Sextic force field of nitrous oxide

The sextic force field in the curvilinear internal coordinates has been studied for the nitrous oxide molecule from the spectroscopic data of ¹⁴N₂¹⁶O, ¹⁴N¹⁵N¹⁶O, and ¹⁵N¹⁴N¹⁶O. The bands below 6600 cm⁻¹ have been used. The force constants in the internal coordinates are converted to those in dimensionless normal coordinates by two successive transformations. The vibration Hamiltonian matrix for each symmetry species of a given isotopic species has been constructed from the harmonic oscillator basis functions, and it is then diagonalized numerically to give the vibrational energy levels and the wavefunctions. The latter have been used for the evaluation of ratational constants. The least-squares refinement has been very successful in the present study, and it is shown that the general quartic force field supplemented by the quintic and sextic stretching diagonal force constants estimated from the Morse function, provided that the terms up to sextic are kept in the dimensionless normal coordinate space, well reproduces the spectroscopic constants such as the vibrational levels, rotational constants, l-type doubling constants, and centrifugal distortion constants. The spectroscopic constants of the isotopic molecules which are excluded from the refinement process are also in good agreement with the computed ones. The bond dissociation energies of the NN and NO bonds estimated from the present results have been critically examined.     

Anharmonic force field for methanol

An ab initio quartic anharmonic force field for methanol has been calculated at the equilibrium position using the CCSD(T) method for the structure and the harmonic potential energy surface, and the MP4(SDQ) method for the anharmonic part of the surface. A triple zeta basis set was employed with symmetrized curvilinear internal valence coordinates in all calculations. The internal coordinate force field constants have been transformed into force constants in the dimensionless normal coordinate representation for various isotopomers. Vibrational term values for CH₃OH, CH₃OD, CD₃OH, and CD₃OD have been obtained using second order perturbation theory. Particular care has been devoted to the inclusion of Fermi resonance interactions between different vibrational states. A good accuracy has been achieved in the calculation of the fundamentals for all the isotopomers, the mean absolute error being 5.8 cm^?1.     

The Degenerate Vibrations of BCl3, BBr3 and BI3 with Application of Keating Coordinates

The experimental works of vibrational spectroscopy and normal coordinate analyses for BCl₃, BBr₃ and BI₃ are reviewed extensively. Harmonic force fields of the E' species are produced using isotopic frequencies and Coriolis constants as additional data, respectively. The usefulness of Keating coordinates versus valence coordinates as basis of force field approximations is discussed. The conclusions are not unequivocal, but they go in favour of the Keating coordinates when the reliability of the different computations is taken into account. Boron trichloride is treated specifically in some detail. Final force fields are proposed for the title molecules with the aid of the mass influence on Coriolis constants.     

Vibrational Spectra and Normal Coordinate Analysis for an Imidazole Bridged Copper,Zinc Binuclear Complex

Abstract

The normal coordinate analysis of a model compound for Cu, Zn-SOD: [(dtma)CuImZn(dtma)]CIO₄ · 2.5H₂O (where dtma = 4-diethylenetriamineacctate; Im = imidazolate) has been carried out by using a Urey-Bradley force field. According to the molecular structure, 240 internal coordinates were established and 174 theoretical vibrational frequencies were calculated. Due to introducing an appropriate set of internal coordinates and force constants in the course of calculation, the calculated frequencies agree well with the observed values, with the average difference 4.40cm^?1 and the maximum deviation 24.2cm^?1 between them, although the structure of the title compound is complicated. Some structural and spectral properties are here discussed.     

Potential energy function of polyatomic molecules: Fourth-order approximation of the potential energy function of CO2: Spectroscopic constants of nine isotopic species

In this paper are given the values of the coefficients involved in the fourthorder expansion, with respect to mass-independent internal coordinates, of the potential energy function of CO₂. This function is applied to the computation of the vibrational energy levels of nine isotopic species of this molecule. A comparison between experimental and theoretical results is given along with the spectroscopic constants of these nine species. The coefficients appearing in the expansion of the potential energy function with respect to dimensionless normal coordinates are also given for each of these molecules.     

Boron Trifluoride: Application of the Keating Bendings to the Degenerate Vibrations

The harmonic force field of the E' species of BF₃ is studied. The Keating force field (KFF) is defined in analogy with the familiar VFF and CFF. In this connection three different coordinate sets are introduced. All of them contain bond stretchings. In addition, the valence coordinates include ordinary (Decius') bendings, the central coordinates nonbond stretchings, and Keating coordinates the Keating's bendings.

The experimental data of vibrational frequencies and Coriolis constants are reviewed extensively, as well as previous normal coordinate analyses. The different coordinate sets are tested for their usefulness as basis of force field approximations. For this purpose two different sets of experimental data are applied. The general conclusion goes in favour of the Keating coordinates.     

Generalized Approach to Relaxed Force Constants

The main purpose of potential constants, i. e., force and compliance constants, is to provide a quantitative understanding of bonding relationships. Compliance constants have been shown to possess several mathematical advantages over conventional force constants.^1-3 Compliance constants, however, are parameters which decrease in magnitude as bond strength increases; consequently, their use as bond strength parameters is not particularly satisfying. The desirability of a measure of bond strength which increases in magnitude as the bond becomes stronger, and at the same time possesses all the advantages of compliance constants is self evident. For this reason, the relaxed force constant T_ii=1/C_ii was introduced by Jones some time ago.⁴ In the present communication, this approach is generalized to include relaxed interaction force constants. A brief discussion of their meaning is also presented.     

Generalized Approach to Relaxed Force Constants

The main purpose of potential constants, i.e., force and compliance constants, is to provide a quantitative understanding of bonding relationships. Compliance constants have been shown to possess several mathematical advantages over conventional force constants.^1-3 Compliance constants, however, are parameters which decrease in magnitude as bond strength increases; consequently, their use as bond strength parameters is not particularly satisfying. The desirability of a measure of bond strength which increases in magnitude as the bond becomes stronger, and at the same time possesses all the advantages of compliance constants is self evident. For this reason, the relaxed force constant T_ii = 1/C_ii was introduced by a Jones some time ago.⁴ In the present communication, this approach is generalized to include relaxed interaction force constants. A brief discussion of their meaning is also presented.     

The internal coordinate path Hamiltonian; application to methanol and malonaldehyde

The internal coordinate path Hamiltonian is introduced for the study of the vibrations of molecules which have one large amplitude motion. The Hamiltonian is represented in terms of a one path coordinate and 3N—7 normal coordinates. The variational method is used to solve the Schrödinger equation. The molecules studied are methanol and malonaldehyde. For methanol the internal coordinate is a dihedral angle, for malonaldehyde it is the difference in the distances between the migrating hydrogen and the neighbouring oxygen atoms. For methanol there is little coupling between the path and the normal coordinates and so no complications were encountered in the calculations which used harmonic surfaces generated by density functional and M?ller—Plesset theory. Fundamental frequencies were predicted. Malonaldehyde is a different story. There is substantial coupling between the path coordinate and several of the normal coordinates. This introduces many complications: an anharmonic surface is essential and large variational configuration interaction calculations are essential for convergence. Furthermore, because the Coriolis terms require the evaluation of derivatives of both the nuclear coordinates and the normal coordinate eigenvectors along the path, great care must be taken with these numerical procedures. B3LYP predicts too low a transition state which overemphasizes the large Coriolis terms near the transition state. This may be one of the reasons why our fundamental vibrations are in poor agreement with observation. It is most encouraging that the tunnelling splitting is 58 cm^?1 (obs. 21.56 cm^?1), obtained with our quartic density functional surface.     

Calculation of the cubic symmetry force constants of methyl bromide and methyl chloride

The cubic symmetry force constants have been calculated for methyl bromide and methyl chloride through the method developed by Hoy et al. (Mol. Phys. 24, 1265–1290 (1972)). The spectroscopic constants recently reported in the literature have been utilized for the present analysis. Out of a total of 38 independent cubic force constants, 6 and 10 constants were constrained to zero for a methyl bromide and methyl chloride, respectively, in which a diagonal force constant of F₆₆₆ was included for both molecules. However, it is noted that those force constants which are only concerned with the A₁ symmetry coordinates have been determined independent of the constraint for both of these molecules.     

Harmonic Force Fields from Scaled SCF Calculations: Program ASYM40

We report an extended version of our normal coordinate program ASYM40, which may be used to transform Cartesian force constants from ab initio calculations to a force field in nonredundant internal (symmetry) coordinates. When experimental data are available, scale factors for the theoretical force field may then be optimized by least-squares refinement. The alternative of refining an empirical force field to fit a wide variety of data, as with the previous version ASYM20, has been retained. We compare the results of least-squares refinement of the full harmonic force field with least-squares refinement of only the scale factors for an SCF calculated force field and conclude that the latter approach may be useful for large molecules where more sophisticated calculations are impractical. The refinement of scale factors for a theoretical force field is also useful when there are only limited spectroscopic data. The program will accept ab initio calculated force fields from any program that presents Cartesian force constants as output. The program is available through Quantum Chemistry Program Exchange. Copyright 2000 Academic Press.     

Derivation of the nonrigid rotation-large-amplitude internal motion Hamiltonian of the general molecule

The nonrigid (effective) rotation-large-amplitude internal motion Hamiltonian (NRLH) of the general molecule with one or more large-amplitude vibrations has been derived to the order of magnitude κ²T_VIB. The derivation takes advantage of the idea of a nonrigid reference configuration and uses the contact transformation method as a mathematical tool. The NRLH has a form fairly similar to that of the effective rotation Hamiltonian of semirigid (i.e., normal) molecules. From a careful examination of the Eckart-Sayvetz conditions and of the Taylor expansions of the potential energy surface in terms of curvilinear displacement coordinates, three types of large-amplitude internal coordinates of different physical meaning (effective large-amplitude internal coordinates, real large-amplitude internal coordinates, and reaction path coordinates) are described. To test the ideas and the formulas the effective bending potential function of the C₃ molecule in its ground electronic and ground stretching vibrational state is calculated from the ab initio potential energy surface given by W. P. Kraemer, P. R. Bunker, and M. Yoshimine (J. Mol. Spectrosc. 107, 191–207 (1984)). The calculations were carried out by using either the effective or the real large-amplitude bending coordinate of C₃. The NRLH theory is compared to the nonrigid bender theory at a theoretical level as well as through the results of the test calculations.     

Torsional internal coordinates in normal coordinate calculations

Expressions for the s vectors of atoms whose motions constitute a torsional internal coordinate are derived by different methods and the relationships between the various forms appearing in the literature are demonstrated. The expressions for the simple case of a four-atom chain are extended to the general case, as exemplified by the alkanes. Certain errors and ambiguities in the treatment of torsional coordinates are noted. Torsional force constants for ethane, propane, isobutane, and neopentane are presented, being obtained by use of the prescribed methods in normal coordinate calculations.     

On effective molecular electronic charge densities and vibrational potential energy functions

Empirical relationships connecting equilibrium internuclear distances, harmonic force constants and atomic numbers for diatomic molecules which were presented in a recent communication by Anderson and Parr (Chem. Phys. Lett.10, 293 (1971)) are discussed in detail for 4b-6b and 1a-7b molecules as sample cases. It is shown how to estimate cubic and quartic force constants for these diatomic molecules using these relationships. Methods for estimating stretching force constants in polyatomic and excited state diatomic molecules are presented; sample cases CO₂, CS₂, OCS and the states of CO are treated.     

Nature of the Electron Excited States and Energy Transfer in Bichromophore Coumarin Molecules

Results of experimental and theoretical research for three bichromophore molecules, trans-stilbene-CH₂-coumarin 120 (I), 4-methylumbelliferone-CH₂-UC 17, and 4-(3-fluoro)-methylumbelliferone-CH₂-UC 17 (II, III), are presented. Schemes of photophysical processes in the bichromophore molecules based on quantum chemical calculations by the INDO method and theory of radiationless transitions in polyatomic organic molecules are suggested. After optical excitation to the strong donor absorption band, the fast internal conversion processes develop there. As a result, the molecule is found in the S ₁ ^* -state localized on the acceptor moiety. It is shown that a mechanism of intramolecular transfer energy in bichromophores different from that proposed by Förster may be realized. Excitation energy, initially located on D, will be transferred from the donor moiety to the acceptor chromophore in convenience of the internal conversion process. The intramolecular electronic energy transfer from energy donor to energy acceptor may be interpreted as the internal conversion process. The rate constants of internal conversion are calculated.     

Force constants for 3-chloropropyne and chloro-2-butyne

Normal coordinate calculations were carried out for H-C=C-CH₂Cl using a valence force field and the force constants obtained were transferred to CH₃-C=C-CH₂Cl. There seem to be small but significant differences in some of the force constants of the -CH₂Cl group of these two molecules. The vibrational assignment of McLachland [1] is confirmed, and the calculations show that the fundamental vibrations are relatively pure except for the C-C symmetric stretch and the skeletal bends.     

Determination of accurate semiexperimental equilibrium structure of proline using efficient transformations of anharmonic force fields among the series of isotopologues

The complete semiexperimental (SE) equilibrium structure of proline (45 degrees of freedom) is determined using the mixed estimation method. The cubic force fields for the parent and eight isotopologues of proline molecule are evaluated at the MP2-FC/cc-pVTZ level in Cartesian coordinates. The accuracy of the SE structure is verified by optimising the structure with the CCSD(T) model and a basis set of quadruple-ζ quality. A significantly more accurate equilibrium structure of proline is obtained when compared to the previous one. It is shown that the employed technique is efficient for the determination of SE equilibrium structures of rather large molecules. A simple transformation of anharmonic force fields between normal coordinate and Cartesian coordinate representations is proposed. The suggested technique allows efficient evaluation of the rotation–vibration interaction constants for a number of isotopologues, once the cubic force field of any species is found either in normal or Cartesian coordinates.     

Application of self-consistent-field ab initio calculations to organic molecules

The local symmetry force constants of propene have been calculated from extended (4–31 G) self-consistent-field ab initio energies. The previously developed scaling method was used to adjust seven scale factors on 84 observed frequencies of propene and deuterated analogues. The latter were taken from the literature. The average difference between observed and calculated frequencies amounted to 8·3 cm^-1 or 0·63 per cent. The stretching force constant of the carbon-carbon single bond was found to be 0·3–0·4 mdyn Å^-1 larger than those of ethane and propane. Force constants of the CH₃ groups in the series: ethane, propane, propene, methanol and dimethyl ether, written in local symmetry coordinates, seem to be transferable within about 2 per cent. Individual CH bond stretching force constants, written in internal coordinates, show significant chemical variations.