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.     

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.     

Separated internal force constants for the ethylene and ethane molecules and their use for calculation of the force field for the propylene molecule

We consider the question of separation of linear combinations of force constants for ethylene and ethane. Introduction of a perturbation into the matrix of the kinematic coefficients allows us to solve the inverted vibrational problem using the matrix method of successive approximations without eliminating dependent coordinates. Such an approach makes it possible to obtain a sufficient system of equations for determining the separated internal force constants. The separated internal force constants determined for ethylene and ethane are used to calculate the force field for propylene. The calculated separated internal force constants for propylene reproduce its vibrational spectrum and the spectrum or propylene-d₆ with average deviation from experimental frequencies of 8 cm^–1. The numerical influence coefficients for stretching vibrations of the C-H bond are linearly related to the lengths of these bonds.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 1, pp. 118–122, Janauary–February, 1986.     

Large Amplitude Motions of Pyruvic Acid (CH3-CO-COOH)

Torsional and rotational spectroscopic properties of pyruvic acid are determined using highly correlated ab initio methods and combining two different theoretical approaches: Second order perturbation theory and a variational procedure in three-dimensions. Four equilibrium geometries of pyruvic acid, Tc, Tt, Ct, and CC, outcome from a search with CCSD(T)-F12. All of them can be classified in the C_s point group. The variational calculations are performed considering the three internal rotation modes responsible for the non-rigidity as independent coordinates. More than 50 torsional energy levels (including torsional subcomponents) are localized in the 406–986 cm⁻¹ region and represent excitations of the ν₂₄ (skeletal torsion) and the ν₂₃ (methyl torsion) modes. The third independent variable, the OH torsion, interacts strongly with ν₂₃. The A₁/E splitting of the ground vibrational state has been evaluated to be 0.024 cm⁻¹ as it was expected given the high of the methyl torsional barrier (338 cm⁻¹). A very good agreement with respect to previous experimental data concerning fundamental frequencies (ν^CAL − ν^EXP ~ 1 cm⁻¹), and rotational parameters (B₀^CAL − B₀^EXP < 5 MHz), is obtained.     

Estimating the hessian for gradient-type geometry optimizations

Optimization methods that use gradients require initial estimates of the Hessian or second derivative matrix; the more accurate the estimate, the more rapid the convergence. For geometry optimization, an approximate Hessian or force constant matrix is constructed from a simple valence force field that takes into account the inherent connectivity and flexibility of the molecule. Empirical rules are used to estimate the diagonal force constants for a set of redundant internal coordinates consisting of all stretches, bends, torsions and out-of-plane deformations involving bonded atoms. The force constants are transformed from the redundant internal coordinates to Cartesian coordinates, and then from Cartesian coordinates to the non-redundant internal coordinates used in the specification of the geometry and optimization. This method is especially suitable for cyclic molecules. Problems associated with the choice of internal coordinates for geometry optimization are also discussed.Fellow of the Alfred P. Sloan Foundation, 1981–83     

Ab initio calculations of the ultraviolet resonance Raman spectra of uracil

An equation been derived to calculate, ab initio, the frequencies and intensities of a resonant Raman spectrum from the transform theory of resonance Raman scattering. This equation has been used to calculate the intensities of the ultraviolet resonance Raman spectra from the first π-π* excited state of uracil and 1,3-dideuterouracil. The protocol for this calculation is as follows: (1) The force constant matrix elements in Cartesian coordinate space, the vibrational frequencies, and the minimum energy ground and excited state geometries of the molecule are calculated ab initio using the molecular orbital program Gaussian 92, (2) the force constants in Cartesian coordinates are transformed into force constants in the space of a set of 3N – 6 nonredundant symmetrized internal coordinates, (3) the G matrix is constructed from the energy minimized ground state Cartesian coordinates and the GFL = LΛ eigenvalue equation is solved in internal coordinate space, (4) the elements of the L and L^?1 matrices are calculated, (5) the changes in all of the internal coordinates in going from the ground to the excited state are calculated, and (6) these results are used in combination with the transform theory of resonance Raman scattering to calculate the relative intensities of each of the 3N – 6 vibrations as a function of the exciting laser frequency. There are no adjustable parameters in this calculation, which reproduces the experimental frequencies and intensities with remarkable fidelity. This indicates that the Dushinsky rotation of the modes in the excited state of these molecules is not important and that the simplest form of the transform theory is adequate. © 1995 John Wiley & Sons, Inc.     

A simple method for derivation of the rovibrational Hamiltonian: application to orthogonal radau coordinate systems as special cases

The molecular Hamiltonian of polyatomic molecules has been obtained. A general choice of internal coordinates depending on external parameters was considered. The rovibrational Hamiltonian for this set of coordinate system was derived in general terms as a function of the external parameters a and b. This procedure is also applicable to various kinds of internal coordinates in a straightforward way. The rovibrational Hamiltonian of triatomic molecules is considered as an application of this general formulation. In addition, orthogonal Radau coordinates are considered as cases of this new approach     

Far-infrared spectrum,barrier to internal rotation,ro structure,and ab initio calculations for acetylacetylene

The far-infrared spectrum has been recorded from 50 to 360 cm^–1 at a resolution of 0.10 cm^–1 for acetyiacetylene (1-butyne-3-one], CH₃C(O)CCH. The fundamental methyl torsion has been observed at 117.94 cm^–1, from which a periodic barrier to internal rotation has been calculated to be 346 cm^–1 (989 cal mol^–1]. Infrared spectra (3500-50 cm^–1] of the gas and solid and the Raman spectra (3500-100 cm^–1) of the gas, liquid, and solid are reported. Utilizing previously reported rotational constants for three isotopic species,r _o structural parameters have been determined for the heavy-atom skeleton. The fundamental vibrational frequencies, barrier to internal rotation, and structural parameters that have been obtained experimentally are compared to those obtained from ab initio Hartree-Fock calculations employing 3-21G, 6-31G, and DZ basis sets and to the corresponding quantities for some similar molecules.     

The exact isotope rule for symmetrically substituted molecules

The vibrational frequencies of isotopically substituted molecules are related exactly and explicitly to the parent molecules through a mixing parameter, following the method developed by Sheth (C. V. Sheth, J. Phys. B: Atom. molec. Phys. 8, 121 (1975)) using Cartesian displacement coordinates. It is shown that the explicit expressions for vibrational frequencies for symmetrical isotopic substitution of a non-linear X Y²-molecule coincide with that of DeWames and Wolfram (R. E. DeWames and T. Wolfram, J. chem. Phys. 40, 853 (1964)) derived from Green's function. The present procedure has the advantage of working with only symmetry coordinates belonging to genuine vibrations as compared to Green's function technique. Explicit expressions for vibrational frequencies for symmetrically substituted pyramidal X Y³-and tetrahedral X Y⁴-molecules are given for the first time involving properly defined mixing parameters. Using these expressions a theoretical justification of Noether's empirical rule (G. Herzberg, Infrared and Raman Spectra. Van Nostrand, New York (1945); H. D. Noether, J. chem. Phys. 11, 97 (1943)) is given for the first time in the cases considered.     

Automatic assignment of 1H‐NMR spectra of small molecules

A novel data‐evaluation procedure for the automatic atom to peak or multiplet assignment of ¹H‐NMR spectra of small molecules has been developed using a fast and robust expert system. The applicability and reliability of the method are demonstrated by comparison of a manually assigned database of ¹H‐NMR spectra with the assignments produced by the automatic procedure. The results of this analysis show an excellent success ratio, indicating that this new algorithm can have a major impact as a time saving tool for the organic chemist. A new graphical feature used to illustrate both the stability and quality of the elementary assignments is also introduced. Copyright © 2013 John Wiley & Sons, Ltd.     

Normal Coordinate Analysis in Cartesian Space I. Planar Symmetric Xn Molecules

Normal coordinate analysis of X_n type molecules can be carried out in the Cartesian space as well as in the internal space. Force constants in Cartesian coordinates for aromatic compounds belonging to D_nh group are calculated. The force constants of benzene are evaluated from vibrational frequencies both in the ground state and the ¹B_1u excited state. The calculated frequencies of planar carbon vibration of annulene of any N are tabulated. The normal coordinates derived from the calculation of 10-annulene are roughly the same of naphthalene derived more elaborated by Scherer. The normal modes in 10-annulene are indeed good approximations to the ones in naphthalene. This conclusion is valid for the other aromatic compounds.     

Electron Transport Through Composite Monolayers

Well-organized thiol monolayers on electrode surfaces are prepared using the Langmuir–Blodgett and self-assembly methods. Planned modification of the molecules building the monolayer allow the electron tunneling efficiency across the monolayer to be controlled. The barrier properties of the monolayers are probed by electrochemical methods. The extent of blocking for all systems under study indicates that contribution of the electroactive molecules that find direct access to the electrode surface can be neglected. These observations permit us to use the monolayers for the determination of the kinetic parameters of Fe(CN)^3– ₆ and IrCl^2– ₆ ion reduction. Such monolayers are employed for the studies of long-range electron transport. We show that insertion of amide bonds in appropriate positions of the alkyl chains of all molecules building the monolayer makes it possible to create a lateral hydrogen-bond network linking the internal amide groups in the monolayer and contributing to the electronic coupling between the redox probe and the electrode. The relation between the location of the amide moiety in the molecule and its importance for the electron tunneling efficiency through the intervening organic medium is discussed.     

Calculation of the Vapour Pressure of Organic Molecules by Means of a Group-Additivity Method and Their Resultant Gibbs Free Energy and Entropy of Vaporization at 298.15 K

The calculation of the vapour pressure of organic molecules at 298.15 K is presented using a commonly applicable computer algorithm based on the group-additivity method. The basic principle of this method rests on the complete breakdown of the molecules into their constituting atoms, further characterized by their immediate neighbour atoms. The group contributions are calculated by means of a fast Gauss–Seidel fitting algorithm using the experimental data of 2036 molecules from literature. A ten-fold cross-validation procedure has been carried out to test the applicability of this method, which confirmed excellent quality for the prediction of the vapour pressure, expressed in log(pa), with a cross-validated correlation coefficient Q² of 0.9938 and a standard deviation σ of 0.26. Based on these data, the molecules’ standard Gibbs free energy ΔG°_vap has been calculated. Furthermore, using their enthalpies of vaporization, predicted by an analogous group-additivity approach published earlier, the standard entropy of vaporization ΔS°_vap has been determined and compared with experimental data of 1129 molecules, exhibiting excellent conformance with a correlation coefficient R² of 0.9598, a standard error σ of 8.14 J/mol/K and a medium absolute deviation of 4.68%.     

A method for the calculation of normal-mode vibrational frequencies using symmetry coordinates. Application to the calculation of secondary deuterium isotope effects on carbocations

A method is introduced for the calculation of normal-mode vibrational frequencies of polyatomic molecules based on numerical differencing of analytical gradients in symmetry coordinates. This procedure requires a number of gradient evaluations equal to the largest number of symmetry coordinates belonging to any single irreducible representation of the molecular point group (plus a single gradient evaluation at the equilibrium configuration), which is fewer than the 3N-6 (N atoms) gradient evaluations needed for schemes based on Cartesian or internal coordinates. While the proposed method will not generally be as efficient as procedures which involve the direct calculation of energy second derivatives analytically (as are now available for single-determinant wavefunctions) it appears to be equally accurate, and it should be the method of choice for frequency calculations involving multideterminant wavefunctions for which analytical second-derivative algorithms have yet to be developed. The method is illustrated by the calculation of equilibrium secondary deuterium-isotope effects on a number of reactions involving simple carbocations.     

Analysis of drugs by AAS via formation of ion pairs

A new procedure for determining nitrogenated bases by forming ion pairs with Fe(SCN)6^3– is studied. The method consists of extracting the ion pair formed by a nitrogenated base and the inorganic complex Fe(SCN)6^3– into an organic phase, and measuring the iron in the organic phase by AAS at 248.3 nm. The optimal experimental conditions for determining amylocaine, avacan, bromhexine, diphenhydramine and papaverine are studied. The organic phase used is 1,2-dichloroethane. The standard deviation of the method varies between 10^–1 and 10^–2. The interferences produced by various substances are studied.     

Vibrational spectra and normal coordinate analysis for cis-diamminetetrachloroplatinum

The normal coordinate analysis of cis-diamminetetrachloroplatinum has been carried out by using a modified Urey—Bradley force field. According to the molecular structure, 45 internal coordinates were established and 33 theoretical vibrational frequencies were calculated. Due to considering the interaction between non-neighbouring stretching vibrations and between bending vibrations and introducing an appropriate set of internal coordinates in the course of calculation, the calculated frequencies agree well with the observed values, with an average difference 3.61 cm⁻¹ between them. The rationality and the reliability of the results are discussed and the questionable empirical assignment of ν(PtCl) in the literature is corrected.     

Building a database of force constants based on scaled ab initio (SQM) results. I. Chlorobenzenes

As part of a project for developing a database of harmonic force constants for organic molecules, the complete force fields for chlorobenzene, ortho-, meta-, para-dichlorobenzene and sym-trichlorobenzene have been determined, on the basis of ab initio Hartree—Fock calculations combined with empirical adjustments. The latter serve to correct for systematic errors in the theory, and are applied at two stages: the geometry is corrected by using empirical offset forces during the optimization; force constants are corrected by a few scale factors according to the SQM (scaled quantum mechanical) force field procedure. With scale factors taken over fixed from benzene and only two new scale factors introduced for the chlorobenzenes, experimental frequencies are reproduced with mean deviations of about 10 cm⁻¹. Some controversial assignments, still present in the deuterated derivatives, are discussed. Theoretical IR and Raman intensities have also been calcuated and used as semiquantitative information to assist assignments.     

Chiral force constants: Recommendations for the presentation of internal coordinate force constants

Some force constants associated with the internal coordinates that sense handedness or chirality can have opposite signs in the enantiomers of chiral molecules. Examples of such force constants include interaction force constants between a torsional and stretching or bending internal coordinates. The sign reversal for these force constants in the enantiomers of chiral molecules or in opposite-handed molecular segments is best recognized by labeling them as chiral force constants. Recognition of chiral force constants suggests that certain guidelines are to be followed in the presentation of internal coordinate force constants. © 1993 by John Wiley & Sons, Inc. © John Wiley & Sons, Inc.     

Conformational Stability,Structural Parameters,Vibrational Frequencies,and Raman and Infrared Intensities of Allylsilane

The Raman spectra (3500 to 30 cm^–1) of allylsilane, CH₂CHCH₂SiH₃, in the liquid with quantitative depolarization ratios and solid states and the infrared spectra (3500 to 30 cm^–1) of the gas and solid have been recorded. Similar data have also been recorded for the Si-d₃ isotopomer. Additionally, the mid-infrared spectra of the normal sample dissolved in liquified xenon as a function of temperature (–100 to –50°C) have been recorded. All these data indicate there is a single conformer, the gauche rotamer, in all three physical states. Utilizing the Si-H stretching frequencies from the infrared spectrum of the gaseous CH₂CHCH₂SiD₂H isotopomer, the three Si-H bond distances (r ₀) are calculated to be 1.484 Å for the gauche conformer. The other r ₀ parameters are estimated from the previously reported rotational constants. The fundamental frequencies for the asymmetric (78 cm^–1) and SiH₃ (137 cm^–1) torsions were obtained from sum and difference bands with the SiH₃ stretches. From the SiH₃ torsional frequency the barrier to internal rotation is calculated to have a value of 731 cm^–1 (8.74 kJ/mol). The optimized geometries, conformational stabilities, harmonic force fields, infrared intensities, Raman activities, depolarization ratios, and vibrational frequencies have been obtained from RHF/6-31G* and/or MP2/6-31G* ab initio calculations. These quantities are compared to the corresponding experimental quantities when appropriate as well as with some corresponding results for some similar molecules.     

Estimation of the contributions of absorption bands for overtones and composite frequencies in infrared spectra of brominated and oxygen-containing organic compounds

Intensities of fundamental, overtone, and composite absorption bands for 27 brominated hydrocarbons and 20 oxygen-containing organic compounds are calculated in an anharmonic approach. The first and second derivatives of the electric dipole moment of the molecule with respect to normal coordinates are determined using ab initio quantum-chemical MP2/6-31G(1d) calculations. For the studied compounds, the average contributions of overtones and composite frequencies to absorption in the region 100–4000 cm⁻¹ is 4.8% for brominated hydrocarbons and 3.2% for oxygen-containing compounds. The major part of the contribution of overtones and composite frequencies falls into the regions (mainly from 1600 to 2800 cm⁻¹) where fundamental transitions are observed rarely. The calculation performed well describe the positions of maxima and the intensities of fundamental, overtone, and composite absorption bands and can be used for the standardless spectrochemical analysis of compounds by their overtone spectra.