Relativistic molecular wavefunctions: XeF2

A new method is presented to calculate binding energies and eigenfunctions for molecules, using the relativistic Dirac hamiltonian. A numerical basis set of four component wavefunctions is obtained from atom-like Dirac-Slater wavefunctions. A discrete variational method has been developed and applied to the linear XeF₂ molecule.     

Simple molecular wavefunctions with correlation corrections

It is shown that the main deficiencies of wavefunctions of Hartree-Fock type (wrong dissociation behavior and absence of correlation between electrons of unlike spin) may be corrected by a simple method. Just sufficient CI is admitted to ensure qualitatively correct dissociation, while the short-range correlation energy is estimated with the Colle-Salvetti functional. Potential energy curves for H₂ and LiH are computed at various levels of approximation and the main features of the method are discussed.     

Approximate molecular electrostatic potentials from semiempirical wavefunctions

Approximate molecular electrostatic potentials (MESPs) are calculated with the asymptotic density model (ADM) on the basis of semiempirical wavefunctions generated by the SINDO1 method. The approximate MESP is adjusted to obtain good agreement with the exact MESP from 6–31G^* ab initio calculations for small molecules. This form of the MESP is used for the study of the reactivity of small and medium size silicon clusters with 5 to 45 atoms. Special attention is given to the reactivity of various Si₄₅ structures proposed in the literature. © 1997 by John Wiley & Sons, Inc.     

Simple molecular wavefunctions with correlation corrections II

The potential curves for the ground state of Li₂ (¹ _g ⁺ ) and FH (¹ _g ⁺ ) are computed. The correlation energy is calculated using a functional of the one- and two-electron density matrices derived from an MC SCF reference wavefunction and is added to the reference energy to obtain a correlated potential curve.     

Visualizing molecular wavefunctions using Monte Carlo methods

Using explicitly correlated wavefunctions and variational Monte Carlo we calculate the electron density, the electron density difference, the intracule density, the extracule density, two forms of the kinetic energy density, the Laplacian of the electron density, the Laplacian of the intracule density, and the Laplacian of the extracule density on a dense grid of points for the ground state of the hydrogen molecule at three internuclear distances (0.6, 1.4, 8.0). With these values we construct a contour plot of each function and describe how it can be used to visualize the distribution of electrons in this molecule. We also examine the influence of electron correlation on each expectation value by calculating each function with a Hartree–Fock wavefunction and then comparing these values with our explicitly correlated values. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

The effect of electronic correlation on molecular wavefunctions

The minimal basis set Hartree-Fock and full-CI wavefunctions of some molecules (N₂, CO, BH₂, CH₄) are analyzed in terms of their valence-bond components. The internal valence correlation has dramatic effects on this distribution. The coefficients of the ionic forms decrease very rapidly with ionicity; the largest coefficients concern neutral determinants with maximum spreading of the p electrons which are multiplied by important factors (3 to 10) by the CI. The neutral components with two electrons is the same p AO are increased to a lesser extent. Correlation decreases the charge fluctuation in a dramatic way. On the other hand the atomic spin fluctuation increases under correlation. When the main atomic configuration is not the ground state one (as in BH₂ or CH₄) the correlation does not increase the components of the atomic ground states, and has little effect on hybridization. These various trends reflect a compromise between the necessity of bond building between electrons of opposite spins and the tendency of the atoms to increase their components in their low energy configurations.     

Limits on the localized interpretation of molecular orbital wavefunctions

A new measure of orbital localizability is proposed. The actual improvement in classical electrostatic interpretations of electronic energy contributions on localization of CH₄, NH₃, H₂O, HF and Ne LCAO wavefunctions is computed to be small. Substantial valence LMO spatial overlapping remains.     

Intrinsic minimal atomic basis representation of molecular electronic wavefunctions

The problem of finding an effective minimal atomic basis that spans the exact occupied wavefunctions of a mean‐field theory at a given molecular geometry, which has a number of special properties, is studied and a new general procedure is developed that (1) solves for a raw minimal set of strongly atom‐centered functions—products of spherical harmonics and molecule‐optimized radial parts—that approximately span the occupied molecular wavefunctions and minimize the sum of their energies, (2) uses projection operators to get a new set of deformed atom‐centered functions that exactly span the occupied space and fall into core and valence subsets, (3) applies a new zero‐bond‐dipole orthogonalization scheme to the core‐orthogonalized valence subset so that for each two‐center product of these functions the projection of its dipole moment along the line going through the two centers is zero. The resulting effective minimal atomic basis is intrinsic to the molecular problem and does not need a free‐atoms input. Some interesting features of the zero‐bond‐dipole orthogonalization are showing up in the atomic population analysis of a diverse set of molecules. The new procedure may be useful for the interpretation of electronic structure, for the construction of model Hamiltonians in terms of transferable molecular integrals, and for the definition of active valence space in the treatment of electron correlation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

The optimization of molecular orbitals for coupled cluster wavefunctions

The purpose of this work is to make the coupled cluster (CC) energy stationary with respect to molecular-orbital (MO) variations in the reference configuration. To achieve this, we have used the Z vector, the solution of a set of perturbation-independent CPHF-like equations, to rotate the MOs. A new energy and gradient calculation is carried out with these non-SCF orbitals to obtain a new Z vector. The process is repeated until the orbitals are optimized (Z = 0), i.e. the contribution to the analytic CC gradient coming from orbital relaxation (CPHF) is zero. At the CCD level the orbitals thus obtained are approximate Brueckner orbitals. At the CCSD level, convergence problems were found in the iterative procedure to optimize the orbitals. Results obtained for several molecules show that CCD wavefunctions constructed from these optimized orbitals are of CCSD quality. We conclude that the presence of exp(t₁) in the CCSD model accounts for most relaxation effects and there is not much to gain by orbital optimization in CCSD wavefunctions.     

Gaussian basis set for molecular wavefunctions containing second-row atoms

A Gaussian basis set consisting of 12s-type and 9p-type functions has been optimized for the second-row atoms. Energy values are also reported for different contractions of this basis set.

---

Zusammenfassung Es wird ein Basissatz von 12s- und 9p-Gaußfunktionen für die Atome der zweiten Periode optimiert. Für verschiedene Kontraktionen dieser Basis werden die Energiewerte angegeben.

---

Résumé On presente un ensemble optimal de fonctions de base gaussiennes pour les atomes de la seconde ligne. Cet ensemble comprend 12 fonctions du type s et 9 fonctions du type p. On etudie egalement l'effet de differentes contractions de cet ensemble sur l'energie totale.

     

The determination of electronic ground and singlet state wavefunctions of BH

An extensive series of CI calculations have been carried out for the BH molecule using averaged natural orbitals. It is shown that energy profiles yielding accurate spectroscopic constants are obtainable for several states simultaneously. Energy values and spectroscopic data for the five lowest singlet states X ¹Σ⁺, A ¹Π, C ¹Δ, B ¹Σ⁺, and C ¹σ⁺have been calculated.     

Ground state wavefunctions of some conjugated carbon compounds — NPSO method

The method of Non-Paired Spatial-Orbitals is applied to the-systems of fulvene, hexatriene and butadiene in their ground states. This type of treatment which was found to be so successful for benzene proves to be satisfactory for these typical non-alternant and polyolefinic systems. Ways for determininga priori the adjustable parameters which appear in the wavefunction are examined and a procedure for setting up the non-pairing function without using any adjustable parameters is proposed.

---

Resume La méthode des orbitales spatiales non-appariées (NPSO) est appliquée aux systèmes de fulvène, hexatriène et butadiène dans leurs états fondamentaux. Ce procédé qui a eu de tel succès au cas de benzène, ce montre satisfaisant par ces systèmes typiques non-alternant et polyéniques. On examine des possibilités par ajustera priori les paramètres dans la fonction d'onde, et on propose une méthode pour obtenir la fonction NPSO sans faire usage d'aucun paramètre ajustable.

---

Zusammenfassung Die NPSO Methode wird auf die-Systeme von Fulven, Hexatrien und Butadien im Grundzustand angewandt. Die beim Benzol erfolgreiche Art der Behandlung erweist sich bei diesen nicht alternierenden und polyolefinischen Systemen als zufriedenstellend. Es werden Wege zura priori Bestimmung der Parameter in der Wellenfunktion geprüft und ein Verfahren zur Aufstellung der NPSO's ohne Benutzung von anzupassenden Parametern vorgeschlagen.

     

The superposition of the wavefunctions centered on the nuclei and the floating wavefunctions for the ground state of the hydrogen molecule

It is shown that the superposition of wavefunctions centered on the nuclei and floating wavefunctions represents the distribution of the electronic charge along the molecular axis in the ground state of the hydrogen molecule more accurately than either of these two functions separately. The mean-square values of electronic coordinates are calculated.     

Self-propelled nanodimer bound state pairs

A pair of chemically powered self-propelled nanodimers can exist in a variety of bound and unbound states after undergoing a collision. In addition to independently moving unbound dimers, bound Brownian dimer pairs, whose center-of-mass exhibits diffusive motion, self-propelled moving dimer pairs with directed motion, and bound rotating dimer pairs, were observed. The bound pairs arise from a solvent depletion interaction, which depends on the nonequilibrium concentration field in the vicinity of dimers. The phase diagram reported in the paper shows regions in monomer interaction energy-diameter plane where these bound and unbound states are found. Particle-based simulations and analytical calculations are used to provide insight into the nature of interaction between dimers that gives rise to the observed bound states.     

Single electron densities: a new tool to analyze molecular wavefunctions

A new partitioning scheme for the electron density of a many-electron wavefunction into single electron densities is proposed. These densities are based on the most probable arrangement of the electrons in an atom or molecule. Therefore, they contain information about the electron-electron interaction and, most notably, the Fermi hole due to the antisymmetry of the many-electron wavefunction. The single electron densities overlap and can be combined to electron pair distributions close to the qualitative electron pairs that represent, for instance, the basis of the valence shell electron pair repulsion model. Single electron analyses are presented for the water, ethane, and ethene molecules. The effect of electron correlation on the single electron and pair densities is investigated for the water molecule.     

Lower excited state wavefunctions for some conjugated carbon compounds — NPSO method

The method of Non-Paired Spatial- Orbitals is applied to the excited states of three typical conjugated hydrocarbons, Benzene, Fulvene and Hexatriene.

---

Resume La méthode des orbitales spatiales non-appariées (NPSO) est appliquée aux états excités de trois hydrocarbures conjugués typiques, soit le benzène, le fulvène et l'hexatriène.

---

Zusammenfassung Die NPSO Methode wird auf die angeregten Zustände von drei typischen konjugierten Kohlenwasserstoffen, Benzol, Fulven und Hexatrien angewandt.

     

Structure factors calculated from molecular wavefunctions. II. Analysis of the molecular charge distribution in diborane

The electron density distribution in the crystal of diborane has been determined using structure factors based on molecular densities. The libration-correction and third-cumulant terms have also been included in the expression for the temperature factor. The equilibrium r_e values for BH bond lengths obtained by this treatment are about 0.02Åshorter than the spectroscopic ones. A total librational motion of the diborane molecule is determined: the root-mean-square oscillations about inertial axis are 11.0° (8), 9.6° (5) and 7.2° (5), respectively. The dynamic theoretical deformation density shows a three-center BHB bond picture for the bridge structure.     

Rovibrational bound states of neon trimer: quantum dynamical calculation of all eigenstate energy levels and wavefunctions

Exact quantum dynamics calculations of the eigenstate energy levels and wavefunctions for all bound rovibrational states of the Ne(3) trimer (J = 0-18) have been performed using the ScalIT suite of parallel codes. These codes employ a combination of highly efficient methods, including phase-space optimized discrete variable representation, optimal separable basis, and preconditioned inexact spectral transform methods, together with an effective massive parallelization scheme. The Ne(3) energy levels and wavefunctions were computed using a pair-wise Lennard-Jones potential. Jacobi coordinates were used for the calculations, but to identify just those states belonging to the totally symmetric irreducible representation of the G(12) complete nuclear permutation-inversion group, wavefunctions were plotted in hyperspherical coordinates. "Horseshoe" states were observed above the isomerization barrier, but the horseshoe localization effect is weaker than in Ar(3). The rigid rotor model is found to be applicable for only the ground and first excited vibrational states at low J; fitted rotational constant values are presented.     

Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model

The model of the full optimized reaction space describes the electronic structure of a molecule in terms of the best wave-function that can be obtained as a superposition of all those configurations which are generate possible occupancies and couplings from a “formal minimal basis” of valence, orbitals on the constituent atoms. These configurations span a “full reaction space”, and MC SCF optimization of the orbitals in terms of an extended set of quantitative basis orbitals determines the full optimized reaction space (FORS). Basic justifications, methodological specifics and sample applications are discussed.