Yurii N. Panchenko

Vibrational spectra and scaled quantum-mechanical molecular force fields☆

Abstract A number of questions connected with the use of scaled quantum-mechanical force fields in interpreting molecular vibrational spectra are considered briefly. The Pulay method of scaling (congruent transformation of the force constant matrix) is noted to be applicable in the case where the relative accuracies of the 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 Hartree–Fock limit. Then it is possible to carry out its correction, preserving to a maximum the features inherent to the molecule under investigation. Several examples of predicting the vibrational spectra of isotopomers, rotational isomers, and related compounds are given. Unlike using force fields obtained by the traditional method of solving the inverse vibrational problem and the additive scheme for transferring the force constants, scaled quantum-mechanical force fields make it possible to perform well-grounded theoretical vibrational analyses of all the related compounds of a molecule.

An ab initio structural and vibrational analysis of gauche,trans,trans- and gauche,cis,trans-hexa-1,3,5-trienes

The results of complete geometry optimizations of the high energy stable gauche,Trans,trans- and gauche,Cis,trans- rotamers of hexa-1,3,5-trienes are reported at the RHF/6-31G//RHF/B-31G level. The angles of rotation around one of the single C-C bonds are found to be 33.7° and 45.5°, respectively. The corresponding harmonic force fields of these molecules are also reported at this level and corrected using scale factors transferred from buta 1,3-diene. Aspecial scale factor was used for the central C=C double bond stretching coordinate to take into account vibronic coupling. The theoretical vibrational frequencies, calculated with the scaled quantum mechanical (SQM) force fields, allow a complete interpretation of the experimental vibrational spectra of these molecules.

Predictive Abilities of Scaled Quantum Mechanical Molecular Force Fields: Application to 1,3-Butadiene

The positions of some IR bands of the s-trans-1,3-butadiene-h6 and -1,1,2-d3 isotopomers in the gas phase have been measured using a Brucker IFS 120 HR spectrometer with a resolution of 2 cm−1. The structural parameters of the s-trans- and s-gauche-1,3-butadiene conformers were optimized completely at the MP2/6-31G* theoretical level and their MP2/6-31G*//MP2/6-31G* quantum mechanical force fields (QMFFs) were calculated. Using only the experimental vibrational frequencies of s-trans-1,3-butadiene-h6 the QMFF of the s-trans conformer was corrected by Pulays scaling method (eight scale factors were involved). The scaled QMFF was used to calculate the mean vibrational amplitudes and the Coriolis coupling constants of s-trans-1,3-butadiene-h6 and the vibrational frequencies of 12 of its deuterated isotopomers. The set of scale factors obtained for correction of the s-trans QMFF was transferred to the QMFF of the s-gauche conformer. Its theoretical vibrational spectrum and those of some deuterated and C13 isotopomers were calculated. The ability of this scaling approach (transferring of scale factors) to predict the vibrational frequencies of rotational conformers and their isotopomers, as well as other molecular characteristics, and to permit detection of perturbations of the experimental bands are discussed.

All-trans- and t,T,t,C,t,T,t-deca-1,3,5,7,9-Pentaenes: Ab Initio Structures, Vibrational Analyses, and Some Regularities in the Series of Related Molecules

Total geometry optimization and calculation of the force constants for all-transand t,T,t,C,t,T,tdeca-1,3,5,7,9-pentaene were carried out at the ab initio, HF/6-31G level. The HF/6-31G//HF/ 6-31G force fields were modified using empirical scale factors transferred from trans-buta-1,3-diene augmented by an additional scale factor for the central formal carbon-carbon double bond coordinates (determined previously for all-trans-hexa-1,3,5-triene). The total number of scale factors was seven. The vibrational problems for both decapentaenes were solved using the respective scaled HF/6-31G//HF/6-31G force field. Infrared intensities and Raman activities were calculated from the unscaled HF/6-31G//HF/6-31G force fields. Complete assignment of all the fundamental vibrational frequencies is given. Geometrical parameters, vibrational frequencies and force constants are compared with the corresponding values of buta-1,3-diene, hexa-1,3,5-triene and octa-1,3,5,7-tetraene. Regularities in the properties of this molecular series are discussed. Special attention is given to the possibility of using the vibrational spectra for detection of distortions from the regular trans structure of these oligoenes.

Philosophy of scaling the quantum mechanical molecular force field versus philosophy of solving the inverse vibrational problem

Abstract The peculiarities characterising the traditional approach used in calculational vibrational spectroscopy and the approach based on using scaled quantum mechanical force fields are considered. Some results on the determination of the equilibrium geometry of benzene in both the harmonic approximation and in the approximation taking into account the kinematic and dynamic anharmonicity corrections by solving the inverse vibrational problem are discussed. Using the quantum mechanical force fields of the C 2 F 6 molecule, calculated at three different theoretical levels as an example, the results of the determination of scale factors by different mathematical techniques are compared.

All ab initio vibrational study of rotational isomerism in oxalyl fluoride, OCF-CFO, and acryloyl fluoride, OCF-CHCH2

Abstract Results of complete geometry optimizations of the rotational isomers of oxalyl fluoride and acryloyl fluoride at a variety of computational levels are reported. These molecules are found to have planar s-trans (anti) and s-cis (syn) conformations. The RHF/6-31G//RHF/6-31G harmonic force fields of these molecules are calculated as analytical second derivatives, and the vibrational frequencies are obtained from the corresponding scaled quantum mechanical force fields. Some reassignments of fundamental frequencies are suggested.

Inverse isotopic shifts in the vibrational spectra of the isotopomers of methanimine, H2C NH

Abstract The inverse isotopic shifts (i.e. the inversion of assignments) in the vibrational spectra of the isotopomers of methanimine are analyzed by calculation of their vibrational spectra using quantum mechanical methods. The completely optimized structure and harmonic force field of methanimine are reported at the RHF/6-31G*, RHF/6-31G**, MP2/6-31*, MP2/6-31G**, MP4(SDTQ)/6-31G* and MP4(SDTQ)/6-31G** levels of computation. Sets of empirical scale factors for the calculated force fields are derived and the corresponding scaled quantum mechanical force fields are computed. The effect of varying the computational level for the scale factors and force fields is discussed. The theoretical vibrational frequencies and their intensities for ten isotopomers of methanimine, obtained using the scaled MP4(SDTQ)/6-31G** and unscaled MP2/6-31G** force fields, respectively, are also reported.

Vibrational anharmonicity and scaling the quantum mechanical molecular force field

Abstract The interrelationship between the scale factors obtained using Pulays method from the anharmonic and the harmonized vibrational frequencies of a light molecule and its heavy analogue is considered in terms of a Morse potential. The determination of the scale factors from the vibrational frequencies of a light molecule is shown to result in smaller deviations of the calculated and experimental vibrational frequencies of its heavy analogue than those of the reverse procedure. In this context, the extent to which Dennisons rule is satisfied is also discussed.

Ab initio vibrational analysis of trans- and gauche-2,3-dimethylbuta-1,3-diene

Abstract The harmonic force fields of the s- trans ( anti ) and gauche conformers of 2,3-dimethylbuta-1,3-diene have been calculated ab initio at the RHF/6-31G//RHF/6-31G level. These force fields have been further refined using scale factors transferred from analogous calculations at the RHF/6-31G level for s- trans -buta-1,3-diene and ethane. A complete assignment of the experimental vibrational frequencies is given. Regularities in the vibrational spectra of the stable conformers of buta-1,3-diene, isoprene (2-methylbuta-1,3-diene) and 2,3-dimethylbuta-1,3-diene are discussed.

Some properties of regular and canonical force fields

Abstract 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.