N. Mohan

Approximation methods for the calculation of force constants of a general valence force field in polyatomic molecules - a review

Abstract The purpose of this review is to make a survey of the various approximation methods for the calculation of force constants in polyatomic molecules using a general valence force field model. These are the solutions for a molecule satisfying at least the mathematical requirements of the inverse eigenvalue problem in the familiar Wilsons G F -formalism. The mathematical basis of these solutions is studied in detail with a view to giving their physical properties, significance and hence the limitations in their practical application.

Molecular constants for NSCl and NSF

Abstract The complete infrared spectrum of gaseous NSCl, including the hitherto unobserved ν 3 , is reported. A set of force constants for gaseous NSCl consistent with a number of pieces of independent data such as the isotopic shifts ( 14 N 32 S 35 Cl, 15 N 32 S 35 Cl, 14 N 32 S 37 Cl, 15 N 32 S 37 Cl, 14 N 34 S 35 Cl and 15 N 34 S 35 Cl), centrifugal distortion constants ( 14 N 32 S 35 Cl), and the inertia defect ( 14 N 32 S 35 Cl) has been computed. Also, the force field of NSF has been redetermined using the vibrational frequencies and the centrifugal distortion constants.

On the Application of Perturbation Theory for the Calculation of Molecular Constants due to Small Mass Changes and on the Determination of Force Constants from Very Heavy Isotope Substitution

The first order perturbation theory has been used to develop the expressions for studying the mass effect on Coriolis coupling constants in isotopically substituted molecules. The corresponding treatment reported by Wilson, Decius, and Cross for the calculation of isotopic frequency shifts has been applied to a large number of molecules with heavy and very heavy atom isotopic substitution, for which the experimental data have been published in recent years. The use of a simple method (L matrix approximation) for the calculation of isotope shifts in molecules with small mass coupling, from the knowledge of the geometrical parameters only, is suggested. The results obtained using the perturbation theory for the calculation of Δv and Δζ are found to be quite encouraging. An outline of the utility of data on very heavy isotopic substitution for the determination of force constants is given with illustrative examples.

A note on the comparison of the high low frequency separation with other apprixmation methods for the calculation of force constants

Abstract The high low frequency separation method is used to describe the different approximation methods for solving n =2 secular determinants. Extension of this procedure to higher-order secular determinants is indicated.

On the matrix formulation of absolute infrared intensities

Abstract The given matrix formulation of the infrared intensities has been used to discuss some properties of the intensities and to derive the Jacobians related to the force constants. Mass effect on the intensities in isotopically substituted molecules is studied using the first order perturbation theory.

Integrated infra-red intensities: Relation to other molecular constants and a simple isotopic sum rule

Some new relations connecting the infra-red intensities to other molecular constants, such as Coriolis constants, mean square amplitudes etc., are reported. All these relations have been derived using the new matrix formulation reported recently. The extremal properties of (∂μ/∂Si )2 and (∂μ/∂6S i)2 are also given. A new isotopic sum rule involving the changes in integrated absorption intensities for symmetric substitutions is also derived. This rule, which is valid for each band separately, is of the form (ΔA (a))i=(ΔA (pp))i, where Ai is the integrated intensity of the ith band and (a) and (pp) refer to mono and multi-substitutions respectively.

Isotopic shifts due to heavy and very heavy atom substitution: a new sum rule and on the sensitivity of force constants to very small frequency shifts

Abstract A new isotopic sum rule involving the shifts in the squares of the vibrational frequencies corresponding to any single vibration (i.e. Δγ nn k ) pertaining to the substitution A p B q C r ⋯ / + A p + B q + C r ⋯ in terms of the corresponding quantities (i.e.Δγ k n ) representing cases where each set of atoms is substituted symmetrically by the isotopic one in succession (e.g. A p B q C r / + A p B q C r , A p B q C r / A p + B q C r , etc.) is given. The sum rule is of the form and holds good (in general) for symmetric substitution involving heavy and very heavy atoms. This serves as a very simple proof (simpler than the Teller-Redlich rule) of the experimental data. An explicit form of the Jacobian ∂ F u /∂ (Δγ/γ) governing the errors in the values of the force constant F 11 in n = 2 cases (γ 1 > γ 2 ) due to uncertainties in the isotopic shifts is presented. A theoretical proof of the important and unexpected fact that even rough values of, for example, Δ v stretch ≈ 3 ± 1 cm −1 give, for molecules exhibiting low frequency stretching fundamentals ( −1 ), reliable values of the force constants is derived.

On the calculation of exact force constants for coordination compounds from metal isotope shifts: The vibrational spectra of [104PdCl6]2−, [110PdCl6]2−, [116SnCl6]2− and [124SnCl6]2−

Abstract It has been shown for many transition metal coordination compounds for which the vibrational frequencies are approximately below 350 cm −1 that the exact value of the metal-ligand bond stretching force constant (important in understanding the nature of the bonding) can be calculated from measured isotope shifts (e.g. metal isotope or 35 Cl/ 37 Cl), even if the isotope shift can be measured only roughly. This follows from the fact that the differences λ i - λ j (λ i ∼ ν 2 i ) in n = 2 cases are very small in the above mentioned cases. From our studies, it is found that even rough values of Δ ν ≈ 4 cm −1 (stretch) accurate to ± 1.0 cm −1 (25 % error) can be used to derive reliable values of the stretching force constant when λ i - λ i ⪅0.085mdyn/(amu A). A theoretical interpretation of this effect in terms of the Jacobians ∂(Δλ i /λ i )/∂ F ij has been given. The method can also be extended to higher dimensional cases (calculation of the pseudo-exact force constants). Some exact force constants derived for the first time from the newly measured metal isotope shifts are also reported. Thus in the case of [PdCl 6 ] 2− and [SnCl 6 ] 2− for example, the measured isotope shifts in ν 3 ( F 1 u of 3·5 ± 0·5 cm −1 ( 104 Pd/ 110 Pd) and 3·2 ± 0.8 cm −1 ( 116 Sn/ 124 Sn) respectively lead to the following values of F 33 ( F 1 u ): [PdCl 6 ] 2− 1·80 ± 0·11 mdyn/A and [SnCl 6 ] 2− 1·55 ± 0·10 mdyn/A.

On the calculation of force constants from mean amplitudes of vibration and isotope effect on mean amplitudes

The extremal properties of both bonded and nonbonded mean amplitudes of vibration are discussed, with a view to see beforehand if real solutions for the force constants could be obtained using such data. A detailed study of the effect of small mass changes in isotopically substituted molecules on mean amplitudes of vibration is made using the first order perturbation theory. Several interesting facts are explained with the help of this approach. The utility of other simple, approximate formulas in this regard is tested using specific examples.

Orbital valency force field: a good approximation to general valence force field for XY4 (Td) and XY3 (D3h) type molecules

Abstract Analytical expressions are derived for determining the symmetry force constants of XY 4 (T d ) and XY 3 (d 3h ) typs molecules in the orbital valency force field model, which proves to be very useful in the interpretation of the structure and bonding in those molecules. The results obtained are compared with the values of symmetry force constants determined using additional data. The orbital valency force field values are generally found to be in good agreement with those of the general valence force field model. The physical significance of internal force constants is discussed and a constraint for the symmetry force constants is given.