Estimation of absorption band contribution for overtones and combined frequencies in the fingerprint region for alkanes, nitriles, amines, and nitroalkanes

In the anharmonic approximation the intensities of fundamental, overtone, and combined absorption bands are calculated in the range from 100 cm^-1 to 4000 cm^-1 for a series of alkanes, nitriles, amines, and nitroalkanes. The first and second derivatives of the molecular dipole moment are calculated by quantum chemical methods in the ab initio approximation using the MP2/6-31G(1d) basis set. Overtones and combined frequencies are found to make a significant contribution (5–20%) to the total absorption. The spectral distribution of this contribution depends on the molecular structure. For nitriles and amines significant absorption of the overtones and combined frequencies is observed in the same regions where fundamental absorption bands characteristic of these compounds are located.     

Spectroscopic calculation of the bond-dissociation energy of CH bonds in fluoro derivatives of methane,ethane, ethene,propene, and benzene

The bond-dissociation energy of CH bonds in fluoro derivatives of methane, ethane, ethene, propene, and benzene is determined by spectroscopic and quantum chemical methods. The spectroscopic values of the bond-dissociation energy of CH bonds are calculated in terms of fundamental absorption bands in the anharmonic approximation by the variational method using the Morse anharmonic basis. The quantum chemical calculations are performed using the 6-311G(3df, 3pd)/B3LYP basis set. The obtained regularities in variations of the CH bond dissociation energy values upon changes in the molecule structure are discussed.     

Importance of anharmonicity, recrossing effects, and quantum mechanical tunneling in transition state theory with semiclassical tunneling. A test case: the H2 + Cl hydrogen abstraction reaction

The hydrogen abstraction reaction from H2 by the Cl atom is studied by means of the variational transition state theory with semiclassical tunneling coefficients on the BW2 potential energy surface. Vibrational anharmonicity and coupling between the bending modes are taken into account. The occurrence of trajectories that recross the transition state is estimated by means of the canonical unified statistical method and by classical trajectories calculations. Different semiclassical methods for tunneling calculations are tested. Our results show that anharmonicity has a small but nonnegligible effect on the thermal rate constants, recrossing can be neglected, and tunneling is adequately described by the least-action approximation, and less successfully by the large-curvature version 3 approximation. However, the large-curvature version 4 and small-curvature approximations lead to a severe underestimation of tunneling. Thermal rate constants calculated using transition state theory including anharmonicity and tunneling agree very well with accurate quantal thermal rate constants over a wide temperature range, although the improvement over the harmonic transition state theory with the microcanonically optimized semiclassical tunneling approximation (based on version 3 of the large-curvature tunneling method) used in a previous study of this reaction is only marginal.     

Quasi-harmonic approximation of thermodynamic properties of ice Ih, II, and III

Several thermodynamic properties of ice Ih, II, and III are studied by a quasi-harmonic approximation and compared to results of quantum path integral and classical simulations. This approximation allows to obtain thermodynamic information at a fraction of the computational cost of standard simulation methods, and at the same time permits studying quantum effects related to zero-point vibrations of the atoms. Specifically, we have studied the crystal volume, bulk modulus, kinetic energy, enthalpy, and heat capacity of the three ice phases as a function of temperature and pressure. The flexible q-TIP4P/F model of water was employed for this study, although the results concerning the capability of the quasi-harmonic approximation are expected to be valid independently of the employed water model. The quasi-harmonic approximation reproduces with reasonable accuracy the results of quantum and classical simulations showing an improved agreement at low temperatures (T< 100 K). This agreement does not deteriorate as a function of pressure as long as it is not too close to the limit of mechanical stability of the ice phases.     

Comparisons of the RPA,SCRPA, Tamm–Dancoff,and full CI methods by analysis of their transition density matrices,oscillator strengths,and energy moments of oscillator strengths for the electric dipole transitions from the ground state of the B+ ion (frozen K-shell model)

The RPA, SCRPA , Tamm–Dancoff, and full CI methods are compared by analyzing their transition density matrices, oscillator strengths, and energy moments of oscillator strengths for the ¹S_ground – ¹P_odd transitions of the 4-electron B⁺ ion in the frozen K-shell approximation. It is found that the RPA gives transition density matrices that are aligned nearly as well as possible along those of the full CI , but have vector lengths that are significantly too long. The corresponding transition energies are significantly too small. These errors compensate to give oscillator strengths for the dominant transition that, for all forms of the oscillator strength, are within 1.6% of the corresponding full CI values. The SCRPA gives better transition density matrices than the RPA , but poorer oscillator strengths. The Tamm-Dancoff approximation gives very good values for the mixed length-velocity form of the oscillator strength. The RPA gives a static electric dipole polarizability that is nearly 20% larger than that of the full CI . The SCRPA gives a value 15% smaller than—and the Tamm-Dancoff approximation gives a mixed length-velocity value that is 11% larger than—that of the full CI . Other energy moments of oscillator strengths are also reported. Certain other approximations related to the RPA and the SCRPA are reported as well.     

On the hypervirial relation in the random phase approximation and the sum rules for ordinary and rotatory intensities in finite bases

It is shown that a one-electron hypervirial relation for transition amplitudes in the random phase approximation (RPA) follows immediately from the double commutator RPA formulation proposed by Rowe. For the transition energy-independent expressions for the ordinary and rotatory intensities it is shown that, in finite basis calculations, the sums of these intensities are independent of whether the single-transition approximation, the Tamm—Dancoff approximation or the RPA method is used. Specific results are quoted for a ab-initio minimal basis calculations on twisted ethylene.     

Neglect of four- and approximation of one-, two-, and three-center two-electron integrals in a symmetrically orthogonalized basis

A new integral approximation for use in molecular electronic structure calculations is proposed as an alternative to the traditional neglect of diatomic differential overlap models. The similarity between the symmetrically orthogonalized and the original basis functions (assumed orthonormal within each atomic set but nonorthogonal between different centers) is used to construct a robust approximation for the two-electron integrals, with the error being quadratic in the deviation between the products of the functions. Invariance properties of this procedure are rigorously proved. Numerical studies on a representative set of molecules at valence-only minimal basis Hartree-Fock level show that the approximation introduces relatively small errors, encouraging its future application in the semiempirical field.     

Investigation of the muffin-tin approximations for potential and charge density in the MS-Xα method by means of calculations of H2O

By detailed analysis of results for H₂O it is shown that both approximations, the muffin-tin approximation of the potential as well as the muffin-tin approximation of the charge density, severely influence the results. Their effects are of the same order of magnitude. Good results for molecular total energies are achieved by roughly compensating the effects from the two approximations, not by minimizing them. The total energy changes drastically when radius or position of the outer sphere are varied. Equilibrium distances strongly depend on the choice of the atomic sphere radii and always are calculated too large, not due to the charge density approximation, but due to the potential approximation. In order to lay hold of angular properties, the sphere radii have to be chosen in a completely different way than for total energies.     

Protein sequence threading,the alignment problem,and a two-step strategy

Conventionally, protein structure prediction via “threading” relies on some nonoptimal method to align a protein sequence to each member of a library of known structures. We show how a score function (force field) can be modified so as to allow the direct application of a dynamic programming algorithm to the problem. This involves an approximation whose damage can be minimized by an optimization process during score function parameter determination. The method is compared to sequence to structure alignments using a more conventional pair-wise score function and the frozen approximation. The new method produces results comparable to the frozen approximation, but is faster and has fewer adjustable parameters. It is also free of memory of the template's original amino acid sequence, and does not suffer from a problem of nonconvergence, which can be shown to occur with the frozen approximation. Alignments generated by the simplified score function can then be ranked using a second score function with the approximations removed. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1455–1467, 1999     

Calculation of the transport and relaxation properties of methane. I. Shear viscosity, viscomagnetic effects, and self-diffusion

Transport properties of pure methane gas have been calculated in the rigid-rotor approximation using the recently proposed intermolecular potential energy hypersurface [R. Hellmann et al., J. Chem. Phys. 128, 214303 (2008)] and the classical-trajectory method. Results are reported in the dilute-gas limit for shear viscosity, viscomagnetic coefficients, and self-diffusion in the temperature range of 80-1500 K. Compared with the best measurements, the calculated viscosity values are about 0.5% too high at room temperature, although the temperature dependence of the calculated values is in very good agreement with experiment between 210 and 390 K. For the shear viscosity, the calculations indicate that the corrections in the second-order approximation and those due to the angular-momentum polarization are small, less than 0.7%, in the temperature range considered. The very good agreement of the calculated values with the experimental viscosity data suggests that the rigid-rotor approximation should be very reasonable for the three properties considered. In general, the agreement for the other measured properties is within the experimental error.     

DFT and CI Studies of Electronic Structure and Photoionization of Sc,Ti, V,Cr, and Co Tris-β-diketonate Complexes

Orbital structure calculations were performed in the density functional theory (DFT) approximation for neutral complexes of Sc, Ti, V, Cr, and Co tris-β-diketonates; for the first three compounds, the structures of the ground ionic states and ionization energies were calculated in the CI approximation with decomposition on the orbitals of DFT. The sequence of the highest occupied orbitals found by this procedure coincides with the order of bands in the PES spectrum, while in the SCF-HF ab initio method, it does not. After the electron removal, all orbitals are stabilized by about 4.5 eV; for the vanadium complex, the removal of one d electron leads to the greatest stabilization of the remaining occupied orbital, which is essentially a d orbital. In CI calculations, using the DFT orbitals for decomposition does not lead to significantly better agreement with experiment when compared to the single-determinantal approximation and to the CI method with orbitals of the ab initio approximation.Original Russian Text Copyright © 2004 by I. S. Osmushko and V. I. Vovna__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 783–791, September–October, 2004.     

On the Dependence of the Light Scattering Intensity on the Averaged Size of Polydisperse Particles: Comments on the Paper by M.S. Dyuzheva et al. (Colloid J., 2002, vol. 64, no. 1, p. 39)

The second stage in the solution of the inverse problem of dynamic light scattering is analyzed; the dependence of the static scattering intensity on the average fraction size is used to calculate the particle size distribution at this stage. The results of the paper by M.S. Dyuzheva et al. (Colloid J., 2002, vol. 64, no. 1, p. 39) concerning this problem are shown to be erroneous. On the basis of calculations within the framework of the Mie theory, the possibility of a power approximation for the particle size dependence of the scattered intensity and the effect of the particle parameters on the power approximation exponents are discussed.     

Theoretical study of Sutherland fluids with long-range, short-range, and highly short-range potential parameters

On the basis of the first-order mean spherical approximation (FMSA) theory the behavior of Sutherland fluids with a number of parameters (gamma=3.1-36) is investigated. The investigation includes its modification by the simplified exponent approximation, renormalization group (RG) transformation, and density functional theory (DFT). For long-range parameters, the original FMSA is found sufficiently good to describe the global phase behavior, including inside the critical region. For short-range parameters, the modified FMSA by the simplified exponent approximation outside the critical region and RG transform inside the critical region are applied. For extremely short-range forces, the success is achieved by its combination with the DFT. This work gives a general sense about the capability of a theory for different ranges of potential, as well as for different thermodynamic states.     

Analytical time-dependent density functional derivative methods within the RI-J approximation, an approach to excited states of large molecules

Time-dependent density functional theory (TDDFT) is now well established as an efficient method for molecular excited state treatments. In this work, we introduce the resolution of the identity approximation for the Coulomb energy (RI-J) to excited state gradient calculations. In combination with nonhybrid functionals, the RI-J approximation leads to speed ups in total timings of an order of magnitude compared to the conventional method; this is demonstrated for oligothiophenes with up to 40 monomeric units and adamantane clusters. We assess the accuracy of the computed adiabatic excitation energies, excited state structures, and vibrational frequencies on a set of 36 excited states. The error introduced by the RI-J approximation is found to be negligible compared to deficiencies of standard basis sets and functionals. Auxiliary basis sets optimized for ground states are suitable for excited state calculations with small modifications. In conclusion, the RI-J approximation significantly extends the scope of applications of analytical TDDFT derivative methods in photophysics and photochemistry.     

“Spectroscopic” Calculations of CH Bond Dissociation Energies for Ethane, Propane, Butane, Isobutane, Pentane, Hexane, and Neopentane Using Fundamental Vibration Frequencies

The fundamental spectrum and the parameters of the potential function of a number of saturated hydrocarbon molecules are calculated in an anharmonic approximation. The calculation is performed by the variational technique using a minimal Morse-harmonic basis. The potential function is taken as the sum of the Morse function for CH bonds and the harmonic function for the skeletal and deformation vibrations. The initial approximation for the potential function is found by ab initio calculations in a 6-31G basis and refined by solving the inverse problem. The calculated CH bond dissociation energies depend significantly on the molecular structure and on the position of CH bonds in the molecule. These energies correlate well with the experimental cleavage energies of these bonds. The changes in the dipole moment of the molecule induced by vibrations were found by ab initio calculations in a 6-31G basis. The calculated IR transmission curves are in good agreement with the experimental curves.     

First principles calculations on structure, bonding, and vibrational frequencies of SiP2

Pyrite type SiP(2) is reinvestigated by first principles calculations on various levels of functionals including local density approximation, generalized gradient approximation, Becke-Lee-Yang-Parr hybrid functional, and the Hartree-Fock method. SiP(2) is seen as a model compound with molecular [P-P] entities and [SiP(6)] octahedra. Structure and bonding are addressed by electronic structure calculations. Special attention is spent on P-P and Si-P bonds in terms of bond lengths and respective stretching modes from simulated Raman spectra. The electronic structure is analyzed in both direct and momentum space by the electron localization function and site projected density of states. The main goals of this work are to understand the nature of chemical bonding in SiP(2) and to compare and contrast the different methods of calculation.     

Localized states in a simple cubic crystal via the next-nearest neighbor approximation

The energy spectrum of localized states in a simple cubic crystal is analysed, using the next-nearest neighbor approximation. The main distinguishing feature between the nearest and next-nearest neighbor approximation is the energy distribution of the localized states. Contrary to the tight-binding approximation, a non-symmetric distribution is found for clean surfaces, and split energy bands are found for surfaces completely covered by adsorbed atoms.     

On the Problem of Nucleation in a Supersaturated Vapor in the Presence of Heterogeneous Centers of Different Natures

The rules for constructing the analytical approximation are formulated for the law of the accumulation of the condensing substance by droplets that have emerged at centers of different natures. The accuracy of the suggested approximation is tested for the limiting cases of homogeneous nucleation and nucleation at centers of the same type. A general algorithm is constructed for describing the nucleation stage at centers of different natures after instantaneous creation of vapor supersaturation. Numerical calculations are conducted for the numbers of droplets formed at positively and negatively charged univalent ions in water vapors.