Solution of the Hartree–Fock problem by expansion onto nested bases

A method for solving the Hartree–Fock problem in a finite basis set is derived, which permits each orbital to be expanded in a different basis. If the basis set for each orbital ?_i contains the basis functions for the preceding orbitals, ?_i?1, ?_i?2,… ?₁, then the ?_i form an orthonormal set. One advantage over the standard Hartree–Fock method is that a different long range behavior for each orbital, as for example is required in the Hartree–Fock-Slater method, can be forced. A calculation on the ground state of beryllium is performed using the nested procedure. Very little energy is lost because of nesting, and the node in the 1s orbital disappears.     

An application of the method of conjugate gradients to the calculation of minimal basis set localized orbitals

Using an STO -3G basis set, energy localized molecular orbitals (LMO ) were determined for the ten electron series HF, H₂O, NH₃, and CH₄ as well as for CH₃OH and C₂H₂F₂. The method of conjugate gradients is shown to be a viable alternative to other non-eigenvalue methods. The characterization of the LMO in terms of first and second moment measures indicates that the STO -3G basis set LMO may be accurately correlated to larger sp basis set LMO . Also, it is shown that the first and second moment measures display a good linear correlation with the classical concept of electronegativity.     

Application of an optimization technique to the discretized version of the Griffin–Hill–Wheeler–Hartree–Fock equations

Application of the SIMPLEX optimization method to define the mesh of the discretized version of the Griffin–Hill–Wheeler–Hartree–Fock (GHWHF ) equations was studied. Improved discretization parameters with respect to the original method were obtained for atomic systems with two or four electrons and for the H₂ molecule. For the atomic systems, the following correlations between the discretization parameters and the total energy were found: N = a · In(ΔE) + b; Ω₀ = a′ · In(ΔΩ) + a″; and In(ΔΩ) = b′ · ln(N) + b″. These equations provide a systematic procedure to reach a desired degree of accuracy in the energy for the atomic systems studied as well as to fix the basis set to be employed. These equations are similar to those found earlier for eventempered basis sets and permit the establishment of a relationship between the two methods. The even-tempered method is also an approximate solution of the GHWHF equations. The optimized integral discretized basis is more efficient in representing small basis sets for atoms and the basis for the hydrogen molecule in comparison to the even-tempered one. The optimization procedure was successfully applied to generate the universal basis for the atomic systems studied.     

Some developments in the spin-extended Hartree-Fock method

All the second-order density matrix spin components for the spin-extended Hartree-Fock method are obtained. The coefficients in the final formulae are only ω_sM, ω_sM±1, ω_sM±2, where ω_sM are the weights of pure states of spin s in the initial unprojected determinant with spin projection M. The eigenvalue problem for the best electron density natural orbitals in the spin-extended method is formulated. All the second-order transition density matrix spin components between pure spin basis functions built of orthogonal orbitals and distinguished by different core choice are also found. This basis may be used on CI calculations.     

Comparison between 6-31 + bond functions and 6-31 G* basis sets in UMP calculations of dissociation energies of the first row element compounds. I

A basis set with bond functions (6-31G + BF) has been tested for its applicability to calculation of dissociation energies of single and multiple bonds by Moeller-Plesset perturbation theory at the second and third orders. Results have been compared with those calculated in the 6-31G* basis set. The 6-31G + BF basis at the MP 2 and MP 3 levels yields better results than 6-31G* basis and the time consumption is less as well. Consideration of the bond functions on the bonds neighboring the bond being broken has no significant influence on the dissociation energies either at the SCF or at the MP 2 levels. If both reactants and products can be characterized by two-center bonds, the 6-31G + BF basis and UMP2 variant of perturbation theory can be recommended for practical calculation of D_e values, especially for the systems where the use of more exact bases is rather difficult.     

Molecular symmetry and ab initio calculations. II. Symmetry-matrix and symmetry-supermatrix in the Dirac-Fock method

The concepts of symmetry-matrix and symmetry-supermatrix introduced in article I [J. Comput. Chem., 10, 957 (1989)] can be generalized to the Dirac-Fock method. By using the semidirect product decomposition of O_h and the linear vector space theory, the irreducible representation basis of O_h for any molecular system (O_h or its subgroups) can be deduced analytically in the nonorthonormal Cartesian Gaussian basis. This method is extended to discuss the double-valued representations of O_h* in the complex Cartesian Gaussian spinor basis. In the double-valued irreducible representation basis of D₂*, the matrix of kinetic operator c(OVERLINE)σ(/OVERLINE)·(OVERLINE)p(/OVELINE) in the Dirac-Fock equation can be reduced into a real symmetric and can be grouped into classes under the operations in D_3d. Therefore, the symmetry-matrix and symmetry-supermatrix can also be used in the Dirac-Fock method to reduce the storage of two electron integrals and calculations of Fock matrix during iterations by a factor of ca. g² (g is the order of the molecular symmetry group). In addition, a method to deal with the nonorthonormal space is presented. © 1996 by John Wiley & Sons, Inc.     

Electric field variant ket for the calculation of dynamic polarizabilities. Application to H2O and N2

The use of a new time-dependent ket, variationally determined as a linear combination of Slater determinants associated with an electric field variant factor, provides an efficient technique for the calculation of dynamic polarizability tensors. Including electron correlation, the method is applied to the evaluation of the frequency-dependent polarizability of H₂O and N₂ and can be used even when the photon energy is near the excitation energy. With relatively small basis sets, calculated polarizabilities and resonance frequencies are in good agreement with experimental values for H₂O but have to be improved for N₂.     

Combinatorial Library Based Engineering of Candida antarctica Lipase A for Enantioselective Transacylation of sec‐Alcohols in Organic Solvent

A method for determining lipase enantioselectivity in the transacylation of sec‐alcohols in organic solvent was developed. The method was applied to a model library of Candida antarctica lipase A (CalA) variants for improved enantioselectivity (E values) in the kinetic resolution of 1‐phenylethanol in isooctane. A focused combinatorial gene library simultaneously targeting seven positions in the enzyme active site was designed. Enzyme variants were immobilized on nickel‐coated 96‐well microtiter plates through a histidine tag (His₆‐tag), screened for transacylation of 1‐phenylethanol in isooctane, and analyzed by GC. The highest enantioselectivity was shown by the double mutant Y93L/L367I. This enzyme variant gave an E value of 100 (R), which is a dramatic improvement on the wild‐type CalA (E=3). This variant also showed high to excellent enantioselectivity for other secondary alcohols tested.     

Disproportionation of 2,5-dichlorosemiquinone radicals in benzene according to unsteady-state kinetic data for the chain reaction between 2,5-dichlorohydroquinone and <Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>′-diphenyl-1,4-benzoquinone diimine

A method for determining the rate constant of disproportionation of 2,5-dichlorosemiquinone radicals (k ₆) from unsteady-state kinetic data for the initiated chain reaction of N,N′-diphenyl-1,4-benzoquinone diimine with 2,5-dichlorohydroquinone have been developed, and two variants of this method are presented. The method is based on the study of the unsteady-state disappearance kinetics of one of the initial reactants (quinone diimine) in its initiated chain reaction with hydroquinone. The unsteadiness of the reaction is due to the presence of semiquinone radicals or initiator radicals accumulated before the start of the reaction at a concentration exceeding the steady-state concentration of semiquinone radicals in the chain reaction. The variants of the method differ in the order of mixing the reactants and initiator, on which the nature and concentration of the radicals accumulated in the system before the reaction depend. In the first variant, a quinone diimine + initiator solution is initially prepared and initiator radicals are accumulated. Hydroquinone is added to this solution (start of the reaction). In the second variant, a hydroquinone + initiator solution is initially prepared and semiquinone radicals from hydroquinone are accumulated. Quinone imine is then added to the solution (start of the reaction). The disproportionation rate constant of semiquinone radicals (k ₆) is derived from the dependence of the decrease in the quinone imine concentration in a certain short time (∼20 s) after the start of the reaction on the initiation rate. The rate constant k ₆ in benzene is (7.3 ± 3.7) × 10⁶ l mol⁻¹ s⁻¹ according to the first variant of the method and (5.0 ± 2.2) × 10⁶ l mol⁻¹ s⁻¹ according to the second one.     

Calculation of the coefficients of the characteristic polynomial from its subgraphs

The characteristic polynomial associated with π-electrons of conjugated molecules are discussed by using subgraphs derived from molecular graphs as a basis for their construction. A practical method has been developed for evaluating the coefficient a_K of conjugated molecules. Applying this method, the general formulas of evaluating the coefficient a_K for homologous conjugated molecules have been obtained. The approach is illustrated on a few simple conjugated systems, including also a few polymeric systems. © 1996 John Wiley & Sons, Inc.     

Elimination of the diagonalization bottleneck in parallel Direct-SCF methods

Summary It is shown that the matrix diagonalization bottleneck associated with thesequential O(N _BFN ³ ) diagonalization of the fock matrix within each iteration of the Direct-SCF procedure may be eliminated, and replaced instead with a combination ofparallel O(N _BFN ^<4 ) andsequential O(N _Sub ³ ) steps. For large basis sets, the relation N_Sub N_BFN between the dimension of the expansion subspace and the number of basis functions leads to a method of wave-function optimization in which the sequential bottleneck is eliminated. As a side benefit, the second-order iterative procedure on which this method is based displays superior convergence properties, and provides greater insight into the behavior of the energy with respect to orbital variations, than the traditional first-order, fixed-point, iterative approaches. The implementation of this method may be incorporated into essentially any existing Direct-SCF program with only minimal, and localized, changes.     

The Structure of La3Au4In7 and its Relation to the BaAl4 Type

La₃Au₄In₇ was prepared by arc‐melting of the elements and subsequent annealing at 970 K. X‐ray diffraction of powders and single crystals yielded I2/m11, mI28, a = 460.42(5) pm, b = 1389.5(1) pm, c = 1039.6(2) pm, α = 90.77(1)°, wR2 = 0.0621, 1089 F² values, 46 variables. The structure of La₃Au₄In₇ is of a new type. It may be considered as a monoclinically distorted, ordered variant of the La₃Al₁₁ type. The structural relation with the family of BaAl₄ related compounds is discussed on the basis of a group‐subgroup scheme. The gold and indium atoms in La₃Au₄In₇ build a three‐dimensional [Au₄In₇] polyanion in which the lanthanum atoms fill distorted pentagonal and hexagonal channels. Within the polyanion short Au–In and In–In distances are indicative of strongly bonding Au–In and In–In interactions.     

Computation of electron repulsion integrals using the rys quadrature method

Following an earlier proposal to evaluate electron repulsion integrals over Gaussian basis functions by a numerical quadrature based on a set of orthogonal polynomials (Rys polynomials), a computational procedure is outlined for efficient evaluation of the two-dimensional integrals I_x, I_y, and I_z. Compact recurrence formulas for the integrals make the method particularly fitted to handle high-angular-momentum basis functions. The technique has been implemented in the HONDO molecular orbital program.     

Generator coordinate Hartree–Fock method applied to the choice of a contracted Gaussian basis for the second-row atoms

The generator coordinate Hartree–Fock (GCHF) method is employed as a criterion for the selection of a 18s12p Gaussian basis for the atoms Na–Ar. The role of the weight functions in the assessment of the numerical integration range of the GCHF equations is shown. The extended basis is then contracted to (10s6p) by a standard procedure and in combination with the previously contracted (7s5p) Gaussian basis for the atoms Li–Ne is enriched with polarization functions. This basis is tested for AlF, SiO, PN, BCl, and P₂. The properties of interest were HF total energies, MP2 dipolar moments, bond distances, and dissociation energies. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 927–934, 1997     

Uniform quality gaussian basis sets for molecular calculations,I. C1 hydrocarbons

The optimality of MO basis sets of Gaussian functions, when constructed from AO basis sets optimized for the neutral atom or for atom ions, is investigated. A formal charge parameter Q is defined and used to adjust the AO basis sets to the molecular environment, by virtue of a simple quadratic expression. Calculations on a series of C₁ hydrocarbons (CH₂, CH₃, CH₃⁺, CH₃^?, CH₄) using 3G basis sets indicate considerable variations in the optimum Q value with the molecular species. The proposed method offers a simple alternative technique to a full molecular basis set optimization.     

平面四方金属苯配合物的二阶超极化率的量子化学计算

反位平面四方型过渡金属有机配合物[XM(PEt₃)₂-C₆H₄-A] (M＝Pd, Pt; X＝Br, I; A＝NO₂, CHO), 具有较高的二阶超极化率. 采用从头算方法对该配合物的二阶超极化率进行了研究. 构型在MP2/Lanl2DZ水平优化. 基组采用赝势价分裂基Lanl2DZ添加弥散函数和极化函数. HF水平计算(个别情况用MP2计算验证)表明, 苯的对位取代基A的吸电子能力越强, 金属对位配体X的供电子能力越强, 则配合物的二阶超极化率越大.     

Collective drift of molecules in liquids according to the incoherent thermal-neutron scattering

The collective transport of molecules in liquids is studied. The main attention is given to determining the corresponding radius r _L of a Lagrangian particle, which is the most important element of the Lagrange theory of thermal hydrodynamic fluctuations and serves a basis for describing the collective drift in liquids. To determine r _L, we use the incoherent thermal-neutron scattering and a direct calculation method. It is found that the results of three independent methods for the determination of r _L are in good agreement with each other and confirm theoretical concepts of the nature of collective transport in liquids.     

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.     

Simple methods for the estimation of ionization constants of substituted pyridine N-oxides in polar aprotic solvents and water

A direct method for the determination of the pK _a values of acids conjugated to substituted pyridine N-oxides has been proposed which is based on the pH measurement of the solution of the basic salt. It has been experimentally shown that the method is reliable when applied to N-oxides of not too low basicity (pK _a >5). Correlation has been performed between the pK _a values in aqueous and aprotic media solutions which shows the great influence of the solvation effect on the acid-base equilibria. The good correlation between the pK _a values in aqueous and non-aqueous solutions enables the pK _a values in water to be estimated with sufficient accuracy, even in the cases when the experimental limitations make the determination impossible which is shown on the basis of selected examples.