Canonical Force Field Research Articles

Quartic canonical force field in curvilinear internal coordinates for XY3 (D3h) molecules. The case of the BH3 molecule.

Using the canonical force field theory, expressions of quadratic, cubic, and quartic canonical force constants are obtained for XY3 (D3h) molecules in curvilinear redundant coordinates, i.e., simple valence internal coordinates (VICs), in terms of force constants in normal coordinates and in independent symmetry coordinates. To carry out this task, it was previously necessary to obtain for the first time the non-linear redundancy relation and the corresponding orthogonal projection onto the pure vibrational manifold for XY3 (D3h) molecules corresponding to a set of seven VICs. As an application, the quartic canonical force field in curvilinear redundant internal coordinates of BH3 is determined from ab initio force fields in normal coordinates calculated at the coupled-cluster singles and doubles level with perturbative treatment of the triples in conjunction with a triple- and quadruple-ζ size basis set. This anharmonic force field so obtained for the borane molecule, and in general for XY3 (D3h) molecules, is uniquely defined (therefore in an unambiguous form) and depending on the same number of parameters, i.e., force constants, when independent coordinates (natural or symmetry) are used in its description.

The theory of the canonical force field revisited

In a previous Letter, Kuczera’s theory of the canonical force field was generalized to the case of redundant curvilinear internal coordinates related by non-linear constraints. A central issue in this theory is the projection from the space of internal coordinates onto the pure vibrational manifold. In this Letter we present a new mathematical treatment of the projection that solves some problems of inconsistency that have arisen when applying the theory to molecules with a central atom. In addition to solving these problems, this treatment greatly simplifies the attainment of the projection and, consequently, the calculation of canonical force constants.

Canonical force field theory in terms of curvilinear internal coordinates: Application to the methane molecule

This Letter generalizes the Kuczera’s theory of the vibrational canonical force field in order to obtain an unambiguous and uniquely defined expression for the anharmonic force field in terms of curvilinear internal coordinates. By using this generalization it has been shown mathematically that the canonical force constants could be transferred between molecules with the same geometrical structure. As illustration, the theory is used to obtain the expressions for the quadratic and cubic canonical force constants of the methane molecule.

The concept of canonical molecular force field

The purpose of this paper is to show the concept of vibrational canonical force field from an intuitive and heuristic point of view. The physical meaning and the mathematical properties of this force field are illustrated by means of the most-simple case of redundant coordinates, i.e. a system having one vibrational degree of freedom whose vibrational motion is described by means of two redundant coordinates. The results obtained in this example are generalized to the case of a system with several degrees of freedom by means of the matrix formulation. This generalization allows to obtain results that are valid for any number of degrees of freedom.

Refined, scaled and canonical force fields for the cis- and trans-3-fluorostyrene conformers. An interplay between theoretical calculations, IR/Raman and INS data

Download options Please wait... Supplementary files Figure S1 JPG (210K) Figure S2 JPG (221K) Figure S3 JPG (200K) Figure S4 JPG (199K) Figure S5 JPG (199K) Figure S6 JPG (201K) Tables S1–S5 DOC (375K) Article information DOI https://doi.org/10.1039/B203915J Article type Paper Submitted 22 Apr 2002 Accepted 26 Jul 2002 First published 06 Sep 2002 Download Citation Phys. Chem. Chem. Phys., 2002,4, 4890-4901 BibTex EndNote MEDLINE ProCite ReferenceManager RefWorks RIS Permissions Request permissions Refined, scaled and canonical force fields for the cis- and trans-3-fluorostyrene conformers. An interplay between theoretical calculations, IR/Raman and INS data J. M. Granadino-Roldán, M. Fernández-Gómez, A. Navarro, L. M. Camus and U. A. Jayasooriya, Phys. Chem. Chem. Phys., 2002, 4, 4890 DOI: 10.1039/B203915J To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page. If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given. If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page. Read more about how to correctly acknowledge RSC content. Social activity Tweet Share Search articles by author J. M. Granadino-Roldán M. Fernández-Gómez A. Navarro L. M. Camus U. A. Jayasooriya

Transferability and Physicochemical Interpretation of Canonical Force Fields in Redundant Internal Coordinates: Pyridazine and 3,6-Dichloropyridazine

The behavior of various force fields for pyridazine and 3,6-dichloropyridazine coming from different origins (i.e., HF/6-31G*, MP2/6-311G**, BLYP/6-31G*, B3LYP/6-31G* previously scaled) and empirical force fields transferred from the benzene molecule is investigated. These potentials are subjected to a linear least-squares refinement with the available experimental information considered as observed data. Moreover, the transferability properties of the force fields for these related molecules are analyzed. From the refined force fields which gave the most satisfactory results in the fitting procedure, the physicochemical meaning of the force constants in terms of redundant simple internal coordinates in the unambiguous canonical form is studied. Although the results are not completely decisive for the pyridazine series, significant conclusions are drawn pertaining to their force fields, some of which are calculated for the first time. First, the utility of canonical force fields is shown through the force...

Unambiguous formalism of molecular vibrations: Use of redundant coordinates and canonical matrices

This paper introduces a new approach to the problem of describing molecular vibrations in redundant valence coordinates. A consistent definition for canonical force field, which is different of that by Kuczera and Pupyshev et al., is outlined. This new definition is also generalized to other matrices like kinetic-energy matrices and transformation matrices between different sets of vibrational coordinates. The importance of such canonical matrices follows from the fact that they are uniquely determined and allow us to consider the redundant coordinates as though they were independent.

Some properties of regular and canonical force fields

A novel class of force-constant matrices which use redundant coordinates (regular force fields) is defined. The basic properties of this new class, which represents a generalization of the canonical force field, are studied. Some pecularities of the canonical force field are also discussed, including their extreme properties among the regular force fields as well as other matrices of force constants, and some analogs to the equations of motion in independent variables. The physical meanings of the canonical and regular force fields are considered, with special attention given to the case of cartesian vibrational coordinates.