Correlation energy extrapolation by intrinsic scaling. III. Compact wave functions

The information gained in the context of extrapolating the correlation energy by intrinsic scaling is used to shorten the full configurational expansions of electronic wave function without compromising their chemical accuracy. The truncations are accomplished by judiciously limiting the participation of the ranges of predetermined approximate sets of natural orbitals in the various excitation categories.     

Correlation energy extrapolation by intrinsic scaling. V. Electronic energy, atomization energy, and enthalpy of formation of water

The method of correlation energy extrapolation by intrinsic scaling, recently introduced to obtain accurate molecular electronic energies, is used to calculate the total nonrelativistic electronic ground state energy of the water molecule. Accurate approximations to the full configuration interaction energies are determined for Dunning's [J. Chem. Phys. 90, 1007 (1989)] correlation-consistent double-, triple- and quadruple-zeta basis sets and then extrapolated to the complete basis set limit. The approach yields the total nonrelativistic energy -76.4390+/-0.0004 hartree, which compares very well with the value of -76.4389 hartree derived from experiment. The energy of atomization is recovered within 0.1 mh. The enthalpy of formation, which is obtained in conjunction with our previous calculation of the dissociation energy of the oxygen molecule, is recovered within 0.05 mh.     

Correlation energy extrapolation by intrinsic scaling. I. Method and application to the neon atom

Remarkably accurate scaling relations are shown to exist between the correlation energy contributions from various excitation levels of the configuration interaction approach, considered as functions of the size of the correlating orbital space. These relationships are used to develop a method for extrapolating a sequence of smaller configuration interaction calculations to the full configuration-interaction energy. Calculations of the neon atom ground state with the Dunning's quadruple zeta basis set demonstrate the ability of the method to obtain benchmark quality results.     

Correlation energy extrapolation by intrinsic scaling. IV. Accurate binding energies of the homonuclear diatomic molecules carbon, nitrogen, oxygen, and fluorine

The method of extrapolation by intrinsic scaling, recently introduced to obtain correlation energies, is generalized to multiconfigurational reference functions and used to calculate the binding energies of the diatomic molecules C2, N2, O2, and F2. First, accurate approximations to the full configuration interaction energies of the individual molecules and their constituent atoms are determined, employing Dunning's correlation consistent double-, triple- and quadruple zeta basis sets. Then, these energies are extrapolated to their full basis set limits. Chemical accuracy is attained for the binding energies of all molecules.     

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

The recently introduced method of correlation energy extrapolation by intrinsic scaling (CEEIS) is used to calculate the nonrelativistic electron correlations in the valence shell of the F(2) molecule at 13 internuclear distances along the ground state potential energy curve from 1.14 A to 8 A, the equilibrium distance being 1.412 A. Using Dunning's correlation-consistent double-, triple-, and quadruple-zeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3 mhartree, by successively generating up to octuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlation energies with respect to these reference functions are then extrapolated to their complete basis set limits. The applicability of the CEEIS method to strongly multiconfigurational reference functions is documented in detail.     

The intrinsic structure of the water surface

An operational procedure to obtain the intrinsic structure of liquid surfaces is applied here to a molecular dynamics simulation of water, with a model of point charges for the molecular interactions. The method, which had been recently proposed and used for simple fluids, is successfully extended to a molecular liquid with the complex bond structure of water. The elimination of the capillary wave fluctuations, in the intrinsic density and orientation profiles, gives a new overall view of the water surface, at the sharpest molecular level, and without the size-dependent broadening observed in the mean profiles. The molecules belonging to the outer liquid layer are clearly identified, and we find that only these molecules exhibit a clear preferential orientation to lie flat on the surface. Moreover, there is a strong correlation between the dipolar structure and the local curvatures of the intrinsic surface, so that at the extrusions of the intrinsic surface the molecular dipoles point preferentially toward the vapor side of the interface. Finally, we have found an intrinsic density layering structure, although the inner structure is strongly damped beyond the second layer.     

Magneto-optical rotation in molecules. IV. The Verdet constant for the nitrogen molecule

The theory of magneto-optical rotation is applied to the calculation of the Verdet constant for the nitrogen molecule. Only two excited states, ¹∑ and ¹Π_u, are considered to take part in the magneto-optical rotation. Using the SCF wave functions, the verdet constant at 5780 Å is calculated to be 5.325 μmin/cm Oe which compares well with the experimental value of 6.273 μmin/cm Oe. The relation with the normal Verdet constant is also discussed.     

CVRQD ab initio ground-state adiabatic potential energy surfaces for the water molecule

The high accuracy ab initio adiabatic potential energy surfaces (PESs) of the ground electronic state of the water molecule, determined originally by Polyansky et al. [Science 299, 539 (2003)] and called CVRQD, are extended and carefully characterized and analyzed. The CVRQD potential energy surfaces are obtained from extrapolation to the complete basis set of nearly full configuration interaction valence-only electronic structure computations, augmented by core, relativistic, quantum electrodynamics, and diagonal Born-Oppenheimer corrections. We also report ab initio calculations of several quantities characterizing the CVRQD PESs, including equilibrium and vibrationally averaged (0 K) structures, harmonic and anharmonic force fields, harmonic vibrational frequencies, vibrational fundamentals, and zero-point energies. They can be considered as the best ab initio estimates of these quantities available today. Results of first-principles computations on the rovibrational energy levels of several isotopologues of the water molecule are also presented, based on the CVRQD PESs and the use of variational nuclear motion calculations employing an exact kinetic energy operator given in orthogonal internal coordinates. The variational nuclear motion calculations also include a simplified treatment of nonadiabatic effects. This sophisticated procedure to compute rovibrational energy levels reproduces all the known rovibrational levels of the water isotopologues considered, H(2) (16)O, H(2) (17)O, H(2) (18)O, and D(2) (16)O, to better than 1 cm(-1) on average. Finally, prospects for further improvement of the ground-state adiabatic ab initio PESs of water are discussed.     

Relative energy of organic compounds II. Halides, nitrogen, and sulfur compounds

The energies of the following types of compounds are characterized by their calculated relative enthalpies: alkyl, alkenyl, and aryl halides; carboxylic acid halides; carbonyl halides; amines; carboxylic acid amides; hydrazine derivatives; nitriles; heteroaromatic compounds; nitro-compounds; organic nitrites and nitrates; organic sulfides; thiols; disulfides; sulfoxides; sulfones; organic sulfites and sulfates; and selected inorganic compounds. Stabilization energy of pyrrol and thiophene has been estimated.     

The electron density of the water molecule

The electron density of the water molecule, as calculated by a standard program, is approximated by linear combinations of spherical Gaussians. The accuracy of the result is studied as a function of the numbers and positions of the Gaussians. Since this shows where the charge is located in the molecule it has immediate physical significance. The building-up of the density can be followed in more and more detail. From these expansions, point charge models of water are readily deduced. These are compared with models of similar kinds used by other authors. Some of the calculations have been repeated with a wavefunction of higher accuracy to investigate the stability of the results. Results show that the more accurate density requires more Gaussians to represent its greater complexity.     

Interaction energy of a water molecule with a single-layer graphitic surface modeled by hydrogen- and fluorine-terminated clusters

In ab initio calculations a finite graphitic cluster model is often used to approximate the interaction energy of a water molecule with an infinite single-layer graphitic surface (graphene). In previous studies, the graphitic cluster model is a collection of fused benzene rings terminated by hydrogen atoms. In this study, the effect of using fluorine instead of hydrogen atoms for terminating the cluster model is examined to clarify the role of the boundary. The interaction energy of a water molecule with the graphitic cluster was computed using ab initio methods at the MP2 level of theory and with the 6-31G(d = 0.25) basis set. The interaction energy of a water molecule with graphene is estimated by extrapolation of two series of increasing size graphitic cluster models (C(6n2)H(6n) and C(6n2)F(6n), n = 1-3). Two fixed orientations of water molecule are considered: (a) both hydrogen atoms of water pointing toward the cluster (mode A) and (b) both hydrogen atoms of water pointing away from the cluster (mode B). The interaction energies for water mode A are found to be -2.39 and -2.49 kcal/mol for C(6n2)H(6n) and C(6n2)F(6n) cluster models, respectively. For water mode B, the interaction energies are -2.32 and -2.44 kcal/mol for C(6n2)H(6n) and C(6n2)F(6n) cluster models, respectively.     

Calculation of molecular electric polarizabilities and dipole moments. II. The LiH molecule

We use a variation–perturbation method to calculate the electric polarizabilities and the electric dipole moment of the LiH molecule. We obtain 4.455 for the perpendicular polarizability and 4.001 (×10^?24 cm³) for the parallel polarizability. Our result for the electric dipole moment at equilibrium nuclear distance is 5.866, which is in excellent agreement with the experimental value 5.828 debye units.     

Scaling factors for the prediction of vibrational spectra. II. The aniline molecule and several derivatives

The structure of aniline was studied by semiempirical, ab initio, and density functional methods. Complete geometry optimization of the minimum energy structure and of the transition states for internal rotation and inversion of the amino group was carried out using several levels. The performance of the different methods in calculating and describing the vibrational frequencies of aniline was determined. The normal modes were characterized by the magnitudes and direction of the displacement vectors. Three procedures were used to obtain the scaled frequencies, two of them new, using specific scale factors and scaling equations from the benzene molecule. The errors obtained were compared with those calculated through other standard procedures. A reassignment of several bands was made. A comparison of the cost‐effective method and procedure of scaling was carried out. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Energy-switching potential energy surface for the water molecule revisited: A highly accurate singled-sheeted form

A global ab initio potential energy surface is proposed for the water molecule by energy-switching/merging a highly accurate isotope-dependent local potential function reported by Polyansky et al. [Science 299, 539 (2003)] with a global form of the many-body expansion type suitably adapted to account explicitly for the dynamical correlation and parametrized from extensive accurate multireference configuration interaction energies extrapolated to the complete basis set limit. The new function mimics also the complicated Sigma/Pi crossing that arises at linear geometries of the water molecule.     

Computing the energy of a water molecule using multideterminants: a simple, efficient algorithm

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule.     

Internal dynamics of the LaI3 molecule. II. Thermal average structure of the molecule and mean square vibration amplitudes

The structural parameters of the effective r _g configuration of the LaI₃ molecule were calculated using the DFT/B3LYP method. The difference between the calculated values of r _e (La-I) and r _g (La-I) is mostly due to the anharmonicity of the ν₁ and ν₂ vibrations and does not exceed the error in determining the distance r _g (La-I) in the electron diffraction experiment. Inclusion of the anharmonicity of the ν₂ and ν₄ deformation vibrations in calculations leads to decreased amplitudes l(I…I) and shrinking effect δ(I…I) compared to the respective values obtained in the harmonic approximation. The LaI₃ molecule proved to be more rigid than predicted by B3LYP calculations.     

Nonadiabatic molecular theory and its application. II. Water molecule

We introduce a new molecular theory beyond the Born–Oppenheimer approximation, where both electrons and nuclei are treated quantum mechanically and equivalently. First, we develop the coupled mean-field theory (CMFT) for both the electronic and nuclear fields. Then, to take into account the dynamic correlation between these particles, we develop a new molecular theory using the generator coordinate method (GCM) based upon the CMFT, which enables us to calculate the molecular eigenstate and eigenvalue directly. Finally, we apply this method to a water molecule and analyze the isotope effect on the vibrational frequency and the particle density. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 629–637, 1998