用诱导自洽方法计算振动力常数的研究

本文提出一种迭代方法计算振动力常数,可以比较清楚地显示基频与振动力常数之间的关系,从而能方便地选择合适的力常数限制条件,得到合理的结果.用本方法对一系列不同分子作了计算,结果比较满意,对计算中一些具体问题作了讨论.     

Mathematical optimization in the determination of the dissociation constants of a tribasic organic acid by 13C NMR spectroscopy

The calculation of dissociation constants from the chemical shifts of (13)C NMR spectra leads to a complicated non-linear equation. Two different mathematical methods for solution of this equation have been chosen--an iterative step method and a matrix pseudo-inversion method. When the iteration method is used the initial guesses for the parameters, the initial value of the step size and the escalation of the iteration must be optimized. For comparison the matrix pseudo-inversion method was used because it gives a unique result. With the optimized step method the results were as accurate or even better than those obtained with the matrix method. Although it takes time to optimize the system, the step method is the more suitable method of solving the problem. The matrix inversion can be done only with a computer with 13 significant digits and exponent capacity larger than +/- 38.     

大分子振动的一般价力场力常数计算方法的研究

本文基于力常数矩阵F_s从UBFF到GVFF的可迁性,提出了一个“由UBFF力常数来限定GVFF力常数”的方法;其次,对“运动学确定力常数法”中Λ矩阵元排序的规则作了进一步研究。     

Ab initio computation of force constants: Part VI. Applications of the force relaxation method for geometry optimization

Techniques to improve the computational efficiency of the force relaxation method are discussed. Force constants for fragments in previously computed smaller molecules can be transferred to construct a guess force constant matrix. Additional force constants that may be needed can be computed by a procedure which uses only one additional force calculation per diagonal force constant required. A scaling technique to improve convergence on the optimized geometry is discussed.     

Separated internal force constants for the ethylene and ethane molecules and their use for calculation of the force field for the propylene molecule

We consider the question of separation of linear combinations of force constants for ethylene and ethane. Introduction of a perturbation into the matrix of the kinematic coefficients allows us to solve the inverted vibrational problem using the matrix method of successive approximations without eliminating dependent coordinates. Such an approach makes it possible to obtain a sufficient system of equations for determining the separated internal force constants. The separated internal force constants determined for ethylene and ethane are used to calculate the force field for propylene. The calculated separated internal force constants for propylene reproduce its vibrational spectrum and the spectrum or propylene-d₆ with average deviation from experimental frequencies of 8 cm^–1. The numerical influence coefficients for stretching vibrations of the C-H bond are linearly related to the lengths of these bonds.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 1, pp. 118–122, Janauary–February, 1986.     

Coriolis coupling constants of cis and trans-1,2-dichloroethylene

Coriolis coupling constants and the inertia defect for cis- and trans-1,2-dichloroethylene have been calculated, using force constants obtained by the iterative consistency method. The results obtained are compared with those of previous workers and it is shown that two sets of force constants which reproduce the vibrational frequencies satisfactorily lead to completely different values for the Coriolis coupling constants.     

Formulation of the vibrational theory in terms of redundant internal coordinates

Using the generalized inverse of matrices and the method of canonical matrices, this paper develops an unambiguous formulation of the theory of small vibrations of molecules which is valid when redundant internal coordinates are used. Such treatment includes the attainment of unambiguous relationships relating the compliance matrix (the generalized inverse of the canonical force constants matrix) with experimental data (vibrational frequencies, Coriolis coupling constants, centrifugal distortion constants and mean-square amplitudes). Moreover, expressions for the elements of the Jacobian matrices of the above magnitudes with respect to the compliance constants have been also obtained as well as some sum rule relationships.     

Force constants and many-body electrostatic interactions in two-dimensional colloidal crystal

A model of a two-dimensional colloidal crystal with a hexagonal lattice, the electrostatic interactions in which are described by the nonlinear Poisson-Boltzmann equation, is considered. The calculation procedure for force constants of this crystal is treated in detail. Properties of system symmetry, which make it possible to significantly decrease the volume of calculations and to classify force constants, are analyzed. Numerical data for force constants of a crystal as functions of lattice parameters at different particle sizes are reported. A method that allows us to disclose the presence of many-body interactions in a system by the behavior of force constants at some interval of the values of lattice parameters is proposed. The application of this method to the system under consideration demonstrated that electrostatic interparticle interactions in the system cannot be reduced to simply a pair interaction of any kind; the introduction of many-body potentials is required for the adequate representation of the elastic properties of a crystal.     

An improved method for the evaluation of transition states

A simple but efficient coupled iteration procedure is proposed for searching saddle points and extrema along the line of constrained minimum energy paths by (analytical) calculation of the derivatives, i.e., the reduced forces and reduced force constants. The advantage of the method is shown with analytical potentials as well as a calculation of HCH? HNC rearrangement, as working examples.     

Calculation of intramolecular force fields from second-derivative tensors

A practical procedure (FUERZA) to obtain internal force constants from Cartesian second derivatives (Hessians) is presented and discussed. It allows a systematic analysis of pair atomic interactions in a molecular system, and it is fully invariant to the choice of internal coordinates of the molecule. Force constants for bonds or for any pair of atoms in general are defined by means of the eigenanalysis of their pair interaction matrix. Force constants for the angles are obtained from their corresponding two-pair interaction matrices of the two bonds or distances forming the angle, and the dihedral force constants are similarly obtained using their corresponding three-pair interaction matrices. © 1996 John Wiley & Sons, Inc.     

Estimating the hessian for gradient-type geometry optimizations

Optimization methods that use gradients require initial estimates of the Hessian or second derivative matrix; the more accurate the estimate, the more rapid the convergence. For geometry optimization, an approximate Hessian or force constant matrix is constructed from a simple valence force field that takes into account the inherent connectivity and flexibility of the molecule. Empirical rules are used to estimate the diagonal force constants for a set of redundant internal coordinates consisting of all stretches, bends, torsions and out-of-plane deformations involving bonded atoms. The force constants are transformed from the redundant internal coordinates to Cartesian coordinates, and then from Cartesian coordinates to the non-redundant internal coordinates used in the specification of the geometry and optimization. This method is especially suitable for cyclic molecules. Problems associated with the choice of internal coordinates for geometry optimization are also discussed.Fellow of the Alfred P. Sloan Foundation, 1981–83     

The effective nuclear charge model—IX. On the transferability of effective nuclear charges defined from homonuclear diatomic molecules

Effective nuclear charges of many triatomic molecules have been calculated inversely by the least squares method (Jacobian matrix method) from the experimental force constants which are determined by normal coordinate analyses using the observed vibrational data. The values of effective nuclear charges thus obtained are compared with those defined from homonuclear diatomic molecules. The results show that the transferability of effective nuclear charges from homonuclear diatomic molecules to triatomic molecules is moderately good. This gives support to the utility of the effective nuclear charge model.     

Inversion of jacobian matrices in metal-ligand-pH studies

Many non-linear regression programs which optimize the stability constants of chemical equilibria make use of Jacobian matrices for both the simulation of speciation by Newton-Raphson iteration and the optimization of parameters by Gauss-Newton iteration. An extended mathematical treatment is described here which shows that the full Jacobian matrix is partitioned into quadrants and that only one of these quadrants has been described in previous studies. This more complete treatment also corrects an error in the sign of the equation given in earlier work for the partial derivatives partial differential log h/ partial differential log beta (or partial differential pX/ partial differential log beta).     

有机金属化合物的振动光谱(Ⅱ)——1,1′-二甲基环戊二烯铁夹心化合物振动光谱的简正坐标计算

测定了(CH_3Cp)_2Fe(Cp=C_5H_4~-)夹心化合物的Fourier变换红外光谱和激光Raman光谱, 并做了指认, 将G-F矩阵法计算得到的Cp_2M(M=Mn,Fe,Ru)夹心化合物的一套力常数, 完整地转移到该分子上, 计算得到的振动光谱频率与测得的基本一致。     

Calculation of Second- and Higher-Order Force Constants Including Electron Correlation Effects and Hartree-Fock Force Constant Scaling

A formalism suitable for practical implementation is suggested for computation of quadratic, cubic, and quartic force constants using the configuration interaction (CI) method. Expressions are compared which involve the Hartree-Fock (HF) harmonic and anharmonic force constants calculated by the HF and CI methods. Also, physical assumptions are formulated to perform scaling of the diagonal harmonic and, which is more important, of anharmonic HF force constants with a common scaling factor. This approach is consistent with the data of ab initio quantum-chemical calculations. A table is presented which compares the results of valence force constant calculations for a series of simple organic molecules.     

NATURE OF THE A AND THE F MATRIX IN THE CALCULATION OF FORCE CONSTANTS OF MOLECULAR VIBRATION

In this paper,calculations of force constants of molecular vibrations are carried out by using Wilson GF matrix method.In the determination of force constants from frequencies and factorization of Gmatrix,an ordering relationship of A matrix(may be n dimensional) relative to L matrix was found according to the ordering of symmetry coordinates.With the help of inverse unitary transformation,a general method to calculate Ft from constants Fs was established.The additivity of Fr depending on the symmetry block was determined to be true.All the force constants in non-planar and planar of urea,thiourea and sclenouroa molecules were calculated by using the general va-leine force field.The calculated values of frequencies were com-pairec with other data given in the literature,and it was shown that the present calculation is in good agreement with the experimental     

Size-extensive vibrational self-consistent field methods with anharmonic geometry corrections

In the size-extensive vibrational self-consistent field (XVSCF) method introduced earlier [M. Ke?eli and S. Hirata, J. Chem. Phys. 135, 134108 (2011)], only a small subset of even-order force constants that can form connected diagrams were used to compute extensive total energies and intensive transition frequencies. The mean-field potentials of XVSCF formed with these force constants have been shown to be effectively harmonic, making basis functions, quadrature, or matrix diagonalization in the conventional VSCF method unnecessary. We introduce two size-consistent VSCF methods, XVSCF(n) and XVSCF[n], for vibrationally averaged geometries in addition to energies and frequencies including anharmonic effects caused by up to the nth-order force constants. The methods are based on our observations that a small number of odd-order force constants of certain types can form open, connected diagrams isomorphic to the diagram of the mean-field potential gradients and that these nonzero gradients shift the potential minima by intensive amounts, which are interpreted as anharmonic geometry corrections. XVSCF(n) evaluates these mean-field gradients and force constants at the equilibrium geometry and estimates this shift accurately, but approximately, neglecting the coupling between these two quantities. XVSCF[n] solves the coupled equations for geometry corrections and frequencies with an iterative algorithm, giving results that should be identical to those of VSCF when applied to an infinite system. We present the diagrammatic and algebraic definitions, algorithms, and initial implementations as well as numerical results of these two methods. The results show that XVSCF(n) and XVSCF[n] reproduce the vibrationally averaged geometries of VSCF for naphthalene and anthracene in their ground and excited vibrational states accurately at fractions of the computational cost.     

Scaling of quantum-mechanical molecular force fields

Comparative analysis of various methods of empirical scaling of quantum-mechanical harmonic molecular force fields has been performed. The efficiency of using each particular scaling technique was shown to depend on the theoretical level of the quantum-mechanical calculation. The Pulay method of scaling (congruent transformation of the force constant matrix) is applicable in the case where the relative accuracies of determination of diagonal and off-diagonal quantum-mechanical force constants are approximately equal. This requirement is satisfied for a quantum-mechanical force field determined close to the HartreeFock limit. This makes it possible to carry out its correction with maximum retention of the peculiarities inherent in the molecule under investigation.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 840–807, April, 1996.     

Equilibrium structure of sulfuric acid

The equilibrium structure of the more stable conformer of H2SO4, of C2 symmetry, has been calculated ab initio using the CCSD(T) method and taking into account the core correlation correction. The accuracy of this structure has been checked by comparing it to that of similar molecules and by estimating the effects of basis set enlargement and of diffuse functions. Furthermore, the quadratic, cubic, and quartic force fields have been calculated at the MP2 level of theory using a basis set of triple-zeta quality. The spectroscopic constants derived from the force field are in satisfactory agreement with the experimental ones. The resulting band origins are compared to literature infrared values, including those for overtone and combination bands. Normal modes of vibration are pictured. Using this force field, semiexperimental equilibrium rotational constants are determined which allows us to check the accuracy of the ab initio structure and to refine it using a mixed regression method.