Green's Function Determination of Force Constants-H2O as Example

Treating isotopically substituted molecule as a perturbed system, Green's function for the perturbation are constructed and related to the force field of vibration. By spectral representation, Green's function is diagonalized in the normal coordinates. Then transforming back to the Cartesian coordinates, the Cartesian force constants are generated without solving the secular equation directly. The relations between the internal force constants and the Cartesian force constants ate given and complete internal force field can be obtained. The results for H₂O are discussed.     

陆森红盐阴离子[Fen_2S_2(No)_4]~(2-)红外光谱的归属

本文报导陆森红盐阴离子简正坐标分析及计算所得的一套力常数。由这套力常数所得的红外光谱波数的计算值与观察值吻合良好,加权平方偏差之和为0.223。根据对称内坐标和力常数的位能分布计算,进行了阴离子的红外光谱的归属。     

Analytical torisionL-tensor formulas for anharmonic force constant transformation

New analytical formulas for the torsionL-tensor are reported, which are used in molecular normal mode analysis calculations for the nonlinear transformation of the force constants from internal coordinates to normal coordinates. The proposed formalism exhibits a relative simplicity as compared to previous reported results. Sample calculations for methanol and hydrazine are presented.     

Vibrational spectra and force constants of Ch3HgI and CD3HgI

The infrared and Raman spectra of CH₃HgI and CD₃HgI were studied in the solid state. All the fundamental wavenumbers are assigned. A general harmonic force field was used as the basis, and the force constants were modified by means of the Jacobian matrix. The force constants fit the observed wavenumbers better than 1 %. The normal coordinates are also given.     

Chiral force constants: Recommendations for the presentation of internal coordinate force constants

Some force constants associated with the internal coordinates that sense handedness or chirality can have opposite signs in the enantiomers of chiral molecules. Examples of such force constants include interaction force constants between a torsional and stretching or bending internal coordinates. The sign reversal for these force constants in the enantiomers of chiral molecules or in opposite-handed molecular segments is best recognized by labeling them as chiral force constants. Recognition of chiral force constants suggests that certain guidelines are to be followed in the presentation of internal coordinate force constants. © 1993 by John Wiley & Sons, Inc. © John Wiley & Sons, Inc.     

Force fields and assignments of the vibrational spectra of acridine and phenazine—an ab initio study

A complete set of force constants and their corresponding scale factors in non-redundant local coordinates were obtained by fitting the in-plane ab initio Hartree–Fock (HF) vibrational frequencies computed using 4-21G and 6-31G^** basis sets to the experimental ones. Using these force constants the potential energy distribution (PED) of the normal modes was obtained and based on the PED the earlier empirical assignments were either confirmed or reassigned for all the in-plane fundamentals. The force constants of acridine and phenazine are compared to those of anthracene to study the similarities and differences. Probable assignment is proposed for the out-of-plane fundamentals of acridine based on Durig's simple scaling of the local force constants.     

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     

Isotope effect on localised phonons in mixed crystal spectra

Well developed progressions in phonon modes have been observed in the electronic spectra of 1,5 naphthyridine in durene. The effects of isotopic substitution of both guest and host molecules indicate that the phonons are largely localised on the guest and that the force constants and/or form of the normal coordinates are isotope dependent.     

A theoretical study of the force field for carbon trioxide

Geometries force constants and harmonic frequencies are calculated for the cyclic (dioxirane) structure of CO₃ by ab initio SCF methods using the 3-21G, 3-21G(*). 6-31G and 6-31G* bases calculated frequency shifts for isotopomeric species agree with experiment and lend support to the vibrational assignments of Jacox and Milligan. Earlier arguments for and against the cyclic, cyclic and open structures of CO₃, based upon the “physical reasonableness” of valence force constants are shown to be invalid owing to the dependence of conventional “rigid” force constants upon the choice of valence coordinates. The use of “relaxed” force constants as a basis for meaningful comparison of force fields for molecules described by different sets of redundant valence coordinates is demonstrated.     

Normal mode calculation and IR band assignments of A-type zeolite

Normal mode calculation of A-type zeolite was carried out with the potential energy functions obtained from the constraint method. Mass-weighted cartesian coordinates and the pseudo-lattice method were used. The assignments of IR absorption bands were made with the calculated normal modes, by using the calculated absorption intensities of the modes and the degrees of contribution of the internal coordinates to the modes. The force constants of internal coordinate motions within the framework were also calculated and are compared with the empirical values.     

Force Constant Calculation in Mass-Weighted Cartesian Coordinates. Linear XYX and XYZ Type Molecules

Force constants of simple linear XYX and XYZ types of molecules have been calculated in using the method of mass-weighted cartesian coordinates. Relations and results between force constants in mass-weighted cartesian coordinates and in internal coordinates were also discussed.     

Normal Coordinate Analysis in Cartesian Space II. Planar Symmetric XYn Molecules

Force constants of planar symmetric XY_n type molecules in the Cartesian space have been derived in terms of the vibrational frequencies. The force constants and normal coordinates of some planar XY₃ molecules with available isotoptic data are worked out. Further study of infrared absorption spectra of square planar XY₄ complex ions will be needed for the present normal coordinate analysis.     

Vibrational spectra of the trifluoromethylsulfinate anion and scaled quantum mechanical force fields for CF3SO2- and CF3SeO2-

The infrared and Raman spectra of KCF(3)SO(2) were obtained and the observed spectral features assigned to the expected normal modes of vibration. Besides, the vibrational properties of the CF(3)SO(2)(-) and CF(3)SeO(2)(-) related anions were studied by means of density functional theory (DFT) techniques. After obtaining the optimized geometrical parameters and conformations, the vibrational wavenumbers and the associated force constants were calculated. The original force fields in cartesian coordinates were transformed to local symmetry coordinates and subsequently scaled to reproduce the experimental wavenumbers. Some trends observed in the force constants of the studied species and of the related CF(3)SO(3)(-) anion could be explained by the differences in geometrical parameters.     

Protonation and solvation of pyrazine

Some properties of neutral, once, and twice-protonated pyrazines and their supermolecules with two water molecules were calculated at CNDO level as functions of solvent polarity. The solvents were assumed to be homogeneous continua in which the solute molecules induce electric charges. Atomic net charges, binding energies, force constants, vibrational frequencies, and potential energy distributions were calculated by applying the CNDO optimized geometries of the isolated molecules as references. Pyrazine force constants were scaled to the pyrazine fundamental frequencies. These scaling factors were transferred to the other molecules. For supermolecules the additional scaling factors were chosen based on the chemical similarity of the coordinates.The symmetries of the monocations are reflected in the charge distribution and in the values of the force constants. With increasing molecular charge and increasing solvent polarity the fundamental shifts become more larger and more negative. The calculated frequencies were assigned to normal modes. The influence of the solvent polarity on the binding energies is very interesting: For isolated species that of the neutral molecules is the lowest and that of the bication is the highest, and with increasing polarity all binding energies increase, but the higher the charge, the quicker the increase and the order reverses.The calculated values for the pyrazine parts of the supermolecules are mostly close to those of the corresponding results of the nonhydrated species with the same charge. The results for the substituents are close to the corresponding free species. The interactions are expressed most frequently in the hydrogen bonds. These are investigated in detail. The NH bond lengths are underestimated as a consequence of the CNDO approximation. For water substitution NH stretching force constants and frequencies are low, and the coupled OH stretching force constants and frequencies are large. For the hydroxoniumion substitutent the situation is opposite: In the case of two hydroxonium ion substituents, the two stretching coordinates are mixed in the corresponding normal modes.     

On the representation of force fields for chemically reacting systems

“Relaxed” force constants are uniquely defined for systems involving redundant coordinates, in contradistinction to the usual “rigid” force constants, and thus their use allows meaningful correlations to be made between force fields calculated for reactants, transition state, and product of a chemical reaction, for example formaldehyde hydration.     

Update of the anharmonic force field parameters of the ozone molecule

A new set of spectroscopic constants of the ¹⁶O₃ molecule (ω_i, x_ij, y_ijk, γ^DD, _i^X, β_ij^X,…), which determine vibrational dependence of band centres and rotational parameters, is derived from recent accurate analysis of high-resolution experimental ro-vibrational spectra through the theoretical approach based on second-order perturbation expansions in normal coordinates accounting for Darling–Dennison resonance interactions. These values are used to update empirical values of anharmonic coefficients (k_ijl, k_ijlm) of the potential function expansion in normal coordinates. Quadratic f_rr, f_r, f_rr′, f as well as cubic f_rst and quartic f_rstl force constants in internal (bond lengths, bond angle) coordinates are also derived. A detailed discussion is devoted to the accuracy of parameter determination for each of four steps of calculations. It is emphasised that the conventional method based on the inversion of formulae of the perturbation theory gives the largest uncertainties at the last step of calculations: the determination of the anharmonic force field in internal coordinates.     

Normal Coordinate Analysis in Cartesian Space I. Planar Symmetric Xn Molecules

Normal coordinate analysis of X_n type molecules can be carried out in the Cartesian space as well as in the internal space. Force constants in Cartesian coordinates for aromatic compounds belonging to D_nh group are calculated. The force constants of benzene are evaluated from vibrational frequencies both in the ground state and the ¹B_1u excited state. The calculated frequencies of planar carbon vibration of annulene of any N are tabulated. The normal coordinates derived from the calculation of 10-annulene are roughly the same of naphthalene derived more elaborated by Scherer. The normal modes in 10-annulene are indeed good approximations to the ones in naphthalene. This conclusion is valid for the other aromatic compounds.     

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。     

Vibrational spectroscopy and normal-mode analysis of Fe(II) octaethylporphyrin

The normal-mode spectrum for the four-coordinated heme compound Fe(II) octaethylporphyrin, Fe(OEP), has been determined by refining force constants to the experimental Fe vibrational density of states measured with nuclear resonance vibrational spectroscopy (NRVS). Convergence of the calculated spectrum to the data was achieved by first imposing D4 symmetry on the model structure as well as the force constants, progressively including different internal coordinates of motion, then allowing the true Ci (or S2) point group symmetry of the C(i)1 Fe(OEP) crystal structure. The NRVS-refined normal modes are in good agreement with Raman and IR spectra at high frequencies. Prior density functional theory predictions for a model porphyrin are similar to the core modes computed with the best-fit force field, but significant differences between D4 and Ci modes underline the sensitivity of porphyrin Fe normal modes to structural details. Some differences between the Ci best fit and the NRVS data can be attributed to intermolecular contacts not included in the normal-mode analysis.