Order Electron Correlation Research Articles

The Potential Energy Surface of Guanine Is Not Flat: An ab Initio Study with Large Basis Sets and Higher Order Electron Correlation Contributions

An investigation of the potential energy surface (PES) of guanine was performed. The (nonplanar) molecular geometries of seven different forms of guanine were studied using the ab initio LCAO-MO method at the MP2 level with valence double-ζ basis sets augmented by d- and p-polarization functions (6-31G(d,p)). Among the studied forms are the four lowest energy tautomers, one rotamer, and two transition state forms for proton transfer between oxo and hydroxo tautomers of guanine N(7)H and N(9)H tautomers. Our best estimation of the relative stabilities of the tautomers includes electron correlation contributions calculated at the MP2/6-31G(d,p) reference geometries at the MP4(SDTQ)/6-31G(d,p), MP4(SDQ)/6-311G(d,p), and MP2/6-311++G(df,pd) levels. Three tautomers (and one rotamer) are located within 10 kJ mol-1 on the MP2 level PES of guanine. The calculated energy barriers for the proton transfer are larger than 150 kJ mol-1 and do not change by more than a few kJ mol-1 upon application of the SCRF model ba...

Direct determination of the quantum-mechanical density matrix using the density equation. II.

With the use of the density equation [Phys. Rev. A 14, 41 (1976)], second-order density matrices of atoms and molecules are calculated directly without any use of the wave function. The decoupling of the third- and fourth-order density matrices is done using the diagrammatic procedure of the Green's-function method, including terms up to second order in electron correlation. In addition to the results given in a previous communication [Phys. Rev. Lett. 76, 1039 (1996)], we give more detailed formulations, discussions, and additional results for ${\mathrm{H}}_{2}\mathrm{O},$ ${\mathrm{NH}}_{3},$ ${\mathrm{CH}}_{4},$ HF, ${\mathrm{N}}_{2},$ CO, and acetylene using double-\ensuremath{\zeta} basis sets, and for ${\mathrm{CH}}_{3}\mathrm{OH},$ ${\mathrm{CH}}_{3}{\mathrm{NH}}_{2},$ and ${\mathrm{C}}_{2}{\mathrm{H}}_{6}$ (staggered and eclipsed) using minimal basis sets. The present density-equation method gave energies as accurate as, and reduced density matrices (RDM's) more accurate than the single and double excitation configuration interaction method. The present method seems to give better quality results as the system becomes large. The convergence was fairly good and the calculated second-order RDM's almost satisfied some necessary conditions of the $N$ representability, the so-called $P,$ $Q,$ and $G$ conditions, while the first-order RDM's were exactly $N$ representable. The variety of the molecules calculated and the quality of the calculated results show that the density-equation method can be a promising alternative to the wave-function approach in quantum mechanics.

Ab initio conformational analysis of ethylene glycol and 1,3-propanediol

In this study we report the results of an ab initio investigation of the conformational properties of ethylene glycol and 1,3-propanediol. We performed HF/6-31++G ∗∗ optimizations of the geometries of 10 ethylene glycol conformers, and HF/4-31+G ∗ optimizations of 23 1,3-propanediol conformers. In the case of ethylene glycol we found the lowest energy conformers to have a gauche OCCO arrangement, stabilized by intramolecular hydrogen bonding. In case of 1,3-propanediol the lowest energy conformers have gauche OCCC arrangements. Intramolecular hydrogen bonding also plays an important role in this molecule. In both molecules we found that the ab initio results agree relatively well with available experimental data. It was also found that the conformational trends in the smaller ethylene glycol molecule are maintained in the larger 1,3-propanediol molecule. The introduction of Møller-Plesset second order electron correlation strengthens the intramolecular hydrogen bonding and the gauche-effect in both molecules.

Relativistic effects in gold chemistry. V. Group 11 dipole polarizabilities and weak bonding in monocarbonyl compounds

Hartree–Fock and Mo/ller–Plesset second order (MP2) calculations have been carried out in order to study the stability and structure of open-shell group 11 monocarbonyl compounds MCO (M=Cu,Ag,Au). AgCO is calculated to be a very weakly bound molecule with a dissociation energy of less than 1 kJ/mol, and this casts some doubt on the previously reported identification of this species in matrix isolation studies. AuCO is stable only if relativistic effects are included, which explains the recently observed anomaly in the strength of the metal–CO interaction within the group 11 series. The metal–carbonyl interactions in CuCO and AuCO are relatively weak, with dissociation energies of about 30 kJ/mol and may be best described as a combination of dispersion, donor–acceptor (charge-transfer) and repulsive interactions. The MP2 Cu–CO dissociation energy of 32 kJ/mol is in good agreement with the estimated experimental value of 23±6 kJ/mol. At the highest level of theory, AuCO possesses a bent geometry with a bond angle of 151° at the MP2 level, but this arrangement lies only 2 kJ/mol below the linear structure. The basis set superposition error and the role of metal f functions are discussed. Dipole polarizabilities are calculated for the group 11 elements at various levels of electron correlation in order to discuss dispersion interactions. These are found to be very sensitive to relativistic and electron correlation effects. For the neutral gold atom, relativistic effects in the dipole polarizability become comparable to electron correlation contributions. The multielectron adjusted group 11 pseudopotentials give reliable results for the atomic and molecular properties discussed.

Diagrammatic analysis of nonlinear response properties in time-dependent Hartree–Fock theory

Nonlinear response properties in Time-Dependent Hartree–Fock (TDHF) theory are analyzed by diagrammatic techniques and compared with the expression in propagator theory. The term that ensures that the quadratic response function is correct through first order in electron correlation emerges in the coupling term between lower order TDHF amplitudes and causes a violation of particle–hole pair conservation. It is shown diagrammatically that the dynamic hyperpolarizabilities can be expressed by lower order solutions in accordance with the 2n + 1 rule. Keywords: nonlinear response property, TDHF, diagrammatic

Correlation effects in the ab initio thermochemistry of benzene

Ab initio calculations of the energy of benzene in three large basis sets demonstrate that there is only a very small basis-set dependence of its resonance energy beyond 6-31G* at the SCF level and to second order in electron correlation.

A theoretical study of the A 1Π←X 1Σ+ system of SiH+

Theoretical studies have been performed on the X 1Σ+ and A 1Π states of SiH+. The complete active space, self-consistent field (CASSCF) and many-body perturbation theory (MBPT) methods were employed for the X 1Σ+ and state while the A 1Π excited state potential energy curve was studied by using CASSCF, multireference contracted configuration interaction (MR CCI, (MR CEPA), and coupled pair functional (CPF) approaches. Excellent agreement was obtained with experiment for the X state spectroscopic parameters (CASSCF): re=1.505 (1.50 Å; D0=3.30 (3.22±0.03) eV; ωe=2161 (2155) cm−1; ΔG1/2=2093 (2089) cm−1, with experimental values within parentheses. The shape of the potential curve for the A state was very sensitive to the basis set and higher order electron correlation. The best results, obtained with the CPF method, were re=1.888 (1.871) Å; D0=0.15 (0.15±0.03) eV; ωe=438 (448) cm−1; ΔG1/2=318 (389) cm−1. The computed f0,0 oscillator strength for the A←X transition was 1.2×10−3 which falls between the laboratory value, (2.4±1)×10−3, and a value obtained from the solar spectrum, 0.5×10−3. The computed life time for the v′=0 state is 956 ns to be compared to the experimental value 1025±80 ns.

Gauge-dependent ket calculations of dynamical polarizabilities of small molecules. Method and application to H 2O

A gauge-invariant ket function theory of magnetic properties, already presented in (ref. 1), is extended to time-dependent electric properties. The perturbed state, variationally determined as a linear combination of Slater's determinants associated with a time-dependent gauge transformation factor, allows the calculation of polarizabilities for different frequencies of the external field; it is applied to H 2O including electron correlation in order to determine its electronic transitions.

Integral dependent spin couplings in symmetry-adapted cluster (SAC) calculations

Numerical examples illustrate the single and double CI (SD CI) and symmetry-adapted cluster (SAC) results with integral dependent spin couplings for correlation energies compared to those with all spin couplings. The SAC with integral dependent spin couplings provides a practically useful method of incorporating higher order electron correlation only when the SCF reference function is a good zeroth-order approximation.

Correlation effects in ion neutralization scattering with the use of a time-dependent coupled-cluster approach.

We consider the problem of ion neutralization scattering from surfaces. For large kinetic energies, the motion of the ion can be treated classically. The electronic part is assumed to be described by a time-dependent Newns-Anderson Hamiltonian. The ion is supposed to have a closed-shell structure with one empty orbital outside the shell, which can take up, at the most, two electrons from the metal. One can obtain a time-dependent Hartree-Fock (TDHF) solution for this using a procedure suggested earlier. [T. B. Grimley, V. C. Jyothi Bhasu, and K. L. Sebastian, Surf. Sci. 124, 305 (1983)]. We show that this solution is defective in that it predicts that the probability that the ion comes back as a neutral species is always less than 0.5, thus illustrating that one has to include electron correlation in order to describe the process correctly.For this we make use of the time-dependent version of the coupled-cluster approach. In this, one assumes the wave function to have the form exp[${T}_{0}$(t)+${T}_{1}$(t)+${T}_{2}$(t)+. . .]\ensuremath{\Vert}${\ensuremath{\Phi}}_{0}$〉 where \ensuremath{\Vert}${\ensuremath{\Phi}}_{0}$〉 is a Slater determinant and ${T}_{n}$(t) can create n-particle hole excitations in it. We take ${T}_{1}$(t) as a linear combination of all possible single-particle hole-excitation operators while ${T}_{2}$(t) is taken as a linear combination of just those two-particle hole-excitation operators which transfer two electrons to the orbital of the ion from the solid, neglect ${T}_{n}$(t) for n>2, and derive differential equations for the matrix elements of the operators ${T}_{1}$(t) and ${T}_{2}$(t). These differential equations are solved numerically to obtain the wave function at any time t.New theorems which enable us to calculate all the expectation values that arise in our treatment of the problem are presented. Also, we have derived expressions for the excitation spectrum, produced as a result of the collision, by particles which come back as ions and also by those which have taken up one or two electrons from the solid. The method is applied to the scattering of lithium ions from the Ni(100) surface and also from a Ni surface contaminated with alkali atoms. The calculations show that TDHF theory is not a bad approximation if one is concerned just with the approach of the ion to the surface. But, in treating an ion which leaves the surface, TDHF fails. The predicted values of charge-transfer probabilities are considerably different in the two theories. Also, calculation of the excitation spectrum produced as a result of the collision show that the spectra are much broader for a contaminated surface having a lower work function than for the clean surface.

An augmented coupled cluster method and its application to the first-row homonuclear diatomics

An augmented coupled cluster scheme to evaluate the higher order electron correlation effects is proposed. The method is carried out in two steps. First, a coupled cluster calculation with all double substitutions (CCD) is performed. The converged CCD wave function is then used in the evaluation of the contribution of single and triple substitutions. The method is correct to fourth order in a perturbation expansion and includes significant fifth and higher order terms. Illustrative calculations on the excitation and dissociation energies of first-row homonuclear diatomic molecules are reported. The low-lying excitation energies of B2 and C2 are accurately calculated. The dissociation energies of B2, C2, N2, O2, and F2 are all uniformly underestimated by 0.1–0.3 eV using large spdf basis sets.

Scaling in second order electron correlation calculations of potential energy curves and spectroscopic constants

The determination of potential energy curves and spectroscopic constants using the method of scaling in second order electron correlation calculations is investigated. An application to the ground state of the fluorine molecule is described using full fourth order many-body perturbation theory within two basis sets.

Finite-field many-body perturbation theory of the Fermi contact nuclear-spin coupling

The Fermi contact term of the nuclear-spin---spin coupling in the HD molecule is calculated using finite-field many-body perturbation theory (FF MBPT). The one-electron states are generated by the Hartree-Fock potential in the presence of the Fermi contact interaction. The procedure through third order in electron correlation gives a value for the Fermi contact term of 37.2 Hz in fair agreement with the best estimated value of 40.0 Hz at the equilibrium internuclear distance. The result suggests that the FF MBPT approach provides a highly efficient and systematic method for the calculation of the Fermi contact term. A possible origin of the general overestimate by the coupled Hartree-Fock method is also discussed.

Many‐body calculation of the electric field gradient in the hydrogen molecule

AbstractThe electric field gradient in the hydrogen molecule has been calculated by diagrammatic many‐body perturbation theory (MBPT) in Gaussian basis sets. The procedure through third order in electron correlation gives a value for the field gradient of 0.34041 a.u., which is 0.8% greater than the accurate value. The result is discussed in terms of the completeness of the basis sets and the convergence of the perturbation expansion.

Many-body perturbation theoretic calculation of the nuclear spin-coupling constant in the hydrogen molecule

The Fermi contact term of the nuclear spin-coupling constant in the HD molecule is calculated by diagrammatic many-body perturbation theory (MBPT) employing extended Gaussian basis sets in the standard Hartree–Fock potential. The calculation through second order in electron correlation gives a value for the coupling constant of 28.1 Hz, which is only 65% of the experimental value. However, Hartree–Fock exclusion principle violating diagrams are found to contribute significantly. By summing these dominant diagrams selectively by the geometric approximation, we obtain a value of 37.0 Hz. The convergence is enhanced with shifted denominators, which finally yield 38.0 Hz within ∼10% of the probable Fermi contact value. Advantages of MBPT in calculating nuclear spin-coupling constants are discussed.

Electron correlation in molecular many-electron systems by diagrammatic many-body perturbation theory: Correlation energies and dipole polarizabilities of the hydrogen molecule

Diagrammatic many-body perturbation theory is used to calculate the electronic energy and the static electric dipole polarizability of the hydrogen molecule in its ground state. An amply extended discrete basis set of Gaussian orbitals is employed to minimize basis set errors and single-electron states are generated by the Hartree–Fock VN potential. The correlation energy is evaluated through third order and with some higher-order corrections included by denominator shifts to recover about 95% of the total correlation energy. Dipole polarizabilities are calculated through second order in electron correlation with an accuracy of ∼2%. Also the energy-denominator decoupling theorem is explicitly proved by invoking combinatorial analysis to implement extensive denominator shifts. Considering the values obtained, some comments are given on the application of partial summation techniques to molecular problems.

Electric dipole polarizability of the hydrogen molecule by many-body perturbation theory

Many-body perturbation theory is used to calculate the static electric dipole polarizability of the hydrogen molecule with a basis set of gaussian orbitals. Corrections complete through second order in electron correlation are calculated, and partial summation of certain classes of diagrams are extensively explored. The results are discussed in connection with the geometric approximation incorporating higher-order corrections.

Multipole polarizabilities and London dispersion forces between neon and helium atoms using double perturbation theory

Using an interchange theorem the polarizability of the neon atom at imaginary frequencies is calculated correct to first order in electron correlation. These results are then used to evaluate the long-range dispersion interactions between two neon atoms and between neon and helium atoms. For neon-neon interactions we find −(5.308 / R6) [1+(11.53 / R2) + (189.5 / R4)], while for neon-helium we find −(2.641 / R6) [1+(10.63 / R2) + (157.9 / R4)].

Accurate Perturbative Calculations for the Lithium Atom Based on the HartreeH0

Perturbative calculations are carried out to obtain eigenvalues of the four lowest-lying eigenfunctions of the Hartree Hamiltonian for the Li atom through third order in electron correlation. The expansions are all reasonably convergent and the theoretical analysis concerning the possibility of using zeroth-order functions which do not possess the exact permutational symmetry is confirmed in this particular case.

Use of the Nonsymmetrical Wavefunction. III. Magnetic Susceptibility of Molecular Hydrogen

The nonsymmetrical (NS) wavefunction is used to calculate the magnetic susceptibility of the hydrogen molecule. Triple perturbation theory with the aid of the interchange theorem allows one to calculate the susceptibility through first order in electron correlation and it is found that the NS function yields reasonable results.