Orbital-orthogonality constraints and basis-set optimization

A new procedure is presented for introducing arbitrary orbital-orthogonality constraints in the variational optimization of otherwise nonorthogonal multiconfiguration electronic wave functions. It is based on suitable analytical changes to the expressions for the first and second derivatives of the electronic energy with respect to the independent variational parameters, and can be applied in the presence of symmetry constraints. It is tested using a second-derivative optimization procedure, the Optimized Basis Set -- Generalized Multiconfiguration Spin-Coupled (OBS-GMCSC) approach, that can treat basis-function exponential parameters as variational parameters, to be optimized simultaneously with configuration, spin-coupling, and orbital coefficients. This enables rigorous optimization of basis-set exponential parameters even for fully orthogonal multiconfiguration wave functions. Test calculations are carried out, with optimized even-tempered basis sets, on Li(2) and on the CH radical. For the latter, special attention is paid to the electronic spin density at the nuclei.     

On the electronic structure of Li2 (X 1\documentclass{article}\pagestyle{empty}\begin{document}$\Sigma^{+}_{\mathrm{g}}$\end{document}) and its changes with internuclear distance

A compact, yet accurate, and strictly virial‐compliant ab initio electronic wavefunction for ground‐state Li₂ is exploited for a study of the molecule's electronic structure and electron density. Symmetry‐breaking problems that emerge at the single‐configuration level are solved in a multiconfigurational spin‐coupled approach that enables simultaneous optimization of angularly correlated “resonating” configurations. Particular emphasis is placed on the accurate determination of the electron density's bifurcation points and of the quadrupole moment as a function of internuclear distance R. Tentative connections are drawn between the R dependence of the electron density's topological structure and quadrupole moment and that of the electronic wavefunction. Computation of the latter constitutes the first application to systems other than isolated atoms of the optimized basis set generalized multiconfiguration spin‐coupled method, which entails use of nonorthogonal orbitals and Slater‐type basis functions with variationally optimized exponential parameters. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 378–397, 2000     

BeH2与HX(X=F,Cl, Br,I)形成的二氢键复合物的结构特征与本质

对BeH2与HX(X=F, Cl, Br, I)形成的二氢键复合物的结构特征及本质进行了探讨. 在MP2/6-311++G(3d,3p)水平优化、频率验证, 得到复合物的分子结构, 用分子间距离及电子密度拓扑理论确认BeH2与卤化氢已形成了二氢键型复合物. 在MP2/6-311++G(3d, 3p)水平下进行基函数重叠误差(BSSE)校正后的结合能在-14.468 kJ·mol-1到-5.464 kJ·mol-1之间.用对称匹配微扰理论(SAPT)对复合物的结合能进行分解, 结果表明, BeH2…HX二氢键复合物中静电能对总吸引能的贡献都是最主要的, 但交换排斥能、诱导能、色散能对总结合能的贡献也很重要. 从BeH2…HF到BeH2…HI, 诱导能对总吸引能的贡献从37.8%逐渐减小到24.0%. 而色散能对总吸引能的贡献从BeH2…HF体系中的16.0%逐渐增加到BeH2…HI体系中的33.8%.     

H2O,H2, HF,F2 and F2O nuclear magnetic shielding constants and indirect nuclear spin–spin coupling constants (SSCCs) in the BHandH/pcJ‐n and BHandH/XZP Kohn–Sham limits

Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H₂O, H₂, HF, F₂ and F₂O nuclear isotropic shielding constants in the BHandH Kohn–Sham basis set limit was shown. The results of two‐ and three‐parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization‐consistent basis sets pcS‐n and pcJ‐n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were more sensitive to the XZP basis set size and generally less accurate than those estimated using pcJ‐n basis set family. The BHandH density functional markedly outperforms B3LYP method in predicting heavy atom shieldings and SSCCs values in the studied systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Optimization of Gaussian basis sets for Dirac-Hartree-Fock calculations

We investigate the optimization of Gaussian basis sets for relativistic calculations within the framework of the restricted Dirac-Hartree-Fock (DHF) method for atoms. We compare results for Rn of nonrelativistic and relativistic basis set optimizations with a finite nuclear-size. Optimization of separate sets for each spin-orbit component shows that the basis set demands for the lower j component are greater than for the higher j component. In particular, the p _1/2 set requires almost as many functions as the s _1/2 set. This implies that for the development of basis sets for heavy atoms, the symmetry type for which a given number of functions is selected should be based on j, not on l, as has been the case in most molecular calculations performed to date.     

Polarized basis sets of Slater-type orbitals: H to Ne atoms

We present three Slater-type atomic orbital (STO) valence basis (VB) sets for the first and second row atoms, referred to as the VB1, VB2, and VB3 bases. The smallest VB1 basis has the following structure: [3, 1] for the H and He atoms, [5, 1] for Li and Be, and [5, 3, 1] for the B to Ne series. For the VB2 and VB3 bases, both the number of shells and the number of functions per shell are successively increased by one with respect to VB1. With the exception of the H and Li atoms, the exponents for the VB1 bases were obtained by minimizing the sum of the Hartree-Fock (HF) and frozen-core singles and doubles configuration interaction (CISD FC) energies of the respective atoms in their ground state. For H and Li, we minimized the sum of the HF and CISD FC energies of the corresponding diatoms (i.e., of H(2) or Li(2)) plus the ground-state energy of the atom. In the case of the VB2 basis sets, the sum that was minimized also included the energies of the positive and negative ions, and for the VB3 bases, the energies of a few lowest lying excited states of the atom. To account for the core correlations, the VBx (x = 1, 2, and 3) basis sets for the Li to Ne series were enlarged by one function per shell. The exponents of these extended (core-valence, CV) basis sets, referred to, respectively, as the CVBx (x = 1, 2, and 3) bases, were optimized by relying on the same criteria as in the case of the VBx (x = 1, 2, and 3) bases, except that the full CISD rather than CISD FC energies were employed. We show that these polarized STO basis sets provide good HF and CI energies for the ground and excited states of the atoms considered, as well as for the corresponding ions.     

Comparative analysis of the applicability of AM1 and CNDO/2 methods for quantitative prediction of the35Cl NQR frequencies of RC-Cl compounds

The³⁵Cl NQR frequencies of a series of RC-Cl compounds were calculated by the AM1 and CNDO/2 methods in the Townes-Dailey approximation. It was shown that neither of these methods can be directly used for the quantitative prediction of NQR frequencies, and their use in the correlation approach is only possible in narrow series. The AM1 method gives better results for saturated compounds.Institute of Organic and Physical Chemistry, Kazan' Scientific Center, Russian Academy of Sciences, 420083 Kazan'. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 5, pp. 1078–1082, May, 1992.     

Electronic structure and biological activity of chosen DDT-type insecticides studied by 35Cl-NQR

A correlation between the electronic structure and biological activity of chosen dichlorodiphenyltrichloroethane (DDT)-type insecticides: 1,1,1-trichloro-2,2-bis(4-chlorophenyl)ethane, 1,1-dichloro-2,2-bis(4-chlorophenyl)ethane, 2,2-bis(p-chlorophenyl)-1,1-dichloroethylene, 2,2-bis(4-chlorophenyl)ethanoic acid and 4,4'-dichlorobenzophenone (used in agriculture) has been analysed on the basis of the (35)Cl-nuclear quadrupole resonance (NQR) spectroscopy. The (35)Cl-NQR resonance frequencies measured at 77 K have been correlated with the lethal dose (LD(50)) parameter that characterises the biological activity of these insecticides.     

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.     

Existence of strictly diabatic basis sets for the two‐state problem

Some new properties of the nonadiabatic coupling elements are derived, in particular the orthogonality and gauge invariance of their longitudinal and transverse components. A method for constructing a strictly diabatic basis set that makes both the transverse and longitudinal components of the nonadiabatic coupling elements of the two‐state problem vanish identically and is based on introducing overlap between the electronic states in the vicinity of the crossing seam is proposed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Performance of numerical atom‐centered basis sets in the ground‐state correlated calculations of noncovalent interactions: Water and methane dimer cases

Numerical atom‐centered basis sets (orbitals) (NAO) are known for their compactness and rapid convergence in the Hartree–Fock and density‐functional theory (DFT) molecular electronic‐structure calculations. To date, not much is known about the performance of the numerical sets against the well‐studied Gaussian‐type bases in correlated calculations. In this study, one instance of NAO [Blum et al., The Fritz Haber Institute ab initio Molecular Simulations Package (FHI‐aims), 2009] was thoroughly examined in comparison to the correlation‐consistent basis sets in the ground‐state correlated calculations on the hydrogen‐bonded water and dispersion‐dominated methane dimers. It was shown that these NAO demonstrate improved, comparing to the unaugmented correlation‐consistent based, convergence of interaction energies in correlated calculations. However, the present version of NAO constructed in the DFT calculations on covalently‐bound diatomics exhibits enormous basis‐set superposition error (BSSE)—even with the largest bases. Moreover, these basis sets are essentially unable to capture diffuse character of the wave function, necessary for example, for the complete convergence of correlated interaction energies of the weakly‐bound complexes. The problem is usually treated by addition of the external Gaussian diffuse functions to the NAO part, what indeed allows to obtain accurate results. However, the operation increases BSSE with the resulting hybrid basis sets even further and breaks down the initial concept of NAO (i.e., improved compactness) due to the significant increase in their size. These findings clearly point at the need in the alternative strategies for the construction of sufficiently‐delocalized and BSSE‐balanced purely‐numerical bases adapted for correlated calculations, possible ones were outlined here. For comparison with the considered NAOs, a complementary study on the convergence properties of the correlation‐consistent basis sets, with a special emphasis on BSSE, was also performed. Some of its conclusions may represent independent interest. © 2013 Wiley Periodicals, Inc.     

Prediction of water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) using correlation‐consistent and polarization‐consistent basis sets in the Kohn–Sham basis set limit

Density functional theory (DFT) was used to estimate water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) in the Kohn–Sham (KS) complete basis set (CBS) limit. Correlation‐consistent cc‐pVxZ and cc‐pCVxZ (x = D, T, Q, 5, and 6), and their modified versions (ccJ‐pVxZ, unc‐ccJ‐pVxZ, and aug‐cc‐pVTZ‐J) and polarization‐consistent pc‐n and pcJ‐n (n = 0, 1, 2, 3, and 4) basis sets were used, and the results fitted with a simple mathematical formula. The performance of over 20 studied density functionals was assessed from comparison with the experiment. The agreement between the CBS DFT‐predicted isotropic shieldings, spin–spin values, and the experimental values was good and similar for the modified correlation‐consistent and polarization‐consistent basis sets. The BHandH method predicted the most accurate ¹H, ¹⁷O isotropic shieldings and ¹J(OH) coupling constant (deviations from experiment of about ? 0.2 and ? 1 ppm and 0.6 Hz, respectively). The performance of BHandH for predicting water isotropic shieldings and ¹J(OH) is similar to the more advanced methods, second‐order polarization propagator approximation (SOPPA) and SOPPA(CCSD), in the basis set limit. Copyright © 2008 John Wiley & Sons, Ltd.     

The confirmation of accurate combination of functional and basis set for transition‐metal dimers: Fe2, Co2, Ni2, Ru2, Rh2, Pd2, Os2, Ir2, and Pt2

Eight kinds of density functionals named B3LYP, PBE1PBE, B1B95, BLYP, BP86, G96PW91, mPWPW91, and SVWN along with two different valence basis sets (LANL2DZ and CEP‐121g) are employed to study the transition‐metal dimers for the elements of group VIII. By comparing the equilibrium bond distances, vibrational frequencies, and dissociation energies of the ground state of these dimers with the available experimental values and theoretical data, we show that the “pure” DFT methods (G96PW91, BLYP, and BP86) with great‐gradient approximation always give better results relative to the hybrid HF/DFT schemes (B3LYP, PBE1PBE, and B1B95). The striking case found by us is that the G96PW91 functional, which is not tested in previous systemic studies, always predicts the dissociation energy to be well. The Ru₂ and Os₂ dimers are sensitive to not only the functionals employed but also the valence basis sets adopted. The natural bond orbital population is analyzed, and the molecular orbitals of the unpaired electrons are determined. Furthermore, our results indicate that the s and d orbitals of these dimers always hybridize with each other except for Rh₂ and Pt₂ molecules. And by analyzing the electron configuration of the bonding atom, the dissociation limit of the ground state is obtained. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

OH⋅⋅⋅N and CH⋅⋅⋅O Hydrogen Bonds Control Hydration of Pivotal Tropane Alkaloids: Tropinone⋅⋅⋅H2O Complex

The effect of monohydration in equatorial/axial isomerism of the common motif of tropane alkaloids is investigated in a supersonic expansion by using Fourier‐transform microwave spectroscopy. The rotational spectrum reveals the equatorial isomer as the dominant species in the tropinone???H₂O complex. The monohydrated complex is stabilized primarily by a moderate O?H???N hydrogen bond. In addition, two C?H???O weak hydrogen bonds also support this structure, blocking the water molecule and avoiding any molecular dynamics in the complex. The water molecule acts as proton donor and chooses the ternary amine group over the carbonyl group as a proton acceptor. The experimental work is supported by theoretical calculations; the accuracy of the B3LYP, M06‐2X, and MP2 methods is also discussed.     

33S NMR spectroscopy 3. Substituent effects on 33S NMR parameters in 2-substituted ethanesulfonates

33S NMR parameters (chemical shifts and linewidths) in 2-substituted sodium ethanesulfonates, XCH2CH2SO3Na (X = H, CH3, OH, SH, NH2, Cl, Br, NH3+) depend upon the electronic properties of substituents. To explain experimental results and obtain additional information on the origin of the observed substituent effect (SE), sulfur isotropic absolute shielding constants have been calculated at DFT level of theory (B3LYP/6-311++G(2d,p)) by gauge-including atomic orbitals (GIAO) method. Data have been interpreted with the aid of natural bond orbital (NBO) method and natural chemical shielding (NCS) analysis. It has been demonstrated that in the class of compounds considered the diamagnetic contribution to sulfur-shielding constant is constant and the observed upfield shift of 33S resonance induced by electron-withdrawing substituents (reverse chemical shift effect) can be related to variations of the paramagnetic contribution. Substituents with different electronic properties cause variations in the polarization of S-C and S-O bonds of the -C-SO3- moiety thus determining changes of the electron density at sulfur nucleus and consequently the expansion or contraction of 3p sulfur orbitals. Also oxygen lone-pairs and sulfur core 2p electrons can play an active role in determining the paramagnetic contribution to sulfur shielding. With regard to linewidth variations, they can be ascribed primarily to changes in the nuclear quadrupole coupling constant values. B3LYP/6-311++G(2d,p) method allows obtaining a good reproducibility of SE on the electric field gradient (EFG) at sulfur, although its values tend to be underestimated significantly. Moreover, 17O shielding constants have been calculated.     

A CASSCF/icMRCI study of the electric field gradient in low-lying electronic states of N2/N2

The electric field gradients (EFG’s) at the nucleus are calculated as a function of internuclear separation in the X²Σ_g⁺ and B²Σ_u⁺ electronic states of the nitrogen molecule cation using the internally contracted multireference configuration interaction (icMRCI) method. The EFG’s and potential energy functions (PEF’s) are used to estimate the ¹⁴N nuclear quadrupole coupling constants (NQCC’s) in the two electronic states as functions of vibrational and end-over-end rotational quantum numbers. The dependences of the computed constants on the basis set and reference configuration space are investigated. Since no counterpart for comparison of the calculated NQCC’s exists, the N₂⁺ results are supported by analogous calculations on the X¹Σ_g⁺ and A³Σ_u⁺ states of N₂, for which established data are available. The overall good quality of the icMRCI wave functions is further corroborated by a favorable agreement of spectroscopic constants derived from the corresponding PEF’s and experimental data. Variations of the EFG with internuclear separation are explained in terms of wave function composition, and used for gaining specific insight into the chemical bonding in N₂⁺ and N₂.     

Revised model core potentials of s-block elements

We developed new model core potentials (MCPs) for s-block elements from Na to Ra, in which the outer core (n-1)s and (n-1)p electrons are treated explicitly together with the ns electrons. By adding suitable correlating functions, we demonstrated that the present MCP basis sets show excellent performance in describing the electronic structures of atoms and molecules, bringing about accurate ionization potentials of atoms and very good spectroscopic constants of ionic and covalent molecules. The results obtained with the new MCPs are very close to the ones obtained using the all-electron correlation consistent basis sets of Dunning.