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Ab initio potential data at the CCSD(T) level of theory with an aug-cc-pVTZ basis was used for an accurate determination of potential energy surface. The resulting potential function is valid for all twelve vibrational degrees of freedom and a torsional reaction path was derived for this potential and then low lying vibrational levels of methanol were calculated by MULTIMODE.

Three different six-dimensional potential energy functions (PEFs) for the electronic ground state X2Sigma-u+ of the N4+ has been investigated. The PEFs were mapped by the RCCSD-T method and the B3LYP and B97-1 density functional approaches. The results showed that both density functional approaches gave good agreement for bending fundamentals but failed to give correctly the symmetric and antisymmetric stretching vibrations. The dissociation energy, the quadropole moment and the dipole polarizibilities were also determined.

The hydration of the actinyl cations, uranyl UO2(super 2+) and plutonyl PuO2(super 2+), has been investigated. Kohn-Sham Density Function Theory calculations using the MAGIC quantuam chemistry code have been performed on the separate uranyl and plutonyl species, and on the complexes AcO2(super 2+).nH2O (AC = U, Pu; N = 4, 5, 6). The results showed that the solvent plays a critical role in the hydration process wherein the solvent molecules were found to behave like actual binding equatorial ligands.

The uranium hexafluoride and plutonium hexafluoride monomer and dimer were investigated using the relativistic density functional approach. Optimization of the U-F distance in the UF6 monomer was carried out at different levels of theory. Atomization energies were derived at all levels and were increased by relativistic effects. A weak interaction between the two monomers in the UF6 dimer was observed at LDAX and BLYP levels, suggesting that the dimer is not stable enough to exist during the key reaction.

A new technique for obtaining exchange-correlation functionals utilizing ab initio numerical exchange-correlation potentials and accurate total energies had been previously shown. The functional expansion was refined to illustrate that substantially enhanced atomization energies can be determined by adjusting the fitting process to include atomization energies rather than total molecular energies.

The evaluation of ≤S⁁2> in density functional theory (DFT) is considered. Wang et al. [J. Chem. Phys. 102, 3477 (1995)] have derived an approximate, local density expression for <<⁁2> and in the present study their formula is evaluated using densities from unrestricted Hartree-Fock (UHF) and a range of DFT exchange-correlation functionals. The results are compared with those obtained by evaluating the conventional UHF expression using the Kohn-Sham orbitals, which is appropriate for the noninteracting system. A generalized gradient approximation for ≤S⁁2> is then proposed and investigated [ABSTRACT FROM AUTHOR]

We report calculations using a reaction surface Hamiltonian for which the vibrations of a molecule are represented by 3N-8 normal coordinates, Q, and two large amplitude motions, s1 and s2. The exact form of the kinetic energy operator is derived in these coordinates. The potential surface is first represented as a quadratic in Q, the coefficients of which depend upon the values of s1,s2 and then extended to include up to Q6 diagonal anharmonic terms. The vibrational energy levels are evaluated by solving the variational secular equations, using a basis of products of Hermite polynomials and appropriate functions of s1,s2. Our selected example is malonaldehyde (N=9) and we choose as surface parameters two OH distances of the migrating H in the internal hydrogen transfer. The reaction surface Hamiltonian is ideally suited to the study of the kind of tunneling dynamics present in malonaldehyde. Our results are in good agreement with previous calculations of the zero point tunneling splitting and in general agreement with observed data. Interpretation of our two-dimensional reaction surface states suggests that the OH stretching fundamental is incorrectly assigned in the infrared spectrum. This mode appears at a much lower frequency in our calculations due to substantial transition state character. [ABSTRACT FROM AUTHOR]

In this paper we extend our density-functional theory calculations, with generalized gradient approximation and hybrid functionals, using Slater-type orbitals (STOs), to the determination of second-order molecular properties. The key to the entire methodology involves the fitting of all STO basis function products to an auxiliary STO basis, through the minimization of electron-repulsion integrals. The selected properties are (i) dipole polarizabilities, (ii) nuclear magnetic shielding constants, and (iii) nuclear spin–spin coupling constants. In all cases the one-electron integrals involving STOs were evaluated by quadrature. The implementation for (ii) involved some complexity because we used gauge-including atomic orbitals. The presence of two-electron integrals on the right-hand side of the coupled equations meant that the fitting procedure had to be implemented. For (iii) in the hybrid case, fitting procedures were again required for the exchange contributions. For each property we studied a number of small molecules. We first obtained an estimate of the basis set limit using Gaussian-type orbitals (GTOs). We then showed how it is possible to reproduce these values using a STO basis set. For (ii) a regular TZ2P quality STO basis was adequate; for (i) the addition of one set of diffuse functions (determined by Slater’s rules) gave the required accuracy; for (iii) it was necessary to add a set of 1s functions, including one very tight function, to give the desired result. In summary, we show that it is possible to predict second-order molecular properties using STO basis sets with an accuracy comparable with large GTO basis sets. We did not encounter any major difficulties with either the selection of the bases or the implementation of the procedures. Although the energy code (especially in the hybrid case) may not be competitive with a regular GTO code, for properties we find that STOs are more attractive. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report the extension of our Slater-type orbital (STO) basis code for density functional theory (DFT) calculations to include “exact exchange,” so that Hartree–Fock and hybrid DFT calculations may be performed. Exchange integrals are evaluated through the insertion of a resolution of the identity, using the same auxiliary STO basis set which was used in our original generalized gradient approximation DFT studies. Three-center two-electron integrals are evaluated by quadrature. A scheme for introducing diatomic auxiliary STO basis sets is introduced, which enables much larger calculations to be performed. We also report an extension to the evaluation of second-order molecular properties using these functionals. Calculations for excitation energies to valence and Rydberg states are included. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The most common form of density functional calculations on molecular systems used generalized gradient approximation exchange-correlation functionals (such calculations can be applied to larger systems because no exact exchange is included). The most efficient and fastest such codes use an auxiliary basis set to fit the density so that only three-center integrals need to be evaluated. The codes DGAUSS and TURBOMOL use Gaussian basis sets, whereas the long-established ADF code uses Slater basis sets. We here examine the use of Slater basis sets. Our new code evaluates all required integrals numerically by quadrature. We report calculations on the G2 molecular set, contrasting them with similar calculations using Gaussian basis sets. Our conclusion, as far as energetics and structure are concerned, is that very similar predictions may be obtained from basis sets of the same size, and at approximately the same cost. [ABSTRACT FROM AUTHOR]

New density functionals, using the kinetic-energy density Tau are reported. The newly introduced variable enhances the performance of previous functionals, leading to highly accurate functionals with and without the use of exact exchange. All these functionals are compared to commonly used functionals for a large test set, looking also at reactions and hydrogen bonded systems. Furthermore, their physical plausibility is discussed. [ABSTRACT FROM AUTHOR]

The purpose of this work is to search for a justifiable form for a molecular dynamic correlation functional. A detailed examination of Colle and Salvetti's derivation of the LYP functional is presented. It is argued that the leading term is all important, and furthermore that it should account for αβ correlation. This term only depends upon the densities, and it has a truncation factor which is obtained from the size of the correlation hole. It is -c∫ρ αρβ/(ρ( 1 + dρ[sup ⅓))dr. It reproduces the αβ correlation energies of (He-Ar) to a very high accuracy. The correlation functional which represents σσ correlation is more complex, because the two particle Hartree-Fock density matrix is zero at electron coalescence. The functional must therefore depend upon (∇p)². Using these and related arguments we have found a four parameter generalized gradient functional which appears to perform nearly as well as the LYP functional. However unlike the LYP functional, it has two identifiable terms for αβ correlation, and two identifiable terms for σσ correlation. Together with our previously derived exchange functional, we have therefore obtained an exchange-correlation functional for molecular studies, the form for which can be more understandably justified. The performance of this new Generalized Gradient Approximation functional for molecular predictions is reported. It is a considerable improvement on the BLYP functional, and is in the category of an optimum Generalized Gradient functional. Finally the present status of the science of searching for exchange-correlation functions is reviewed. It is suggested that it may not be possible to find a local functional which is significantly more accurate for chemistry than the presently used Generalized Gradient Approximation functionals. [ABSTRACT FROM AUTHOR]

The vibrational-rotational energy levels of the hydrogen peroxide isotopomers H[sub 2]O[sub 2], D[sub 2]O[sub 2], HOOD, and H[sub 2][sup 18]O[sub 2] have been predicted by the variational method using a high-quality ab initio six-dimensional potential energy surface. The calculated energy levels are found to be in good agreement with available experimental data. The predicted spectroscopic constants for various isotopomers can be useful in a future analysis of the rotational-torsional spectra and experimental determination of the equilibrium structure of hydrogen peroxide. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The theory for the calculation of nuclear shielding constants with London atomic orbitals using density functional theory is presented. The theory includes the use of a local exchange–correlation functional which depends on both the electron density ρ(r) and the paramagnetic current density jp(r). The resulting coupled-perturbed Kohn–Sham equations are presented, together with the working expression for the nuclear shielding tensor. The entire theory has been programmed and exhaustively checked, using standard Gaussian basis sets. A variety of ρ(r) dependent exchange–correlation functionals have been used, together with a current dependence suggested by Vignale, Rasolt, and Geldart. Certain numerical difficulties arose with this form which necessitated a cutoff in its evaluation for low densities. Calculations have been performed on HF, N2, CO, F2, H2O, and CH4. Including the current dependence is seen here to have a slightly deshielding effect. The major deficiency in the reported calculations appears to arise from the use of local functionals which give poor values for the Kohn–Sham eigenvalues. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The full nonrelativistic quantum mechanical vibrational (J=0) kinetic energy operator for sequentially bonded N-atom molecules, expressed in valence stretch, bend, and torsion internal coordinates, is explicitly given. Certain properties of the operator and its possible applications are discussed. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Density functional calculations with accurate quadrature and large basis sets are reported on ozone, thiozone, methylene, and the beryllium dimer. The Kohn–Sham self-consistent procedure is used throughout and nonlocal gradient corrected functionals (B-LYP, B-P) are used. The systems and properties chosen are notoriously difficult problems for accurate computation, nevertheless, the density functional methods perform well. It is found, in line with calculations on more straightforward problems, that the functionals involving gradient corrections are more reliable than local density functionals. The B-LYP prediction is within 5 kcal/mol of the most accurate ab initio data on the C2v–D3h energy gap in ozone and thiozone. The B-LYP functional performs reasonably well on the vibrational frequencies of ozone whilst the B-P functional gives very accurate results for the structural parameters of ozone. B-LYP is used to estimate the singlet–triplet splitting in methylene with the triplet treated in both a restricted and unrestricted formalism. In either case the correct energy gap is reproduced within 2 kcal/mol. The bond length and low frequency of the beryllium dimer are reproduced accurately by the gradient corrected functionals but the binding energy is overestimated. However, B-LYP only overestimates the binding energy by 4 kcal/mol, which is an encouraging result given the difficulty of the problem. This paper can therefore be seen as further evidence that density functionals methods, and in particular methods based on nonlocal functionals, can predict molecular properties reasonably accurately for systems that have multireference character. [ABSTRACT FROM AUTHOR]

A new efficient and fully symmetry-adapted finite-basis variational method for calculating the rovibrational eigenstates (J≥0) of any sequentially bonded four-atom molecule is presented. The exact kinetic-energy operator TVR in valence coordinates is used in a scheme of successive basis-set contractions. The success of the method is demonstrated with new results for the molecules HCCH, HOOH, and HCNO, respectively linear, nonlinear, and quasilinear. The complexity of TVR contributes little to the computational cost, yielding a Hamiltonian matrix whose elements can all be cheaply calculated from products of arbitrarily accurate one-dimensional integrals; the dominant cost is that of matrix diagonalization. Matrices of up to 6000×6000 are used to obtain low-lying levels converged to small fractions of 1 cm-1, even for the difficult case of HOOH. The generalization to J≥0 allows the calculation of Π states for HCCH and HCNO and effective rotational constants for HCCH, all usefully converged. For the first time nine-dimensional rovibrational wave functions for four-atom systems are calculated without dynamical approximation and with basis sets well completed in all degrees of freedom. For HCCH it is straightforward to obtain hundreds of rovibrational (J=0,1,2) levels converged to better than 1.5 cm-1, opening up the possibility of the systematic refinement of the nuclear potential function VN. [ABSTRACT FROM AUTHOR]

Existing methods for the calculation of the correlation energy of open shell atoms and molecules using Mo\ller–Plesset perturbation theory are discussed with special emphasis on recent advances in methods based on the restricted Hartree–Fock wave function. The convergence of the Mo\ller–Plesset series is examined to high order for a number of small systems and it is shown that some of the methods offer significant advantage over traditional unrestricted Mo\ller–Plesset theory. The optimized bond length and vibrational frequencies of CN, NO, and O2 are also compared for second and fourth order Mo\ller–Plesset theory, and again it is found that the same methods give much better results than the corresponding unrestricted results. Further supporting calculations are presented on the electron affinity of CN and the dissociation energy of HCN. The new methods involve relatively minor adaptation of existing unrestricted Mo\ller–Plesset (UMP) codes, and in the light of their superior performance are recommended instead of UMP theory for open shell molecules. [ABSTRACT FROM AUTHOR]

This is the fourth in a series of papers on the ab initio calculation of the third and fourth derivatives of the energy of a molecule. In this paper we examine anharmonic effects in the infrared and Raman spectra of benzene. The following spectroscopic properties have been calculated; ab initio anharmonic corrections (ω-ν) and estimates of the harmonic frequencies ω for all 30 vibrational modes of C6H6 and C6D6, a complete set of anharmonic constants x and g for C6H6, intensities for the infrared spectrum of C6H6 up to 6148 cm-1, and anharmonic corrections to the Raman scattering factors for the fundamental modes of C6H6. In addition, we have improved on previous calculations of the equilibrium geometry of benzene, using Mo\ller–Plesset perturbation theory and a triple zeta plus double polarization (TZ2P) basis. We have also calculated a zero-point vibrationally averaged geometry which is in good agreement with the experimental R0 value. All these calculations are based on a Hartree–Fock quartic potential, cubic dipole surface, and quadratic polarizability surface, using a double-zeta plus polarization (DZP) basis. This is the first time a complete anharmonic potential has been obtained for a molecule of this size; the computer time required was minimized by the use of analytic derivative programs in favor of finite-difference programs. The quartic potential is presented in three coordinate systems.We discuss efficient algorithms for the nonlinear transformation of the potential from normal coordinates to valence coordinates and for symmetry checking the potential. The approximations used in our calculations have been examined and we find that the use of a Hartree–Fock DZP potential together with a perturbative treatment of the vibrational Hamiltonian is just as accurate for D6h benzene as for smaller molecules. In order to examine correlation effects in the B2u modes 14 and 15, basis-set limit second-order Møller–... [ABSTRACT FROM AUTHOR]

The Brueckner doubles variant of coupled cluster theory has recently been reintroduced by the authors. The use of Brueckner orbitals means that the governing equations for T2 take a particularly simple form. Here we give the details for the evaluation of the gradient of the Brueckner doubles energy for (a) the unrestricted spin–orbital formalism and (b) the closed-shell restricted formalism. Applications are presented for H2O, NH3, CH4, H2CO, C2H2, HCN, and CO2 and comparisons are made with the Hartree–Fock, second order Mo\ller–Plesset and quadratic configuration interaction models and with experiment. [ABSTRACT FROM AUTHOR]

The definition of frequency-dependent polarizabilities α(-ω;ω), β(-2ω;ω,ω), β(-ω;ω,0), and β(0;ω,-ω) is discussed, and it is argued that the most convenient definitions are as energy derivatives, a pseudo-energy being defined as the expectation value of [H-i(∂/∂t)]. This definition outlines a straightforward procedure for obtaining frequency-dependent polarizabilities for all quantum chemistry methods including those which account for the effects of electron correlation. It is demonstrated at the self-consistent field level of theory that αλμ(-ω;ω) cos ωt may be considered as the derivative of the static dipole moment μλ with respect to the strength Eωμ of a frequency-dependent field Eωμ cos ωt (as is usual), or as the derivative of an appropriately defined frequency-dependent dipole moment μμ cos ωt with respect to a static field E0λ. In this way, polarizabilities may be determined from finite static field calculations on lower-order tensors. Therefore, α(-ω;ω) cos ωt is defined within second-order Mo\ller–Plesset perturbation theory (MP2) as the second derivative of the MP2 energy with respect to one static and one frequency-dependent field.An analytic expression is given for αλμ(-ω;ω) at the MP2 level of theory. An MP2 frequency-dependent dipole expression is also defined, which if finite static field calculations are applied, gives the same values for αλμ(-ω;ω). MP2 values are reported for α(-ω;ω) of formaldehyde and ammonia for a range of frequency ω=0.01–0.1 a.u. From comparison of the self-consistent field (SCF) and MP2 values of the frequency-dependent contribution to α(-ω;ω), it is concluded that it is appropriate to use an SCF frequency-dependent correction in conjunction... [ABSTRACT FROM AUTHOR]