Symmetry of localized orbitals in molecules with spin-orbit interaction

We construct representations of crystallographic point groups induced by double-valued irreducible representations of their local subgroups. Using the tetrahedral molecule Bi₄ as an example, we illustrate application of the results obtained to the symmetry analysis of localized molecular orbitals obtained from relativistic calculations.Translated from Teoreticheskaya i éksperimental'naya Khimiya, Vol. 24, No. 1, pp. 91–95, January–February, 1988.     

Pseudosymmetry analysis of molecular orbitals

We introduce a pseudosymmetry analysis of molecular orbitals by means of the newly proposed irreducible representation measures. To do that we define first what we consider as molecular pseudosymmetry and the relationships of this concept with those of approximate symmetry and quasisymmetry. We develop a general algorithm to quantify the pseudosymmetry content of a given object within the framework of the finite group algebra. The obtained mathematical expressions are able to decompose molecular orbitals by means of the irreducible representations of any reference symmetry point group. The implementation and usefulness of the pseudosymmetry analysis of molecular orbitals is demonstrated in the study of σ and π orbitals in planar and nonplanar polycyclic aromatic hydrocarbons and the t_2g and e_g character of the d‐orbitals in the [FeH₆]^3? anion in its high spin state along the Bailar twist pathway. © 2013 Wiley Periodicals, Inc.     

Molecular and electron structure of heteropoly complexes. 4. Reduced forms of heteropolyanions

Conclusions There is a linear correlation between the band energies of the first intervalence transition and the half-wave potentials for reduction in the isostructural heteropolyanions with equal charge, XM₁₁ZO₄₀ ^n–. The intervalence transition is due to excitation of an electron from the orbital localized on the reduced atom to orbitals localized on atoms in the coordination sphere. The authors suggest that the less the delocalization of the electrons over the whole structure, the greater will be the intensity of the intervalence transition.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 2, pp. 274–278, February, 1978.     

Configuration-interaction calculations for the ground state of OF2, NO 2 − , CN−: Canonical orbitals and exclusive orbitals

The C.I. method is applied to already published double- SCF wave functions for OF₂, NO ₂ ^– and CN^–. All doubly excited configurations are considered. The second order approximation values presented for those cases are compared with the exact energy values in some minor cases. An attempt has been made to improve the rate of convergency of the process by transforming the canonical SCF occupied orbitals into localized ones and the virtual canonical orbitals into a particular type of localized orbitals. These latter show also an intuitively acceptable spatial conformation.

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Zusammenfassung Die CI Methode wird auf bereits bekannte Doppel-Zeta-SCF-Wellenfuntionen für die Systeme OF₂, NO ₂ ^– und CN^– angewandt. Dabei werden alle doppelt angeregten Konfigurationen berücksichtigt. Um die Konvergenz zu verbessern, werden versuchsweise die kanonischen und besetzten SCF-Orbitale in lokalisierte Orbitale und die virtuellen kanonischen Orbitale in einen besonderen Typ von lokalisierten Orbitalen transformiert. Die letzteren zeigen eine besonders geeignete räumliche Anpassung.

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Résumé Pour un calcul de intéraction de configurations, comprenant toutes le configurations à double excitation, on a employé des fonctions d'onde SCF sur une base doublée. Pour le calcul complet on a essayé des formules d'approximation, qu'on a pu vérifier avec le calcul exact sur des cas réduits.Pour améliorer la vélocité de convergence du procés on a transformé les orbitales canoniques SCF en orbitales localisées et aprés on a construit, selon un procedé particulier, des orbitales virtuelles localisées qui montrent une conformation dans l'espace qui est intuitivement satisfaisante.

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Work supported by the Consiglio Nazionale delie Ricerche.     

Calculation of the electronic structure of metalloporphyrin dianions by the restricted Hartree-Fock method

The metalloporphine dianions (Me-P)^2– with D_4h symmetry for the nuclear skeleton have an e_g ² electronic configuration, which generates the triplet state ³A_2g and the three single states ¹B_1g, ¹B_2g, and ¹A_1g. With the aid of projection operators of the symmetry group, SCF equations have been formulated for such systems with open shells of degenerate orbitals, where the Roothaan method is not directly applicable. Calculations of the individual states of (Me-P)^2– and its analogs have been performed by the proposed method in the -electronic approximation. In accordance with Hund's rule, it has been found that the lowest level in the multiplet is the triplet level and that the subsequent singlet levels of (Me-P)^2– are 340 (¹B_1g), 2560 (¹B_2g), and 3010 (¹A_1g cm^–1 above it. A comparison of the -electron densities of (Me-P)^2– and Me-P has revealed, first, that the additional charge is distributed along the periphery of the macrocycle (the maximum increase takes place at the bridging atoms) and, second, that a number of bonds are strengthened, rather than weakened. The results obtained correlate well with the data on the reactivity and vibrational spectra of the dianions of porphyrins.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 2, pp. 153–160, March–April, 1986.     

Completeness criteria for explicitly correlated Gaussian geminal bases of axial symmetry

The completeness criteria for the basis set of explicitly correlated Gaussian-type geminals adapted to C_∞v symmetry are given. Specifically, we show that any pair function of Σ⁺ symmetry can be expanded in terms of products involving two spherical Gaussian orbitals located on the internuclear axis and a Gaussian correlating factor with a positive exponent. Pair functions corresponding to other irreducible representations of C_∞v can be expressed as linear combinations of products of a σ⁺ function and an angular factor depending on the azimuthal angles. The minimal set of the angular factors needed for completeness is given. These factors are relevant also for other explicitly correlated bases. © 1997 John Wiley & Sons, Inc.     

Many body perturbation methods in a discrete orbital basis: Application to CH4 and Ne

Discrete basis many body perturbation calculations have been performed on Ne and CH₄ in a basis which mimics Boys' oscillator orbitals. The L-shell correlation energy obtained for Ne was –0.347 which is to be compared with the best numerical basis many body perturbation result of –0.336 ± 0.01 obtained by Lee, Dutta and Das and the best variational result of –0.322 obtained by Sasaki and Yoshimine. An analysis of 3- and 4-body corrections (pair-pair repulsions) and the effects of many body EPV renormalization for both localized and canonical SCF orbitals is presented.     

Reactions of chromium(III) complexes with ferricyanide. Magnetism of K2[Cr(salen)(H2O)][Fe(CN)6]·H2O and the crystal structure of [trans-Cr(tn)2Cl2]3[Fe(CN)6]·6H2O [salen2− = N,N′-ethylenebis(salicylideneaminato) dianion,tn = 1,3-diaminopropane]

Two Cr^III–Fe^III complexes, K₂[Cr(salen)(H₂O)][Fe(CN)₆]·H₂O (1) and [trans-Cr(tn)₂Cl₂]₃[Fe(CN)₆]·6H₂O (2), have been prepared. Crystal structure determination shows that complex (2) possesses an ionic salt structure. General physical measurements and magnetic studies indicate that (1) assumes a cyanide-bridged dinuclear structure, and that the Cr^III–Fe^III magnetic coupling through the cyanide bridge is antiferromagnetic, which can be rationalized by the overlap of magnetic orbitals of the same symmetry.     

Second-order magnetic parameters of PH3 and P(CH3)3 and the magnetic isoscreening lines for P-H and P-C bonds

A variational method has been used with Gaussian orbitals to calculate the susceptibilities of localized P-H and P-C bonds in PH₃ and P(CH₃)₃. An additive scheme has been used with localized molecular fragments to determine the susceptibility and proton screening, where the values agree well with experiment. Diagrams for nuclear magnetic isoscreening lines for the P-H and P-C bonds have been calculated.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 4, pp. 487–491, July–August, 1986.     

Theoretical study on the electronic spectrum of TcO 4 −

Summary The theoretical electronic spectrum of TcO ₄ ^– calculated by the SAC(symmetry adapted cluster)/SAC-CI method is presented. The spectrum is in good agreement with the experimental one. The observed peaks are assigned and the existence of several absorptions in the energy region higher than that observed is predicted. The difference and the similarity between the electronic spectra of TcO ₄ ^– and MnO ₄ ^– are clarified. The spectral difference between TcO ₄ ^– and MnO ₄ ^– is due to a remarkably high energy shift of the 3¹T₂ state of TcO ₄ ^– .     

Characteristic features of excess charge localization in stepwise three-electron reduction of Ni-octaethylporphin

We have investigated the electronic structure of Ni-octaethylporphin anions (NiOEP) by¹H NMR. We have established that in (NiOEP)–, the excess electron is localized in the orbital of the nickel, while the second and third extra electrons in (NiOEP)^2- and (NiOEP)^3- are localized in the orbitals of the ligand. We conclude that spin density is transferred between the d orbitals of the Ni and the orbitals of the porphyrin ligand.Institute of Molecular and Atomic Physics, Academy of Sciences of Belarus, 70 Prospekt Frantsiska Skoriny, Minsk 220072, Belarus. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, No. 6, pp. 345–347, November–December, 1996. Original article submitted February 22, 1996.     

On the defects of molecular symmetry-lobe orbitals

It is proved that two molecular symmetry-lobe orbitals, belonging to different irreducible representations, can have a non-negligible overlap. Using a previously reported multipolar analysis of Gaussian-lobe orbitals (GLOs), it is demonstrated that such defects occur when individual symmetry orbitals (SOs) are both contaminated in a given Y_1m subspace, even if such contaminations are very small. A numerical application illustrates this result in the case of the NH₃ molecule, and it is shown that axial-GLOs allow for the exact cancellation of the symmetry defects.     

Die Bindungsverhältnisse in der Clusterverbindung CZr6I14

Summary The electronic properties of the cluster compound CZr₆I₁₄ are discussed on the basis of EHT results. In the model cluster CZr₆I ₁₈ ^4– the calculated Zr-Zr distance in the metal octahedron is enlarged by encapsulation of the interstitial C as well as by the surrounding ligands. The interstitial bond is realized by the two bond orbitals a_1g, t_1u, and, additional, by three t_1u orbitals of the 5 p(I) band. The Zr-Zr bonds are week. The cluster CZr₆I ₁₈ ^4– is held together by strong C-Zr and Zr-I bonds.

     

Unrestricted CNDO-MO calculations. II. MnO 4 2− and CrO 4 3−

The electronic structures of the tetrahedral molecule ions MnO ₄ ^2– and CrO ₄ ^3– have been investigated within an unrestricted CNDO-MO approximation [Theoret. Chim. Acta (Berl.)20, 317 (1971)]. Calculations assuming the unpaired electron occupies the 3a ₁, 2e, and 4t2 molecular orbitals indicate that the 3a ₁ and2e orbitals have similar orbital energies and that the 4t ₂ orbital is at a higher energy. The experimentally indicated2e orbital for the unpaired electron is obtained with expanded O^1– type atomic orbitals for oxygen and valence metal orbitals of the expanded 3d and plus one ion 4p types. The metal 4s orbitals must be held to the neutral atom type. The optimum valence orbitals above with a slightly contracted 4s type metal orbitals yield the minimum total energy and places the unpaired electron in the 3a ₁ orbital. Since the contracted 4s metal orbital produces results that are not in agreement with experimental data, the method used apparently does not adequately take into account the increased electron-electron repulsions that contracted 4s orbitals produce.     

Quantum-chemical investigation of structure and valence isomerizations of perdehydrotetrasilacyclobutadiene

The structure and valence isomerizations of perdehydrotetrasilacyclobutadiene (Si₄) are discussed on the basis of concepts of cyclic ^– and ^–conjugation. Calculations by the MINDO/3 and MNDO methods established two types of geometric configurations with D_4h symmetry for both the singlet and triplet states of perdehydrotetrasilacyclobutadiene, differing in inversion of the HOMO and LUMO. Neither D_4h configuration of the singlet state corresponds to minima on the potential energy surface, and these configurations are distorted, one toward a rectangular structure with D_2h symmetry with alternation of bond lengths in the ring, and the other toward a rhombic bicyclic structure with D_2h symmetry. The latter structure corresponds to the global minimum on the potential energy surface of the Si₄.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 4, pp. 414–420, July–August, 1987.     

Ab initio Calculation of the charge distribution and the ligand field splitting in the tetrahedral halo complexes CuCl 4 2− 4 and NiCl 4 2−

The charge distribution and the ligand field splitting in the tetrachloro complexes CuCl ₄ ^2– and NiCl ₄ ^2– have been investigated by means of the restricted Hartree-Fock method. A rather large basis set of contracted Gaussian type orbitals has been employed. The charge distributions have been analysed by means of Mulliken population analyses. The ligand field splitting 10Dq has been compared with literature results known for the octahedral cluster NiF ₆ ^4– occurring in KNiF₃. A detailed analysis has been carried out for CuCl ₄ ^2– . From calculations on a selected number of states of NiCl ₄ ^2– the Racah parameters B and C have been obtained.     

Electronic structure of octacyanides of molybdenum IV and V according to the SCCC MO method

The SCCC MO method has been used to calculate the electronic structure and spectrum of Mo(CN) ₈ ^4– and Mo(CN) ₈ ^3– ions of a D _4d symmetry. All metal-ligand and ligand-ligand interactions and all overlap integrals (over products of HF atomic orbitals) have been included within the SCCC MO scheme. Basing on these calculations a new assignment of some absorption bands is proposed. The overall agreement between the calculated and observed electronic spectrum is satisfactory.

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Zusammenfassung Elektronenstruktur und Spektrum der [Mo(CN)₈]^–4- und [Mo(CN)₈]^–3-Ionen in D _4d -Symmetrie wurden mit der SCCC-MO-Methode berechnet. Alle Metall-Ligand- und Ligand-Ligand-Wechsel-wirkungen und Überlappungsintegrale wurden berücksichtigt. Die Bandenzuordnung wurde neu vorgenommen. Die Übereinstimmung der berechneten und gemessenen Spektren ist befriedigend.

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Résumé Application à Mo(CN) ₈ ^4– et Mo(CN) ₈ ^3– de la méthode SCCC MO basée sur des orbitales atomiques HF approchées, en tenant compte du recouvrement et de toutes les interactions ligand-ligand. Dans la partie I on discute le cas de la symétrie D _4d . L'accord global avec l'expérience est satisfaisant en ce qui concerne les spectres. On montre aussi que toutes les attributions antérieures basées sur la théorie du champ cristallin semblent inadéquates.

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The authors are grateful to Prof. W. Jakób, Dr. Z. Stasicka and Dr. A. Samotus for many interesting discussions, to Prof. J. Chojnacki for providing us with new X-ray results before publication and to Dr. A. J. Sadlej for a help in dealing with the computer.     

Ab initio SCF studies of the molecular structure of XeF6, IF 6 − , and TeF 6 2− in non-octahedral geometries

All-electron SCF calculations in contracted large Gaussian basis sets were performed for the molecules in the isoelectronic series XeF₆, IF ₆ ^– , and TeF ₆ ^2– . Molecular equilibrium geometry of these molecules was studied first in O _h symmetry. Then, the gradient minimization technique was used to determine molecular structure of the studied systems near the local minima corresponding to C _3v and C _2v geometries involved in the internal motion.In the O _h symmetry, TeF ₆ ^2– and IF ₆ ^– are bound by 172 and 104 kcal/mol, respectively. The total energy of XeF₆ is larger than the sum of total energies of the constituent atoms by 192 kcal/mol. Lowering the symmetry to C _3v and C _2v results in an energy gain of about 20 kcal/mol for all studied systems.     

The Three-Center, Four-Electron Bond in Hexacoordinated AB6-Type Main Group Molecules: An Alternative Model of Bonding without d-Orbital Participation in the Central Atom

The hexacoordinated AB₆-type main group molecules have long been thought to have sp³d² hybridization on the central atom, accounting for their molecular geometry (octahedral). However, the s-p-d hybridization does not explain how an energetically unfavorable np nd excitation in an atom of nonmetallic elements, such as sulfur and phosphorus, can be achieved. In this article, the author has re-examined bonding in SF₆ and PF₆^– (O_h symmetry) and proposed that the linear F—S—F and F—P—F bonds in both species are formed via the overlap of the 3p orbital on the central atom with terminal ligand orbitals, resulting in a three-center, four-electron bond. This alternative model, which does not involve d orbitals in bonding, is supported by a partial charge analysis using Allens electronegativity approach. SF₆ or PF₆^– can be characterized by several ionic resonance structures containing a postulated SF₄²⁺ or PF₄⁺ cation (octet on sulfur or phosphorus). The three-center, four-electron bond model can also be used to study bonding in hexacoordinated AB₅E (e.g., halogen pentafluorides) and AB₄E₂ (e.g., xenon tetrafluoride) explaining well the molecular geometry. The author believes that all the results will be useful in updating chemistry texts.     

Electronic structure and optical spectra of transition metal complexes by the effective Hamiltonian method

Summary A semiempirical effective Hamiltonian treatment is proposed for transition metal complexes, taking into accountd-electron correlations, weak covalency of the metal-ligand bonds and the electronic structure of the ligand sphere. The technique uses the variation wave function which differs from the usual Hartree-Fock antisymmetrized product of molecular orbitals extended over the whole complex. The scheme is implemented and parameters describing the metal-ligand interactions are adjusted to reproduced-d-excitation spectra of a number of octahedral MF ₆ ^4– (M=Mn, Fe, Co, Ni) anions, Mn(FH) ₆ ²⁺ cation, CoCl ₆ ^4– anion, and a tetrahedral CoCl ₄ ^2– anion. The values of the parameters are reasonable, thus confirming the validity of the proposed scheme.