Automatic Geometry Optimization Research Articles

Structural Significance of Conformational Preferences and Ribose-Ring-Puckering of Hyper Modified Nucleotide 5'-Monophosphate 2-Methylthio Cyclic N6-Threonylcarbamoyladenosine (p-ms2ct6A) Present at 37th Position in Anticodon Loop of tRNALys.

Structural significance of conformational preferences and ribose ring puckering of newly discovered hyper modified nucleotide, 5'-monophosphate 2-methylthio cyclic N6-threonylcarbamoyladenosine (p-ms2ct6A) have been investigated using quantum chemical semi-empirical RM1 and molecular dynamics simulation techniques. Automated geometry optimization of most stable structure of p-ms2ct6A has also been carried out with the help of abinitio (HF SCF, DFT) as well as semi empirical quantum chemical (RM1, AM1, PM3, and PM6) methods. Most stable structure of p-ms2ct6A is stabilized by intramolecular interactions between N(3)…HC(2'), N(1)…HC(16), O(13)…HC(15), and O(13)…HO(14). The torsion angles alpha (α) and beta (β) show the significant characteristic patterns with the involvement of intramolecular hydrogen bonding to provide stability to the p-ms2ct6A. Further, molecular dynamics simulations of p-ms2ct6A revealed the role of ribose sugar ring puckering i.e. C2'-endo and C3'-endo on the structural dynamics of ms2ct6A side chain. The modified nucleotide p-ms2ct6A periodically prefers both the C2'-endo and C3'-endo sugar with 'anti' and 'syn' conformations. This property of p-ms2ct6A could be useful to recognize the starting ANN codons. All atom explicit MD simulation of anticodon loop (ACL) of tRNALys of Bacillus subtilis containing ms2ct6A at 37th position showed the U-turn feature, base stacking ability with other adjacent bases and hydrogen bonding interactions similar to the isolated base p-ms2ct6A. The ribose sugar puckering contributes to the orientation of the side chain conformation of p-ms2ct6A. Thus, the present study could be helpful to understand the structure-function relationship of the hypermodified nucleoside, ms2ct6A in recognition of the proper codons AAA/AAG during protein biosynthesis.

Description of Sudden Polarization in the Excited Electronic States with an Ensemble Density Functional Theory Method.

Sudden polarization (SP) is one of the manifestations of electron transfer in the electronically excited states of molecules. Proposed initially to explain the unusual reactivity of photoexcited olefins, SP often occurs in the excited states of molecules possessing strongly correlated diradical ground state. Theoretical description of SP involves mixing between the singly excited and the doubly excited zwitterionic states, which makes it inaccessible with the use of the popular linear-response time-dependent density functional theory methods. In this work, an extended variant of the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS, or SSR) method is applied to study SP in a number of organic diradical systems. To this end, the analytical derivative formalism is derived and implemented for the SSR(3,2) method (see the main text for explanation of the acronym), which enables the automatic geometry optimization and obtains the relaxed density matrices as well as the electron binding energies and respective Dyson's orbitals. Application of the new method to SP in the lowest singlet excited state of ethylene agrees with the results obtained previously with the use of multireference methods of wavefunction theory. A number of interesting manifestations of SP are observed, such as the charge transfer in photoexcited tetramethyleneethene (TME) diradical mediated by the vibrational motion and conductivity switching in the excited state of a donor-acceptor dyad placed in an external electric field.

A Continuous, Semi-Automated Workflow: From 3D City Models with Geometric Optimization and CFD Simulations to Visualization of Wind in an Urban Environment

The concept and implementation of Smart Cities is an important approach to improve decision making as well as quality of life of the growing urban population. An essential part of this is the presentation of data from different sources within a digital city model. Wind flow at building scale has a strong impact on many health and energy issues in a city. For the analysis of urban wind, Computational Fluid Dynamics (CFD) has become an established tool, but requires specialist knowledge to prepare the geometric input during a time-consuming process. Results are available only as predefined selections of pictures or videos. In this article, a continuous, semi-automated workflow is presented, which ❶ speeds-up the preparation of CFD simulation models using a largely automated geometry optimization; and ❷ enables web-based interactive exploration of urban wind simulations to a large and diverse audience, including experts and layman. Results are evaluated based on a case study using a part of a district in Stuttgart in terms of: ➀ time saving of the CFD model preparation workflow (85% faster than the manual method), ➁ response time measurements of different data formats within the Smart City platform (3D Tiles loaded 30% faster than geoJSON using the same data representations) and ➂ protocols (3DPS provided much higher flexibility than static and 3D container API), as well as ➃ subjective user experience analysis of various visualization schemes of urban wind. Time saving for the model optimization may, however, vary depending on the data quality and the extent of the study area.

Performance Analysis and Optimization of Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) for Vertical Excitation Energies and Singlet-Triplet Energy Gaps.

The mixed-reference spin-flip (MRSF) time-dependent density functional theory (TDDFT) method eliminates the notorious spin contamination of SF-TDDFT, thus enabling identification of states of proper spin-symmetry for automatic geometry optimization and molecular dynamics simulations. Here, we analyze and optimize the MRSF-TDDFT in the calculations of the vertical excitation energies (VEEs) and the singlet-triplet (ST) gaps. The dependence of the obtained VEEs and ST gaps on the intrinsic parameters of the MRSF-TDDFT method is investigated, and prescriptions for the proper use of the method are formulated. For VEEs, MRSF-TDDFT displays similar or better accuracy than SF-TDDFT (ca. 0.5 eV), while considerably outperforming the LR-TDDFT for the ST gaps. As a result, a new functional of STG1X (dubbed here), especially for ST gaps is suggested on the basis of splitting between the components of the atomic multiplets.

Conical Intersections in Organic Molecules: Benchmarking Mixed-Reference Spin-Flip Time-Dependent DFT (MRSF-TD-DFT) vs Spin-Flip TD-DFT.

The mixed-reference spin-flip time-dependent density functional theory (MRSF-TD-DFT) method eliminates the erroneous spin contamination of the SF-TD-DFT methodology, while retaining the conceptual and practical simplicity of the latter. The availability of the analytic gradient of the energy of the MRSF-TD-DFT response states enables automatic geometry optimization of the targeted states. Here, we apply the new method to optimize the geometry of several S1/S0 conical intersections occurring in typical organic molecules. We demonstrate that MRSF-TD-DFT is capable of producing the correct double-cone topology of the intersections and describing the geometry of the lowest-energy conical intersections and their relative energies with accuracy matching that of the best multireference wavefunction ab initio methods. In this regard, MRSF-TD-DFT differs from many popular single-reference methods, such as, e.g., the linear response TD-DFT method, which fail to produce the correct topology of the intersections. As the new methodology completely eliminates the ambiguity with the identification of the response states as proper singlets or triplets, which is plaguing the SF-TD-DFT calculations, it can be used for automatic geometry optimization and molecular dynamic simulations not requiring constant human intervention.

Eliminating spin-contamination of spin-flip time dependent density functional theory within linear response formalism by the use of zeroth-order mixed-reference (MR) reduced density matrix.

The use of the mixed reference (MR) reduced density matrix, which combines reduced density matrices of the MS = +1 and -1 triplet-ground states, is proposed in the context of the collinear spin-flip-time-dependent density functional theory (SF-TDDFT) methodology. The time-dependent Kohn-Sham equation with the mixed state is solved by the use of spinor-like open-shell orbitals within the linear response formalism, which enables to generate additional configurations in the realm of TD-DFT. The resulting MR-SF-TDDFT computational scheme has several advantages before the conventional collinear SF-TDDFT. The spin-contamination of the response states of SF-TDDFT is nearly removed. This considerably simplifies the identification of the excited states, especially in the "black-box" type applications, such as the automatic geometry optimization, reaction path following, or molecular dynamics simulations. With the new methodology, the accuracy of the description of the excited states is improved as compared to the collinear SF-TDDFT. Several test examples, which include systems typified by strong non-dynamic correlation, orbital (near) degeneracy, and conical intersections, are given to illustrate the performance of the new method.

Conformational Preferences of Modified Nucleoside 5-Taurinomethyluridine, τm(5)U Occur at 'wobble' 34th Position in the Anticodon Loop of tRNA.

Conformational preferences of hypermodified nucleoside 5-taurinomethyluridine 5'-monophoshate 'p-τm(5)U' (-CH2-NH2(+)-CH2-CH2-SO3(-)) have been investigated using semi-empirical RM1 method. Automated geometry optimization using ab initio molecular orbital HF-SCF (6-31G**) and DFT (B3LYP/6-31G**) calculations have also been made to compare the salient features. The RM1 preferred most stable conformation of 'p-τm(5)U' has been stabilized by hydrogen bonding interactions between O(11a)…HN(8), O1P(34)…HN(8), and O1P(34)…HC(10). Another conformational study of 5-taurinomethyluridine side chain has also been performed in context of anticodon loop bases of E. coli tRNA(Leu). The atom O(11a) of τm(5)U(34) side chain interacts with adenosine (A35) as well as ribose-phosphate backbone which might provide structural stability to the anticodon loop. The glycosyl torsion angle of τm(5)U retains 'anti'-conformation. The solvent accessible surface area calculations revealed the role of τm(5)U in tRNA(Leu) anticodon loop. MD simulation results are found in agreement with RM1 preferred stable structure. The MEPs calculations of τm(5)U(34):G3 model show unique potential tunnels between the hydrogen bond donor and acceptor atoms as compared to τm(5)U(34):A3 model. Thus, these results could pave the way to understand the role of τm(5)U(34) to recognize UUG/UUA codons at atomic level in the mitochondrial disease, MELAS.

Conformational Preferences of Modified Nucleoside N(4)-Acetylcytidine, ac4C Occur at “Wobble” 34th Position in the Anticodon Loop of tRNA

Conformational preferences of modified nucleoside, N(4)-acetylcytidine, ac(4)C have been investigated using quantum chemical semi-empirical RM1 method. Automated geometry optimization using PM3 method along with ab initio methods HF SCF (6-31G**), and density functional theory (DFT; B3LYP/6-31G**) have also been made to compare the salient features. The most stable conformation of N(4)-acetyl group of ac(4)C prefers "proximal" orientation. This conformation is stabilized by intramolecular hydrogen bonding between O(7)···HC(5), O(2)···HC2', and O4'···HC(6). The "proximal" conformation of N(4)-acetyl group has also been observed in another conformational study of anticodon loop of E. coli elongator tRNA(Met). The solvent accessible surface area (SASA) calculations revealed the role of ac(4)C in anticodon loop. The explicit molecular dynamics simulation study also shows the "proximal" orientation of N(4)-acetyl group. The predicted "proximal" conformation would allow ac(4)C to interact with third base of codon AUG/AUA whereas the 'distal' orientation of N(4)-acetyl cytidine side-chain prevents such interactions. Single point energy calculation studies of various models of anticodon-codon bases revealed that the models ac(4)C(34)(Proximal):G3, and ac(4)C(34)(Proximal):A3 are energetically more stable as compared to models ac(4)C(34)(Distal):G3, and ac(4)C(34)(Distal):A3, respectively. MEPs calculations showed the unique potential tunnels between the hydrogen bond donor-acceptor atoms of ac(4)C(34)(Proximal):G3/A3 base pairs suggesting role of ac(4)C in recognition of third letter of codons AUG/AUA. The "distal" conformation of ac(4)C might prevent misreading of AUA codon. Hence, this study could be useful to understand the role of ac(4)C in the tertiary structure folding of tRNA as well as in the proper recognition of codons during protein biosynthesis process.

Structural significance of hypermodified nucleic acid base hydroxywybutine (OHyW) which occur at 37th position in the anticodon loop of yeast tRNAPhe

Conformational preferences of hypermodified nucleic acid base hydroxywybutine (OHyW) have been studied using quantum chemical single point semi-empirical PM3 method. Automated geometry optimization using semi-empirical RM1, molecular mechanics force field (MMFF) along with ab-initio HF-SCF (6-31G** basis set) and DFT (B3LYP/6-31G** basis set) calculations have also been made to compare the salient features. Molecular electrostatic potentials (MEPs) depict the polarities of hydroxywybutine (OHyW) side chain. Another conformational study showed that hydroxywybutosine side chain interacts with adjacent bases within the anticodon loop of tRNAPhe. The solvent accessible surface area (SASA) calculations revealed the structural role of hydroxywybutine in anticodon loop. Explicit molecular dynamics (MD) simulation has been done over the PM3 most stable structure of OHyW. The hydroxywybutine side chain prefers ‘distal’ conformation i.e. spreads away from the cyclic five membered imidazole moiety of modified tricyclic guanine base. The predicted preferred conformation of hydroxywybutine may prevent extended Watson–Crick base pairing during protein biosynthesis process. This conformation of OHyW stabilized by intramolecular interactions between O(6)⋯HO(16), O(6)⋯HC(15) and O(20)⋯HC(17). Further stabilization is also expected from interactions between O(22)⋯HC(16) and O(23)⋯HC(15). Explicit molecular dynamics (MD) simulation over the PM3 most stable structure of OHyW support the preferred geometry by preserving the ‘distal’ orientation of hydroxywybutine side chain and intramolecular hydrogen bonding interactions. MD simulation study revealed the role of hydroxyl group of OHyW to avoid fluctuations and prevent multiple iso-energetic conformations of hydroxywybutine side chain as compared to wybutine (yW).

Conformational Preferences of Hypermodified Nucleoside Lysidine (k2C) Occurring at “Wobble” Position in Anticodon Loop of tRNAIle

Conformational preferences of hypermodified nucleoside, 4-amino-2-(N6-lysino)-1-(β-D-ribofuranosyl) pyrimidinium (Lysidine or 2-lysyl cytidine), usually designated as k2C, have been investigated theoretically by the quantum chemical perturbative configuration interaction with localized orbitals (PCILO) method. The zwitterionic, non-zwitterionic, neutral, and tautomeric forms have been studied. Automated geometry optimization using molecular mechanics force field (MMFF), semi-empirical quantum chemical PM3, and ab initio molecular orbital Hartree-Fock SCF quantum mechanical calculations have also been made to compare the salient features. The predicted most stable conformations of zwitterionic, non-zwitterionic, neutral, and tautomeric form are such that in each of these molecules the orientation of lysidine moiety (R) is trans to the N(1) of cytidine. The preferred base orientation is anti (χ = 3°) and the lysine substituent folds back toward the ribose ring. This results in hydrogen bonding between the carboxyl oxygen O(12a) of lysine moiety and the 2′-hydroxyl group of ribose sugar. In all these four forms of lysidine O(12a)…H-C(9) and O(12b)…H-N(11) interactions provide stability to respective stable conformers. Watson-Crick base pairing of lysidine with A is feasible only with the tautomeric form of usual anti oriented lysidine. This can help in recognition of AUA codon besides in avoiding misrecognition of AUG.

Effect of interstitial hydrogen on structural and electronic properties of BaTiO3

Abstract We investigate the geometry and electronic structure of an interstitial H atom in the BaTiO3 crystal considering both cubic and tetragonal crystallographic lattices. A quantum-chemical method based on the Hartree-Fock formalism is used throughout the study. Interstitial H is found to bind to one of the O atoms, forming the so-called OH group. At equilibrium, the O-H distances are found to be 0.89 and 0.91 Å for cubic and tetragonal lattices respectively. The performed automated geometry optimization procedure of the defective region shows considerable outward movements of atoms closest to the impurity. The role of the H impurity in ferroelectric polarization in the BaTiO3 crystal is analysed using the results obtained in connection with the available experimental data on ferroelectric perovskites.

Conformational Preferences of Anticodon 3′-Adjacent Hypermodified Nucleic Acid Base cis-or trans-Zeatin and its 2-methylthio Derivative, cis-or trans-ms2Zeatin

Conformational preferences of the hypermodified nucleic acid bases N6-(Δ2 -cis-hydroxyisopentenyl)adenine, cis-io6Ade also known as cis-zeatin, and N6-(Δ2 -trans-hydroxyisopentenyl)adenine, trans-io6ade or trans-zeatin, and 2-methylthio derivatives of these cis-ms2io6Ade or cis-ms2zeatin, and trans-ms2io6Ade or trans-ms2zeatin have been investigated theoretically by the quantum chemical Perturbative Configuration Interaction with Localized Orbitals (PCILO) method. Automated geometry optimization using quantum chemical MNDO, AMI and PM3 methods has also been made to compare the salient features. The predicted most stable conformation of cis-io6Ade, trans-io6Ade, cis-ms2io6Ade and trans-ms2io6Ade are such that in each of these molecules the isopentenyl substituent spreads away (has “dista” conformation) from the five membered ring imidazole moiety of the adenine. The atoms N(6), C(10) and C(11) remain coplanar with the adenine ring in the predicted preferred conformation for each of these molecules. In cis-io6Ade as well as cis- ms2io6Ade the hydroxyl oxygen may participate in intramolecular hydrogen bonding with the H-C(10)-H group. In trans-io6Ade the hydroxyl group is oriented towards the H-C(2) instead. This orientation is retained in trans-ms2io6Ade, possible O-H…S hydrogen bonding may be a stabilizing factor. In all these four modified adenines C(11)-H is favourably placed to participate in intramolecular hydrogen bonding with N(1). In cis-ms2io6Ade as well as trans-ms2io6Ade the 2-methylthio group preferentially orients on the same side as C(2)-N(3) bond, due to this nonobstrusive placing, orientation of the hydroxyisopentenyl substituent remains unaffected by 2-methylthiolation. Thus the N(1) site remains shielded irrespective of the 2-methylthiolation status in these various cis-and trans-zeatin analogs alike. Firmly held orientation of hydroxyisopentenyl substituent in zeatin isomers and derivatives, in contrast to adaptable orientation of isopentenyl substituent in i6Ade and ms2i6Ade, may account for the increased efficiency of suppressor tRNA and reduced codon context sensitivity accompanied with the occurrence of ms2-zeatin (ms2io6Ade) modification.

Oxygen-vacancy defects on the SrTiO3(001) surface: a quantum-chemical study

Abstract A quantum-chemical study of the technologically important SrTiO3(001) non-polar surface and of O-vacancy defects therein is reported in the present work. The computations are made using a method developed for periodic systems (crystals), which is based on the Hartree-Fock theory. The atomie rearrangement due to the surface creation is obtained for pure SrTiO3 by means of the periodic large-unit-cell model and uses an automated geometry optimization procedure. The same technique is employed to study the electronic, structural and optical properties of the material due to the presence of the O vacancy and F centre (two electrons in an O vacancy). The computations are carried out for both cubic and tetragonal lattices. The results obtained are discussed in terms of the available experimental data.

The hydration of the uranyl dication: Incorporation of solvent effects in parallel density functional calculations with the program PARAGAUSS

AbstractThe parallel density functional program PARAGAUSS has been extended by a tool for computing solvent effects based on the conductor‐like screening model (COSMO). The molecular cavity in the solvent is constructed as a set of overlapping spheres according to the GEPOL algorithm. The cavity tessellation scheme and the resulting set of point charges on the cavity surface comply with the point group symmetry of the solute. Symmetry is exploited to reduce the computational effort of the solvent model. To allow an automatic geometry optimization including solvent effects, care has been taken to avoid discontinuities due to the discretization (weights of tesserae, number of spheres created by GEPOL). In this context, an alternative definition for the grid points representing the tesserae is introduced. In addition to the COSMO model, short‐range solvent effects are taken into account via a force field. We apply the solvent module to all‐electron scalar‐relativistic density functional calculations on uranyl, UO22+, and its aquo complexes in aqueous solution. Solvent effects on the geometry are very small. Based on the model [UO2(H2O)5]2+, the solvation energy of uranyl is estimated to be about −400 kcal/mol, in agreement with the range of experimental data. The major part of the solvation energy, about −250 kcal/mol, is due to a donor–acceptor interaction associated with a coordination shell of five water ligands. One can interpret this large solvation energy also as a compounded effect of an effective reduction of the uranyl moiety plus a solvent polarization. The energetic effect of the structure relaxation in the solution is only about 8 kcal/mol. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

Periodic LUC study of F centers in cubic and tetragonal SrTiO 3

Modified for crystals, the quantum-chemical computational approach and the periodic Large Unit Cell (LUC) model are used for calculating structural, electronic and optical properties of F centers (two electrons trapped by an oxygen vacancy). The automated geometry optimization is carried out for the ground state of defect in both cubic and tetragonal crystalline lattices of SrTiO 3. The wave functions of two extra electrons extend over the two vacancy-closest Ti atoms and over other nearby atoms. The absorption energies are calculated using the ΔSCF scheme after the performance of system's geometry optimization. The obtained results are discussed in a comparative manner for two different crystallographic phases.

Quantum-chemical studies of free and potassium-bound hole polarons in SrTiO3 cubic lattice

Quantum-chemical computations based on the Hartree–Fock theory have been carried out for a free and impurity-bound hole polarons in SrTiO3 crystal. Comparing hole localization energy versus lattice relaxation energy, the estimation of spontaneous hole self-trapping in the cubic lattice of pure SrTiO3 has been made. The one-site hole spatial configuration has been found to be the only feasible hole geometry in both pure and potassium-doped SrTiO3 crystals after carefully carried out automated geometry optimization. The ΔSCF calculated absorption energy for the potassium-bound hole polaron was found to be equal to 0.35 eV.

The implementation of analytical energy gradients based on a quasi‐relativistic density functional method: The application to metal carbonyls

AbstractThe capabilities of the quasi‐relativistic scheme due to J. G. Snijders at al. [Mol. Phys, 38, 1969 (1979) Ibid., J. Phys. Chem. 93, 3050 (1989)] has been extended by deriving expressions for the energy gradients with respect to the total energy EQR and implementing them into the ADF program system [B. to Velde and E. J. Baerends, Int. J. Quantum Chem. 33, 87 (1988)]. This implementation enables automated geometry optimization at the relativistic level. The new scheme has been applied together with a self‐consistent nonlocal density functional scheme, NL–SCF + QR, to the calculation of MCO bond lengths and the first bond dissociation energy (FBDE) in the binary transition metal carbonyls M(CO)5 (M = Fe, Ru, Os) and M(CO)6 (M = Cr, Mo, W). The calculated MCO bond lengths are in good agreement with available experimental data with an error typically smaller than 0.01 Å. The calculated FBDES are 45.7 (Fe), 33.0 (Ru), 34.7 (Os), 46.2 (Cr), 39.7 (Mo), and 43.7 (W) kcal/mol, respectively. These values compare well with the available experimental estimates of 42 (Fe), 28 (Ru), 31 (Os), 37 (Cr), 41 (Mo), and 46 (W), respectively. The relativistic effects are found to contract MCO bonds by between 0.07 and 0.16 A and strengthen the FBDEs by 5‐11 kcal/mol for third‐row compounds. The relativistic stabilization of the FBDES among the 5d elements makes, in general, the MCO bond of the 4d element weakest within a triad. © 1995 John Wiley & Sons, Inc.

Automatic geometry optimization: Study of the AlX 3 and Al 2X 6 (X  F, Cl, Br, I) systems by the EHT method and by the EHT method with electrostatic correction

The automatic optimization technique using analytical first derivatives of the potential energy was used to study the structural characteristics and energetics of the AlX 3 monomers and the Al 2X 6 dimers in the framework of the standard EHT method and of its modification with electrostatic corrections as recently suggested by Anderson [10]. It is demonstrated that the latter technique does not significantly improve the results compared to those obtained by the conventional EHT method. Marked nonrigidity of the AlXAlX ring in the Al 2X 6 dimers was found.

Automatic geometry optimization: study of the AIX 3 and Al 2X 6 (X = F, Cl, Br, I) systems by the eht method and by the EHT method with electrostatic correction

The automatic optimization technique using analytical first derivatives of the potential energy was used to study the structural characteristics and energetics of the AIX 3, monomers and the Al 2,X 6 dimers in the framework of the standard EHT method and of its modification with electrostatic corrections as recently suggested by Anderson [10]. It is demonstrated that the latter technique does not significantly improve the results compared to those obtained by the conventional EHT method. Marked nonrigidity of the AlXAIX ring in the AI 2X 6 dimers was found.

Automatic geometry optimization for molecules with d orbitals. III. The EHT method with electrostatic corrections

AbstractA procedure has been developed for automatic optimization of molecular structures in the EHT method with possible inclusion of electrostatic correction terms, operating with analytical formulas for the first derivative of the total energy in Cartesian coordinates in the s, p, d basis of Slater orbitals. Illustrative examples are given of optimization of the structural parameters of FeCl3, Fe2Cl6, FeCl4, FeCl4−, FeCl2, and FeCl and of optimization of the reaction pathways of the dissociation of Fe2Cl6 yielding the other species of the above set. The values are in good argreement with the available experimental data; this agreement is discussed briefly in connection with the general applicability of the EHT method combined with automatic geometry optimization to theoretical study of compounds containing transition metal atoms.