Infrared and Raman spectra and theoretical study of methyl trifluoromethyl sulfone, CF3SO2CH3

The infrared and Raman spectra were obtained for liquid CF3SO2CH3, as well as the infrared spectrum of the gaseous substance. The molecular geometry was optimized by means of the Hartree-Fock (HF), second order electron correlation (MP2) and density functional theory (DFT) procedures of quantum chemistry, resulting in a structure with Cs symmetry. The wavenumbers corresponding to the normal modes of vibration were calculated using the DFT (B3LYP/6-31G**) approximation and their agreement with the measured values improved after scaling of the associated force field. An assignment of bands is proposed on the basis of such calculations and the comparison with related molecules.     

SINDO1 calculations of vibrational frequencies of adsorbed molecules

A scaling procedure is used for the force constants generated by the SINDO 1 method in internal coordinates to achieve better agreement with experimental frequencies of molecules. The procedure is subsequently used to calculate frequency shifts for adsorbed molecules. The results for CO₂ and CO adsorption at NaCl cluster surfaces are in good agreement with experimental data. © 1995 John Wiley & Sons, Inc.     

A general procedure for obtaining wave functions obeying the virial theorem

The virial theorem for molecules is shown to have two different forms, one employing the energy gradient the other involving the Hellmann–Feynman force. While the former VT can be fulfilled by a uniform scaling of the basis set, the latter cannot be satisfied in certain basis sets, and can give unrealistic results in others. The scaling procedure is applied to molecules at nonstationary points on the potential energy surface and it is found that energy components can change substantially, especially at short bondlengths, while the change in total energy is small. The effects on molecular properties are also small.     

Scaled in Cartesian Coordinates Ab Initio Molecular Force Fields of DNA Bases: Application to Canonical Pairs

The model of Regularized Quantum Mechanical Force Field (RQMFF) was applied to the joint treatment of ab initio and experimental vibrational data of the four primary nucleobases using a new algorithm based on the scaling procedure in Cartesian coordinates. The matrix of scaling factors in Cartesian coordinates for the considered molecules includes diagonal elements for all atoms of the molecule and off-diagonal elements for bonded atoms and for some non-bonded atoms (1–3 and some 1–4 interactions). The choice of the model is based on the results of the second-order perturbation analysis of the Fock matrix for uncoupled interactions using the Natural Bond Orbital (NBO) analysis. The scaling factors obtained within this model as a result of solving the inverse problem (regularized Cartesian scale factors) of adenine, cytosine, guanine, and thymine molecules were used to correct the Hessians of the canonical base pairs: adenine–thymine and cytosine–guanine. The proposed procedure is based on the block structure of the scaling matrix for molecular entities with non-covalent interactions, as in the case of DNA base pairs. It allows avoiding introducing internal coordinates (or coordinates of symmetry, local symmetry, etc.) when scaling the force field of a compound of a complex structure with non-covalent H-bonds.     

Transfer of force constants and scaling factors in vibrational problems

This paper discusses the predictive abilities of the methods of force constant and scaling factor transfer to the force fields of related molecules in solving vibrational problems for the latter. It is noted that the method of scaling the quantum mechanical force fields and transferring the scaling factors is preferable. The vibrational spectra of the rotational isomers of butadiene-1,3 are considered as an example. The vibrational frequency assignments are tested using a matrix analogous to the Duschinsky matrix.     

Filter-spline backgrounds in gas-phase electron diffraction analysis

A filter-spline procedure is developed for a computer background adjustment in the gas-phase electron diffraction analysis of molecules. The procedure allows estimation of the principal internuclear distances and amplitudes of vibration without any a priori information on the molecular structure. The parameters thus found can be further used as starting points in structure analysis. The procedure is illustrated by treatment of intensity data for cyclooctane.     

Orientational dynamics of isotopically diluted H2O and D2O

We use femtosecond midinfrared pump-probe spectroscopy to compare the ultrafast dynamics of HDO dissolved in D2O and H2O. For both systems the vibrational energy relaxation proceeds through an intermediate state. The relaxation leads to heating of the sample, which is observed in the transient spectra. In order to obtain the correct anisotropy decay, the ingrowing heating signal is subtracted from the raw data. For the OD vibration this procedure works well. For the OH vibration, however, we find an additional effect that leads to a severe distortion of the anisotropy. We show that this effect can be explained by a slightly faster reorientation of excited molecules during their relaxation as compared to unexcited molecules. We construct a model that includes this effect and is able to reproduce the experimental data. Using this model we show how the distorted anisotropy can be corrected.     

A corresponding states principle for the equation of state of hard body fluid mixtures

A theoretically based corresponding-states principle is developed for athermal mixtures consisting of hard molecules. The principle states that when scaled appropriately, the excess compressibility factor for such mixtures reduces to a universal function of the effective packing fraction of the mixture. The latter represents the number density reduced by means of the effective molecular volume, which is defined as the volume a molecule excludes to any point of another molecule and depends on the geometry of both molecules. The scaling factor is related to a sort of effective nonsphericity parameter for the mixture that depends on composition as well as the nonsphericity parameters of the molecules which form the mixture and their effective molecular volumes. The universal function represents the excess compressibility factor of a pure hard-sphere fluid. Results are in good agreement with available simulation data.     

Ab initio prediction of vibrational spectra: A database approach

Efforts to develop a database of quadratic force fields for organic molecules are described. The database is based on systematic ab initio calculations, scaled to reproduce the experimentally observed frequencies. The choice of the theoretical method, the basis sets, geometries, internal coordinates and the scaling procedure are discussed. A key point in the procedure is the automatic generation of the internal valence coordinates. This is also very advantageous for geometry optimization. The database should permit the prediction of vibrational frequencies for most organic molecules to 10–20 cm⁻¹, together with semiquantitative intensities. The accuracy is sufficient to identify unknown compounds from a list of reasonable candidates.     

On a definition of bond energies based on localized molecular orbitals

A theoretical model is presented for defining bond energies based on localized molecular Orbitals. These bond energies are obtained by rearranging the total SCF energy including the nuclear repulsion term to a sum over orbital and orbital interaction terms and then to total orbital terms, which can be interpreted as the energies of localized orbitals in a molecule. A scaling procedure is used to obtain a direct connection with experimental bond dissociation energies. Two scale parameters are employed, the C-C and the C-H bond dissociation energy in C₂H₆ for A-B and C-H type bonds, respectively. The implications of this scaling procedure are discussed. Numerical applications to a number of organic molecules containing no conjugated bonds gives in general a very satisfactory agreement between experimental and theoretical bond energies.     

Gas-phase and Ar-matrix SQM scaling factors for various DFT functionals with basis sets including polarization and diffuse functions

Scaling factors for Pulay's scaled quantum mechanical (SQM) scheme have been determined for four different widely used DFT functionals (PBE, B3LYP, B3PW91, and M06-2X) and for two basis sets (6-31++G** and aug-cc-pVTZ) by fitting computed results to 347 fundamental experimental vibrational frequencies of 33 molecules. Measurements in the gas phase and in solid argon matrices were used independently in the fitting procedure in order to provide a simple method of estimating matrix shifts. The accuracy of the new scaling factors is demonstrated on test molecules including hydrogen-bonded systems and molecules containing chlorine and sulfur atoms.     

Specificity of internal rotation in aldehydes with three-membered rings

The results of anharmonic calculations of low-frequency vibrations of aldehyde molecules containing a three-membered cycle with a π-bond are presented. The theoretical exploration of the conformational behavior and geometrical structure of two related molecules is carried out and potential energy surface sections along the coordinates of internal rotation and non-planar vibration close in frequency are constructed and analyzed. The possibility of kinematic coupling of these two vibrations and the complexity of their forms are especially considered.     

Fingerprint scaling increases the probability of identifying molecules with similar activity in virtual screening calculations.

Results of systematic virtual screening calculations using a structural key-type fingerprint are reported for compounds belonging to 14 activity classes added to randomly selected synthetic molecules. For each class, a fingerprint profile was calculated to monitor the relative occupancy of fingerprint bit positions. Consensus bit patterns were determined consisting of all bits that were always set on in compounds belonging to a specific activity class. In virtual screening calculations, scale factors were applied to each consensus bit position in fingerprints of query molecules. This technique, called "fingerprint scaling", effectively increases the weight of consensus bit positions in fingerprint comparisons. Although overall prediction accuracy was satisfactory using unscaled calculations, scaling significantly increased the number of correct predictions but only slightly increased the rate of false positives. These observations suggest that fingerprint scaling is an attractive approach to increase the probability of identifying molecules with similar activity by virtual screening. It requires the availability of a series of related compounds and can be easily applied to any keyed fingerprint representation that associates bit positions with specific molecular features.     

Two-electron integrations in the quantum theory of atoms in molecules

A method to compute two-electron integrals over arbitrary regions of space is introduced and particularized to the basins appearing in the quantum theory of atoms in molecules. The procedure generalizes the conventional multipolar approach to account for overlapping densities. We show that the approach is always convergent and computationally efficient, scaling as N(4) in the worst, two-center case. Several numerical results supporting our claims are also presented.     

An attempt to decompose the force constants for some diatomic molecules by the derivatives of the electronic kinetic energy

The force constants for several diatomic molecules were calculated by the derivatives of the electronic kinetic energy within the restricted Hartree–Fock formalism. The uniform scaling procedure was utilized in order to satisfy the virial theorem. The decomposition of the force constant was performed by partitioning the derivatives of the kinetic energy in several ways.     

Ab initio computation of force constants: Part VI. Applications of the force relaxation method for geometry optimization

Techniques to improve the computational efficiency of the force relaxation method are discussed. Force constants for fragments in previously computed smaller molecules can be transferred to construct a guess force constant matrix. Additional force constants that may be needed can be computed by a procedure which uses only one additional force calculation per diagonal force constant required. A scaling technique to improve convergence on the optimized geometry is discussed.     

Geometry optimization of molecular clusters and complexes using scaled internal coordinates

Scaled internal coordinates are introduced for use in the geometry optimization of systems composed of multiple fragments, such as solvated molecules, clusters, and biomolecular complexes. The new coordinates are related to bond lengths, bond angles and torsion angles by geometry-dependent scaling factors. The scaling factors serve to expedite the optimization of complexes containing outlying fragments, without hindering the optimization of the intramolecular degrees of freedom. Trial calculations indicate that, at asymptotic separations, the scaling factors improve the rate of convergence by a factor of 4 to 5.     

Scaling factors for vibrational frequencies and zero-point vibrational energies of some recently developed exchange-correlation functionals

The scaling factors for the vibrational frequencies and zero-point vibrational energies evaluated at various combinations of recently developed exchange-correlation functionals and various basis sets are reported. The exchange-correlation functionals considered are B972, B98, HCTH, OLYP, O3LYP, G96LYP, PBE0 and VSXC functionals; the basis sets employed are 3-21G, 6-31G*, 6-31G**, 6-31+G, 6-311G*, 6-311G**, 6-311G(df,p), 6-311+G(df,p), cc-pVDZ and aug-cc-pVDZ. The experimental harmonic frequencies of 122 small molecules and the zero-point vibrational energies of 39 small molecules are used to determine the scaling factors through the least-square fitting procedure. It was found that the scaling factors do not depend significantly on the basis sets considered. The vibrational frequency scaling factors evaluated by using the B98 and PBE0 functionals are recommended on the basis of smallest root mean square error. The zero-point vibrational energy scaling factors evaluated from the B972 functional with Pople's double-zeta basis set and the HCTH functional with Pople's triple-zeta basis set are recommended on the basis of smallest root mean square error.     

Analytical energy gradients for local second-order Møller-Plesset perturbation theory using density fitting approximations

An efficient method to compute analytical energy derivatives for local second-order M?ller-Plesset perturbation energy is presented. Density fitting approximations are employed for all 4-index integrals and their derivatives. Using local fitting approximations, quadratic scaling with molecular size and cubic scaling with basis set size for a given molecule is achieved. The density fitting approximations have a negligible effect on the accuracy of optimized equilibrium structures or computed energy differences. The method can be applied to much larger molecules and basis sets than any previous second-order M?ller-Plesset gradient program. The efficiency and accuracy of the method is demonstrated for a number of organic molecules as well as for molecular clusters. Examples of geometry optimizations for molecules with 100 atoms and over 2000 basis functions without symmetry are presented.