characteristic, which indicates the possibility of interpreting it in terms of a soliton.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 6, pp. 716–719, November–December, 1990.     

Electronic–Rotational Coupling and c 1 Σ – u –b 1 Σ + g Transition Probability in the Oxygen Molecule

A theory was proposed for the formation of intensity of the forbidden singlet–singlet c ¹ _u ^– b ¹ _g ⁺ transition in the oxygen molecule. The dipole moments of transitions that contribute to the formation of the intensity of the c–b transition in the range of internuclear distances of 1.2–2.0 Å were calculated using the configuration interaction method with a valence triple-zeta basis set. Based on these results, the electric dipole moment for the c ¹ _u ^– b ¹ _g ⁺ transition was calculated.     

An ab initio study of the structures and enthalpies of the hydrogen-bonded complexes of the acids H2O,H2S,HCN, and HCl with the anions OH−, SH−, CN−, and Cl−

Ab initio calculations at second-order Møller-Plesset perturbation theory with the 6-31 + G(d,p) basis set have been performed to determine the equilibrium structures and energies of a series of negative-ion hydrogen-bonded complexes with H₂O, H₂S, HCN, and HCl as proton donors and OH^–, SH^–, CN^–, and Cl^– as proton acceptors. The computed stabilization enthalpies of these complexes are in agreement to within the experimental error of 1 kcal mol^–1 with the gas-phase hydrogen bond enthalpies, except for HOHOH^–, in which case the difference is 1.8 kcal mol^–1. The structures of these complexes exhibit linear hydrogen bonds and directed lone pairs of electrons except for complexes with H₂O as the proton donor, in which cases the hydrogen bonds deviate slightly from linearity. All of the complexes have equilibrium structures in which the hydrogen-bonded proton is nonsymmetrically bound, although the symmetric structures of HOHOH^– and ClHCl^– are only slightly less bound than the equilibrium structures. MP2/6-31 + G(d,p) hydrogen bond energies calculated at optimized MP2/B-31 + G(d,p) and at optimized HF/6-31G(d) geometries are similar. Using HF/6-31G(d) frequencies to evaluate zero-point and thermal vibrational energies does not introduce significant error into the computed hydrogen bond enthalpies of these complexes provided that the hydrogen-bonded proton is definitely nonsymmetrically bound at both Hartree-Fock and MP2.