Force fields and vibrational spectroscopy: A discussion on status and future prospects

A start is given for a discussion about the use of force fields for describing and interpreting molecular geometries, relative energies and vibrational spectra. The development of modern, generic force fields, e.g. Class II force fields, has diminished the necessity for specific force fields, and they should be applied in far more cases than they are being used now.     

Infrared and Raman spectra, ab initio calculations and vibrational assignment for 3-fluoro-1-butyne

The infrared (3500-80 cm⁻¹) and Raman (3500-20 cm⁻¹) spectra of 3-fluoro-1-butyne, CH₃CHFCCH, have been recorded for the gas and solid. Additionally, the Raman spectrum of the liquid has also been recorded to aid in the vibrational assignment. Ab initio electronic structure calculations of energies, geometrical structures, vibrational frequencies, infrared intensities, Raman activities and the potential energy function for the methyl torsion have been calculated to assist in the interpretation of the spectra. The fundamental torsional mode is observed at 251 cm⁻¹ with a series of sequence peaks falling to lower frequency. The three-fold methyl torsional barrier is calculated to be 1441 ± 20 cm⁻¹ (4.12 ± 0.06 kcal mol⁻¹) where the uncertainty is partly due to the uncertainty in values of the V₆ term. A complete vibrational assignment is proposed based on band contours, relative intensities, and ab initio predicted frequencies. Several fundamentals are significantly shifted in the condensed phases compared to values in the vapor state.     

Raman and infrared spectra, conformational stability, barriers to internal rotation, vibrational assignment, and ab initio calculations of 3-methyl-3-butenenitrile

The Raman (3500-30 cm⁻¹) spectra of liquid and solid and the infrared (3500-40 cm⁻¹) spectra of gaseous and solid 3-methyl-3-butenenitrile, CH₂C(CH₃)CH₂CN, have been recorded. Both cis and gauche conformers have been identified in the fluid phases but only the cis form remains in the solid. Variable temperature (−55 to −100 °C) studies of the infrared spectra of the sample dissolved in liquid xenon have been carried out. From these data, the enthalpy difference has been determined to be 163±16 cm⁻¹ (1.20±0.19 kJ mol⁻¹), with the cis conformer the more stable rotamer. It is estimated that there is 48±2% of the gauche conformer present at  25°C. A complete vibrational assignment is proposed for the cis conformer based on infrared band contours, relative intensities, depolarization ratios and group frequencies. Several of the fundamentals for the gauche conformer have also been identified. The vibrational assignments are supported by normal coordinate calculations utilizing ab initio force constants. Complete equilibrium geometries have been obtained for both rotamers by ab initio calculations employing the 6-31G(d), 6-311G(d,p), 6-311+G(d,p) and 6-311+G(2d,2p) basis sets at the levels of restricted Hartree-Fock (HF) and/or Møller-Plesset perturbation theory to the second order (MP2). Only with the 6-311G(2d,2p) and 6-311G(2df,2pd) basis sets with or without diffuse functions is the cis conformer predicted to be more stable than the gauche form. The potential energy terms for the conformational interchange have been obtained at the MP2(full)/6-311+G(2d,2p) level, and compared to those obtained from the experimental data. The results are discussed and compared to the corresponding quantities obtained for some similar molecules.     

Infrared, and Raman spectra, conformational stability, normal coordinate analysis, ab initio calculations, and vibrational assignment of 1-chlorosilacyclobutane

The infrared spectra (3500–40 cm⁻¹) of gaseous and solid and the Raman spectra (3500–30 cm⁻¹) of liquid and solid 1-chlorosilacyclobutane, c-C₃H₆SiClH, have been obtained. Both the axial and equatorial conformers with respect to the chlorine atom have been identified in the fluid phases. Variable temperature (−105 to −150°C) studies of the infrared spectra of the sample dissolved in liquid krypton have been carried out. From these data, the enthalpy difference has been determined to be 211±17 cm⁻¹ (2.53±0.21 kJ/mol), with the equatorial conformer being the more stable form and the only conformer remaining in the annealed solid. At ambient temperatures, approximately 26% of the axial conformers are present in the vapor phase. A complete vibrational assignment is proposed for the equatorial conformer, and many of the fundamentals of the axial conformers have also been identified. The vibrational assignments are supported by normal coordinate calculations utilizing ab initio force constants. Complete equilibrium geometries, conformational stabilities, harmonic force fields, infrared intensities, Raman activities, and depolarization ratios have been determined for both rotamers by ab initio calculations employing the 6-31G(d) basis set at the levels of restricted Hartree–Fock (RHF) and/or Moller–Plesset (MP) to second order. Structural parameters have also been obtained using MP2/6-311+G(d,p) ab initio calculations. The r₀ parameters for both conformers are obtained from a combination of the ab initio predicted values and the twelve previously reported microwave rotational constants. The results are discussed and compared to those obtained for some similar molecules.     

Theoretical modeling of infrared spectra of benzoic acid and its deuterated derivative

Theoretical simulation of the ν_s stretching band is presented for benzoic acid and its OD derivative at 300 K. The simulation takes into account an adiabatic coupling between the high-frequency O–H(D) stretching and the low-frequency intermolecular OO stretching modes, linear and quadratic distortions of the potential energy for the low-frequency vibrations in the excited state of the O–H(D) stretching vibration, resonance interaction between the two hydrogen bonds in the dimer, and Fermi resonance between the fundamental ν OH(D) stretching and the overtone of the δ O–H(D) bending vibrations.

Infrared, far-infarared, Raman and low-frequency Raman spectra of the polycrystalline benzoic acid and its deuterated form have been measured. The geometry and experimental frequencies are compared with the results of our B3LYP/6-311++G** and B3LYP/cc-pVTZ calculations.     

Infrared and Raman spectra, conformational stability, normal coordinate analysis, ab initio calculations, and vibrational assignment of 1-fluoro-1-methylsilacyclobutane

The infrared (3500–40 cm⁻¹) spectra of gaseous and solid 1-fluoro-1-methylsilacyclobutane, c-C₃H₆SiF(CH₃), have been recorded. Additionally, the Raman spectrum (3500–30 cm⁻¹) of the liquid has been recorded and quantitative depolarization values have been obtained. Both the axial and equatorial (with respect to the methyl group) conformers have been identified in the fluid phases. Variable temperature (−55–−100°C) studies of the infrared spectra of the sample dissolved in liquid xenon have been carried out. From these data, the enthalpy difference has been determined to be 267±10 cm⁻¹ (3.19±0.12 kJ mol⁻¹), with the axial conformer being the more stable form and the only conformer remaining in the polycrystalline solid. A complete vibrational assignment is proposed for the axial conformer and many of the fundamentals for the equatorial conformer have also been identified. The vibrational assignments are supported by normal coordinate calculations utilizing ab initio force constants. Complete equilibrium geometries have been determined for both rotamers by ab initio calculations employing the 6-31G* and 6-311++G** basis sets at the levels of restricted Hartree–Fock (RHF) and/or Moller–Plesset (MP) to second order. The results are discussed and compared to those obtained for some similar molecules.     

Ab initio and DFT calculations for the structure and vibrational spectra of cyclopentene and its isotopomers

Ab initio calculations using the MP2/cc-pVTZ basis set do an excellent job of predicting the inversion barrier (247 vs. 232 cm⁻¹) and dihedral angle (26°) of cyclopentene. DFT calculations also do an excellent job of predicting the vibrational frequencies of the d₀, d₁, d₄, and d₈ isotopomers. They have also allowed the reassignments of several of the vibrational frequencies.     

Infrared and Raman spectra, conformational stability, ab initio calculations of structure, and vibrational assignment of 2-hexyne

The infrared spectra (3500–50 cm⁻¹) of the gas and solid and the Raman spectra (3500–50 cm⁻¹) of the liquid and solid have been recorded for 2-hexyne, CH₃–CC–CH₂CH₂CH₃. Variable temperature studies of the infrared spectrum (3500–400 cm⁻¹) of 2-hexyne dissolved in liquid krypton have also been recorded. Utilizing four anti/gauche conformer pairs, the anti(trans) conformer is found to be the lower energy form with an enthalpy difference of 74±8 cm⁻¹ (0.88±0.10 kJ/mol) determined from krypton solutions over the temperature range −105 to −150 °C. At room temperature it is estimated that there is 42% of the anti conformer present. Equilibrium geometries and energies of the two conformers have been determined by ab initio (HF and MP2) and hybrid DFT (B3LYP) methods using a number of basis sets. Only the HF and DFT methods predict the anti conformer as the more stable form as found experimentally. A vibrational assignment is proposed based on the force constants, relative intensities, depolarization ratios from the ab initio and DFT calculations and on rotational band contours obtained using the calculated equilibrium geometries. From calculated energies it is shown that the CH₃ group exhibits almost completely free rotation which is in agreement with the observation of sub-band structure for the degenerate methyl vibrations from which values of the Coriolis coupling constants, ζ, have been determined. The results are compared to similar properties of some corresponding molecules.     

An experimental and theoretical study of molecular structure and vibrational spectra of 2-chloronicotinic acid by density functional theory and ab initio Hartree–Fock calculations

In this work, the Fourier transform Raman and Fourier transform infrared spectra of 2-chloronicotinic acid (2-CNA) are recorded in the solid phase. The molecular geometry, vibrational frequencies, infrared intensities and Raman scattering activities of 2-CNA in ground state have been calculated by using ab initio Hartree–Fock (HF) and density functional (B3LYP and B3PW91) methods with 6-31G(d) and 6-311G(d) basis sets level. On the basis of the comparison between calculated and experimental results and the comparison with related molecule, assignments of fundamental vibrational modes are examined. The optimized geometric parameters (bond lengths and bond angles) obtained by using HF show the best agreement with the experimental values of 2-CNA. Comparison of the observed fundamental vibrational frequencies of 2-CNA and calculated results by density functional (B3LYP and B3PW91) and Hartree–Fock methods indicates that B3LYP is superior to the scaled Hartree–Fock and B3PW91 approach for molecular vibrational problems.     

Infrared and Raman spectra, conformational stability, ab initio calculations and vibrational assignment for 1,2-pentadiene (ethyl allene)

The infrared (3500-50 cm⁻¹) and Raman (3500-20 cm⁻¹) spectra of 1,2-pentadiene, H₂C=C=C(H)CH₂CH₃ (ethyl allene), have been recorded for both the gaseous and solid states. Additionally, the Raman spectrum of the liquid has been obtained with qualitative depolarization values. In the fluid phases both the cis and gauche conformers have been identified, with the gauche rotamer being the predominant form although it may not be the conformer of lowest energy. In the solid state only the cis conformer remains after repeated annealing of the crystal. The asymmetric torsion of the cis conformer is observed as a series of Q-branch transitions beginning at 103.4 cm⁻¹ and falling to lower frequency. An estimate of the potential function governing conformer interconversion is provided. A complete assignment of the normal modes for the cis conformer is given and several of the fundamentals are assigned for the gauche rotamer. Ab initio electronic structure calculations of energies, conformational geometries, vibrational frequencies, and potential energy functions have been made to complement and assist the interpretation of the infrared and Raman spectra. In particular, the transitions among torsional energy levels for both the symmetric (methyl) and asymmetric (ethyl) motions have been calculated. The results are compared to the corresponding quantities for some similar molecules.     

Far infrared spectra, conformational equilibria, vibrational assignments, ab initio calculations and structural parameters for 2-bromoethanol

The far infrared spectrum from 370 to 50 cm⁻¹ of gaseous 2-bromoethanol, BrCH₂CH₂OH, was recorded at a resolution of 0.10 cm⁻¹. The fundamental O–H torsion of the more stable gauche (Gg′) conformer, where the capital G refers to internal rotation around the C–C bond and the lower case g to the internal rotation around the C–O bond, was observed as a series of Q-branch transitions beginning at 340 cm⁻¹. The corresponding O–H torsional modes were observed for two of the other high energy conformers, Tg (285 cm⁻¹) and Tt (234 cm⁻¹). The heavy atom asymmetric torsion (rotation around C–C bond) for the Gg′ conformer has been observed at 140 cm⁻¹. Variable temperature (−63 to −100°C) studies of the infrared spectra (4000–400 cm⁻¹) of the sample dissolved in liquid xenon have been recorded. From these data the enthalpy differences have been determined to be 411±40 cm⁻¹ (4.92±0.48 kJ/mol) for the Gg′/Tt and 315±40 cm⁻¹ (3.76±0.48 kJ/mol) for the Gg′/Tg, with the Gg′ conformer the most stable form. Additionally, the infrared spectrum of the gas, and Raman spectrum of the liquid phase are reported. The structural parameters, conformational stabilities, barriers to internal rotation and fundamental frequencies have been obtained from ab initio calculations utilizing different basis sets at the restricted Hartree–Fock or with full electron correlation by the perturbation method to second order. The theoretical results are compared to the experimental results when appropriate. Combining the ab initio calculations with the microwave rotational constants, r₀ adjusted parameters have been obtained for the three 2-haloethanols (F, Cl and Br) for the Gg′ conformers.     

Matrix and ab initio infrared spectra of germanium carbonyls

Germanium monocarbonyl has been prepared by high-temperature vaporization of Ge with excess carbon powder or CO co-condensation and trapped in various matrices at 12 K. Fourier transform infrared spectra, ab initio (MP2 and CISD) and density function (Becke3LYP) calculations suggested a linear species with the formula GeCO. A weak feature appearing only in annealed N₂ and CO matrices containing GeCO has tentatively been assigned to germanium dicarbonyl on grounds of isotopic substitution and theoretical calculations. SCF and CI methods predict a bent structure for this complex.     

Vibrational spectra, conformations, ab initio calculations and vibrational assignments of 3-pentyn-2-ol

The infrared spectra of 3-pentyn-2-ol, CH₃CCCH(OH)CH₃, have been recorded as a vapour and liquid at ambient temperature, as a solid at 78 K in the 4000–50 cm⁻¹ range and isolated in an argon matrix at ca. 5 K. Infrared spectra of the solid phase at 78 K were obtained before and after annealing to temperatures of 120 and 130 K. The IR spectra of the solid were quite similar to that of the liquid.

Raman spectra of the liquid were recorded at room temperature and at various temperatures between 295 and 153 K. Spectra of an amorphous and annealed solid were recorded at 78 K. In the variable temperature Raman spectra, some bands changed in relative intensity and were interpreted in terms of conformational equilibria between the three possible conformers. Complete assignments were made for all the bands of the most stable conformer in which OH is oriented anti to C₁(a_Me). From various bands assigned to a second conformer in which OH is oriented anti to H_gem(a_H), the conformational enthalpy differences was found to be between 0.4 and 0.8 kJ mol⁻¹. The highest energy conformer with OH anti to C₃(a_C) was not detected.

Quantum-chemical calculations have been carried out at the MP2 and B3LYP levels with a variety of basis sets. Except for small basis set calculations for which the a_H conformer had slightly lower energy, all the calculations revealed that a_Me was the low energy conformer. The B3LYP/cc-pVTZ calculations suggested the a_Me conformer as more stable by 0.8 and 8.3 kJ mol⁻¹ relative to a_H an a_C, respectively. Vibrational wavenumbers and infrared and Raman band intensities for two of the three conformers are reported from B3LYP/cc-pVTZ calculations.     

Anharmonic vibrational spectroscopy calculations with electronic structure potentials: comparison of MP2 and DFT for organic molecules

Density functional theory (DFT) technique is the most commonly used approach when it comes to computation of vibrational spectra of molecular species. In this study, we compare anharmonic spectra of several organic molecules such as allene, propyne, glycine, and imidazole, computed from ab initio MP2 potentials and DFT potentials based on commonly used BLYP and B3LYP functionals. Anharmonic spectra are obtained using the direct vibrational self-consistent field (VSCF) method and its correlation-corrected extension (CC-VSCF). The results of computations are compared with available experimental data. It is shown that the most accurate vibrational frequencies are obtained with the MP2 method, followed by the DFT/B3LYP method, while DFT/BLYP results are often unsatisfactory. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

Ab initio and DFT studies of the molecular structures and vibrational spectra of succinonitrile

The Molecular structure, conformational stability and vibrational frequencies of succinonitrile NCCH2CH2CN have been investigated with ab initio and density functional theory (DFT) methods implementing the standard 6-311++G* basis set. The potential energy surfaces (PES) have been explored at DFT-B3LYP, HF and MP2 levels of theory. In agreements with previous experimental results, the molecule was predicted to exist in equilibrium mixture of trans and gauche conforms with the trans form being slightly lower in energy. The vibrational frequencies and the corresponding vibrational assignments of succinonitrile in both C2h and C2 symmetry were examined theoretically and the calculated Infrared and Raman spectra of the molecule were plotted. Observed frequencies for normal modes were compared with those calculated from normal mode coordinate analysis carried out on the basis of ab initio and DFT force fields using the standard 6-311++G* basis set of the theoretical optimized geometry. Theoretical IR intensities and Raman activities are reported.     

Low-frequency vibrational modes and static vibrational hyperolarizabilities of long-chain molecules: polyenes and polyacetylene

A model for calculating vibrational frequencies of Transverse Acoustical Modes (TAM) of all-trans polyenes of any length is presented. Based on the results obtained, the relevance of TAM modes in determining static vibrational polarizability and second vibrational hyperpolarizability of very long polyenes (polyacetylene) in real materials is discussed. The major role of the Effective Conjugation Coordinate (ECC) in determining the second vibrational hyperpolarizability is also presented and compared to that of the TAM modes.

The results obtained point out the limitations of calculations on isolated molecules when the behaviour of real materials in the low-frequency domain is under investigation.     

Density functional theory study of vibrational spectra, and assignment of fundamental vibrational modes of 1-bromo 4-fluoronaphthalene

The FTIR and FT-Raman spectra of 1-bromo 4-fluoronaphthalene have been recorded in the regions 4000-100cm(-1) and 3500-100cm(-1), respectively. The spectra were interpreted with the aid of normal coordinate analysis based on DFT (density functional theory) using standard B3LYP/6-311+G** basis set combination for the most optimized geometry. Normal coordinate calculations performed with the DFT force field and subsequently corrected by a recommended set of scale factors, yielded fairly good agreement between observed and calculated frequencies. On the basis of the comparison between calculated and experimental results, assignments of fundamental modes were examined.     

Structure and vibrational spectra of dinitromethane and trinitromethane

The molecular geometries of dinitromethane and trinitromethane were optimized and their harmonic force fields were calculated by the DFT/B3LYP method. The force fields obtained made it possible to interpret reliably the vibrational spectra of dinitromethane, trinitromethane and a number of isotopomers of trinitromethane. Some general conclusions on geometry and vibrational spectra of the molecules under study are made. The hybrid density functional method used is shown to predict the reliable structural parameters and vibrational frequencies for polynitromethanes.     

Density functional theory study of vibrational spectra, and assignment of fundamental vibrational modes of succinimide and N-bromosuccinimide

This work deals with the vibrational spectroscopy of succinimide and N-bromosuccinimide. The mid and far FTIR and FT-Raman spectra were measured in the condensed state. The fundamental vibrational frequencies and intensity of vibrational bands were evaluated using density functional theory (DFT) using standard B3LYP/6-31G(*) and B3LYP/6-311+G(**) methods and basis set combinations. The vibrational spectra were interpreted, with the aid of normal coordinate analysis based on a scaled quantum mechanical force field. The infrared and Raman spectra were also predicted from the calculated intensities. Comparison of simulated spectra with the experimental spectra provides important information about the ability of the computational method to describe the vibrational modes. Unambiguous vibrational assignment of all the fundamentals were made using the total energy distribution (TED).     

Structure and vibrational spectra of the salts of mononitroalkanes

The molecular geometries of the anions of nitromethane and 2-nitropropane were optimised and their harmonic force fields were calculated by the RHF/6-311G(d,p), MP2/6-311G(d,p) and B3LYP/6-311G(d,p) methods. The force fields obtained made it possible to reliably interpret the IR and Raman spectra of the Na⁺ salt of nitromethane, d₂-nitromethane and 2-nitropropane. The assignment proposed significantly improves the interpretation of vibrational spectra known so far. Some general conclusions on geometry and vibrational spectra of the salts of mononitroalkanes studied are made. The hybrid density functional method used (B3LYP) is shown to be in better agreement with experimental data available than the Hartree–Fock methods.