A theoretical study of the heats of formation of some small molecules using non-empirical wavefunctions

Total energies, obtained from non-empirical LCAO-MO-SCF calculations on a series of reactions involving only closed-shell molecules and ions, have been used to calculate the heats of formation H ₂₉₈ ⁰ of a large number of small molecules. The Double- basis set calculations, after empirical corrections for inadequacies in the basis set and systematic errors found in all calculations involving oxygen and carbon atoms, usually predict the heats of formation within 10 kcal/mole of the experimental value. A series of similar calculations predicts the heats of formation of some negative ions for which experimental values are either not available or are unreliable.     

Use of noninteger n‐generalized exponential type orbitals with hyperbolic cosine in atomic calculations

The efficiency of noninteger n‐generalized exponential type orbitals (NGETO) r^n*?1 e with hyperbolic cosine (HC) cosh (βr^μ) as radial basis functions in atomic ground state total energy calculations is studied. By the use of these functions, the combined Hartree‐Fock‐Roothaan calculations have been performed for some closed and open shell neutral atoms and their anions and cations with Z ≤ 21. The performance of new basis functions within the minimal basis framework has been compared with numerical Hartree‐Fock (NHF) results. Our total energy values are significantly close to NHF results. The presented minimal basis total energies obtained from the noninteger NGETO with HC are notably better than minimal basis functions total energies previously reported in the literature. It is found that the accuracy of new noninteger NGETO with HC almost correspond to the accuracy of the conventional double‐zeta functions. All the nonlinear parameters are fully optimized. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Analytical irreducible representation bases of the single and double icosahedral groups and their applications

An equivalent basis of icosahedral molecules is introduced in which the basis functions can be transformed under the operations in the icosahedral group (I_h). In this equivalent basis, the irreducible representation basis (IRB) of I_h, including the double‐valued IRB of I, is deduced analytically based on the method introduced in the literature [J. Comput. Chem. 17 , 851 (1996)]. Therefore the concepts of symmetry‐matrix and symmetry‐supermatrix can be used in the single‐ and multiconfiguration self‐consistent field methods (including relativistic effects) to reduce the storage of two‐electron integrals and calculations of Fock matrix during iterations by a factor of ca. 10,000. In addition, the equivalent basis of I_h can also be used to reduce the calculations of atoms and representations of rank ≥ 2 tensors. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 615–624, 2000     

Tables of accurate STF HF wavefunctions from B to Ca

Accurate Slater type function (STF) Hartree-Fock (HF) wavefunctions are calculated and tabled from B to Ca. The STF's have a form of r ⁿ e ^-r and the powers (n) of r are carefully determined. The total atomic energies agree with those of numerical HF (NHF) within the error of 4×10^–6 a.u. and 1×10^–5 a.u. for B to F and for Ne to Ca, respectively. The STF HF basis sets given will be useful to benchmark calculations for the molecular, solid, and atomic electronic states. Applications of the STF HF basis to molecular calculations are given and briefly discussed. Sample calculations are performed on the N₂ and P₂ molecules.     

A CASSCF study of the singlet-singlet and triplet-triplet spectroscopy of naphthalene

Ab initio complete active space (CAS) SCF calculations have been carried out for the singlet and triplet excited states of naphthalene molecule. The CASSCF active space comprised 10-type molecular orbitals. The basis set was of ANO type and included both diffuse functions and polarization functions. The calculated excitation energies and transition moment provide a sound theoretical basis for the assignment of the experimental singlet-singlet and triplet-triplet spectra of the naphthalene molecule.     

Ab initio molecular orbital calculations

A series of non-empirical calculations on furan, pyrrole and 1,2,5-oxadiazole are reported in which the effect of polarisation functions added to the minimal 7s 3p basis on each atom is studied. The effect on these planar molecules is largely through the rather than the-system. A comparison with the results of work with scaled functions is reported. Both series are shown to lead to much improved agreement with the electron spectroscopy energy levels. The effect on the dipole moments of these changes in basis is more variable but, with the exception of furan, the agreement with experiment is improved in the present method.

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Zusammenfassung Für die Moleküle Furan, Pyrrol und 1,2,5-Oxadiazol wurde eine Reihe von nichtempirischen Rechnungen durchgeführt, in denen der Einfluß von zusätzlichen Polarisationsfunktionen zur minimalen 7s 3p-Basis an jedem Atom untersucht wird. Die Ergebnisse werden mehr durch die Art der Beschreibung des Systems der-Elektronen als durch diejenige der-Elektronen beeinflußt. Ein Vergleich mit den Ergebnissen bei Verwendung skalierter Funktionen wird durchgeführt. Beide Reihen von Ergebnissen zeigen eine verbesserte Übereinstimmung zu den Energiemeßwerten der Elektronenspektroskopie. Die Änderungen des berechneten Dipolmoments bei derartigen Basisvariationen sind größer als bei früheren Methoden. Die Übereinstimmung mit dem Experiment wird, mit Ausnahme von Furan, jedoch verbessert.

     

Isomerism and Vibrational Spectra of Alkali Metal Perrhenates: Ab Initio CISD+Q Calculations

The equilibrium geometric parameters, isomerization energies, force fields, vibrational frequencies and intensities in the IR spectra of MReO₄ molecules (M = Li, Na, K) are calculated by the configuration interaction method including all singly and doubly excited configurations with Davidson's correction for quartic excitations in expanded basis sets using effective relativistic core potentials. The calculations indicate that the chemical bonds between the metal atoms and the ReO₄ anion group are highly polar. It is found that the MReO₄ molecule has two isomers. The basic isomer with C_2v symmetry has bidentate b coordination of the M⁺ cation to the ReO ₄ ^- anion. The excited isomer is of C_3v symmetry and corresponds to monodentate m coordination of M⁺. The low relative energies of the m isomers (17-29 kJ/mole) and the low energy barriers to the intramolecular mb rearrangements (5-11 kJ/mole) indicate that MReO₄ molecules are structurally nonrigid systems where the M–XO₄ chemical bonds are polytopic. The results of calculations are compared with the available literature data on the structure and vibrational spectra of MReO₄ molecules.     

Ab initio study,including electron correlation,of the electronic structures,the dipole moments,the static polarizabilities and of the harmonic force fields of H2CO,H2CS and H2SiO

Ab initio calculations including electron correlation (on the PNO-CI and CEPA-PNO levels) are carried out for the isovalence electronic molecules H₂CO, H₂CS and H₂SiO, and for comparison also for H₂O and CO. The CEPA equilibrium distances are accurate to within 0.003 Å, while SCF results show significantly larger errors. The harmonic force constants on CEPA level are satisfactory as well, but for stretching of double or triple bonds inclusion of singly substituted configurations is imperative. Dipole moments were obtained with an error of 0.1 Debye from CEPA calculations with sufficiently large basis sets and inclusion of singly substituted configurations. The dipole polarizabilities are less sensitive to correlation effects but require larger basis sets.The population analysis reveals that the SiO bond in H₂SiO is highly polar and thatd-AO's cannot be regarded as valence AO's in any of the molecules of this study. The binding energy of H₂SiO (with respect to H₂Si(¹ A ₁) + O(³ P)) is predicted as 140 ± 5 kcal/mol. The contributions of different pairs in terms of localized orbitals to the correlation energy of the molecules of this study are analyzed.     

General quantum mechanical operators. An open-ended approach for one-electron integrals with Gaussian bases

A universal computational approach for evaluating integrals over gaussian basis functions for general operators of the form is presented. The implementation is open-ended with respect to the types of basis functions (s, p, d, f, g, h…) and with respect to the integers that specify the operator. These one-electron integrals comprise operators associated with electrical and magnetic properties of molecules and include those needed to find multipole polarizabilities, multipole susceptibilities, chemical shifts, and so on. The scheme also generates the usual kinetic, nuclear attraction, and overlap operators.     

Maximum radius of convergence perturbation theory: test calculations on Be,Ne, H<Subscript>2</Subscript> and HF

Maximum radius of convergence (MAXR _c) perturbation theory [(2000) Journal of Chemical Physics 112:6997] is tested on the beryllium and neon atoms using calculations that are truncated in high orders. Calculations are also performed on the ground-state potential-energy curves of H₂ and HF. The neon atom calculations use the 3-21G basis set with added diffuse s and p functions. All other calculations use the STO-3G minimum basis set. MAXR _c perturbation theory consistently performs well. The Epstein–Nesbet and Møller–Plesset perturbative expansions frequently diverge or exhibit slow convergence compared to the expansions obtained from MAXR _c. AcknowledgementsJ.P. Fi. acknowledges support for a grant from the Japanese Society for the Promotion of Science.Contribution to the Björn Roos Honorary Issue     

The convergence of the Rayleigh-Ritz Method in quantum chemistry

Two sufficient criteria for the convergence of the Rayleigh-Ritz Method (RRM) with respect to the eigenvalues (E-convergence) of non-relativistic electronic Hamiltonians of molecules are discussed and compared. Moreover, a necessary and sufficient criterion is given. By example (Sect. 9) it is shown that the L ²-completeness of the basis is not sufficient to guarantee E-convergence. The convergence of the wave functions in different norms (-convergence) is also investigated. In particular, sufficient conditions for the one-particle basis functions (orbitals) are given, such that a CI calculation in this basis is both E- and -convergent.     

The influence of solvation on π *←n and π *←π transition energies in molecules containing Aza or carbonyl groups

The influence of solvation on ^*n and ^* transition energies of formaldehyde, acetaldehyde, acetone, pyridine and 1,2-, 1,3-, 1,4-diazabenzenes has been investigated through CNDO calculations.A static solvation model which distinguishes a) molecules directly involved in hydrogen bonding with solute, b) the layer of molecules in contact with the solute molecule and c) the main of molecules farther from solute, is presented.Blue and red shifts due to solvent effects are correctly predicted by calculations for each model.     

Nonempirical Study of Nuclear Dynamics in Nonrigid LiReO4 and K2SO4 Molecules

The previously developed nonempirical model for M _k XY _n (k 1) nonrigid molecules describing the motion of k M nuclei relative to a quasirigid XY _n fragment is used to study the dynamics of nuclei in LiReO₄ and K₂SO₄ molecules. The parameters of the kinetic and potential parts of the model Hamiltonian and dipole moment functions are determined from results of ab initio calculations of the molecules and their fragments by the Hartree—Fock and CISD + Q configurational interaction methods. The dynamic problem is solved by the variational method. Energy levels, transition frequencies, transition dipole moments, and mean geometrical parameters of the molecules are calculated. It is shown that the lowest energy levels of LiReO₄ and K₂SO₄ molecules can be described with high accuracy in a harmonic approximation using a quasirigid, single–minimum model, whereas for the energy levels located near and above the barriers of intramolecular rearrangements, these approximations are completely unsuitable.     

New method for approximate Hartree–Fock calculations using density approximations and coulomb field corrections. I

A method is proposed that reduces the computational effort of HF calculations considerably by reducing the number of two-electron integrals that have to be calculated. The following concepts are used: (i) approximation of the electron density by only few functions for the Coulomb part of the HF matrix; (ii) modification of this approximate density, to improve its Coulomb field; (iii) in the exchange part, a basis function χ is replaced by a function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \chi $\end{document} consisting of fewer Gaussian lobes; (iv) the error caused by this replacement is reduced by a modification of the densities \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \chi _i \tilde \chi _j $\end{document} in the exchange integrals. The computation time of the integral part is reduced by a factor 6 for molecules containing five first-row atoms as, e.g., CF₄, if one uses a 7S/3P basis set contracted to (5, 1, 1/3). The integral time increases roughly with n³, if n is the number of Gaussian lobes.     

On the effectiveness of exponential type orbitals with hyperbolic cosine functions in atomic calculations

Unconventional basis functions, constructed from exponential type orbitals (ETOs) with hyperbolic cosine functions, are applied to Roothaan-Hartree-Fock calculations of atoms within the minimal basis sets framework. The most popular ETOs, Slater type orbitals, B functions and \(\psi ^{(\alpha ^*)}\) functions with \(\alpha ^*=2\), and two types of hyperbolic cosine functions, \(\cosh (\beta r)\) and \(\cosh (\beta r+\gamma )\), are used in this work. The performance of the present basis functions is investigated and compared to the conventional double-zeta Slater-type basis set and numerical Hartree-Fock results. The improvement in the atomic energies clearly demonstrates how the accuracy increases when we move from ETO to ETO with hyperbolic cosine basis functions. The resulting improved minimal basis sets can also be useful in molecular calculations.     

Relativistic Gaussian basis sets for the atoms hydrogen to neon

Gaussian basis sets for use in relativistic molecular calculations are developed for atoms and ions with one to ten electrons. A relativistic radial wavefunction coupled to an angular function of l-symmetry is expanded into a linear combination of spherical Gaussians of the form r ^l exp (–r ²). One set of basis functions is used for all large and small components of the same angular symmetry. The expansion coefficients and the orbital exponents have been determined by minimizing the integral over the weighted square of the deviation between the Dirac or Dirac-Fock radial wavefunctions and their analytical approximations. The basis sets calculated with a weighting function inversely proportional to the radial distance are found to have numerical constants very similar to those of their energy-optimized non-relativistic counterparts. Atomic sets are formed by combining l-subsets. The results of relativistic and non-relativistic calculations based on these sets are analyzed with respect to different criteria, e.g. their ability to reproduce the relativistic total energy contribution and the spin-orbit splitting. Contraction schemes are proposed.Dedicated to Prof. Dr. A. Neckel on occasion of his 60th birthday     

Application of open-shell coupled cluster theory to the ground state of GaAs

Summary Theoretical calculations at the coupled cluster level of theory including all single, double and perturbative triple excitations, CCSD(T), are carried out for the^3– ground state of GaAs. Employing a (7s5p3d1f) basis set, the theoretical predictions forr _e (2.560 Å), _e (217 cm^–1),D _e (1.84 eV), and IP (7.80 eV), are in good agreement with recent experimental results. The importance of includingf-type polarization functions in the basis set and the effect of correlating 3d electrons are discussed in detail.     

Thermodynamic properties and valence-force field of alkanethiols and dialkyl sulfides

The consistent valence-force field of alkanethiols (AlkSH), dialkyl sulfides (AlkSAlk"), and alkanedithiols (HSRSH, R is alkylene) was determined for the first time by the solution of an inverse spectral problem. The vibrational spectra of 40 linear and branched molecules AlkSH, RSR", and HSRSH were calculated. Their thermodynamic functions (enthalpy, entropy, thermal capacity, and free Gibbs energy) were determined by methods of statistical mechanics in the 298—1500 Ê temperature interval. Within the framework of the additive-group approach, the quantitative relationships structure—property were considered for the thermodynamic functions of AlkSH, AlkSAlk", and HSRSH, and the parameters of the relationships were calculated. The results of calculations and experimental data were compared.     

Natural spin orbital analysis of diatomic molecular wave functions in terms of generalized diatomic orbitals

The original idea of the model applied to HeH⁺ excited states is: One electron occupies a diatomic orbital similar to the HeH⁺⁺ ground state 1s function. The other electron occupies an orbital which can be represented by a linear combination of functions similar to H ₂ ⁺ excited state functions. One or two screening parameters are variationally optimized to compensate for the smallness of the one-electron basis.CI calculations have been performed for five excited HeH⁺ states covering a wide range of internuclear distances. The CI wave functions have been submitted to a natural spin orbital analysis. The strongly occupied NSOs are compared with the original model functions.Dedicated to Professor Hermann Hartmann on occasion of his 65th birthday on May 4th, 1979.