Potential energy calculations for the double internal rotation in acetone and dimethylamine

In the present work, the problem of the determination of the potential energy surface of double rotor molecules is examined in the case of acetone and dimethylamine. From the symmetry adapted functional form for the potential of acetone that of dimethylamine is deduced and the minimum number of conformations to be calculated is derived in order to have a reliable surface (minimal expansion). The potential energy functions for acetone and dimethylamine are then determined using different standard procedures. Special emphasis is put on the electronic correlation effects in the calculation. It is found that these effects significantly improve the potential energy function.     

二氧化钚分子的多体展式势能函数

从导出基态PuO2分子的电子状态X5Σ g正确地判断其离解极限出发,采用MP2方法,应用相对论有效原子实模型(RECP)优化出PuO2(X5Σ g)分子稳定构型为线性OPuO(D∞h),其平衡核间距Re=0.18004nm.同时也计算出振动频率,并优化出存在亚稳态的Pu-O-O(C∞v)构型.使用多体项展式理论方法,导出了基态PuO2分子的分析势能函数.该势能表面准确地再现了O-Pu-O(D∞h)平衡结构和亚稳态的Pu-O-O(C∞v)构型.然后根据势能函数等值图讨论了O(3Pg) PuO反应的势能面静态特征.     

Localized exchange-correlation potential from second-order self-energy for accurate Kohn-Sham energy gap

A local Kohn-Sham (KS) exchange-correlation potential is derived by localizing the second-order self-energy operator, using approximations to the linear response Sham-Schlüter equation. Thanks to the use of the resolution-of-identity technique for the calculation of the self-energy matrix elements, the method is very efficient and can be applied to large systems. The authors investigate the KS energy gaps and lowest excitation energies of atoms and small- and medium-size molecules. Reference KS energy gaps (from accurate densities) of atoms and small molecules can be reproduced with great accuracy. For larger systems they found that the KS energy gap is smaller than the one obtained from the local-density approximation, showing the importance of an ab initio correlation in the Kohn-Sham potential.     

The correlation between molecular polarizability of PAHs and their retention data on various stationary phases in reversed-phase HPLC

Summary The equation for the potential energy of interactions established for gas-liquid chromatography has been confirmed in reversed phase liquid chromatography. Equations derived for molecular polarizabilities of PAHs and their retention data have very high correlation coefficients. The results indicate that the inductive effect between solute and stationary phase is the main one and the dispersive effect is very small compared with the inductive effect but its contribution increases with the carbon chain length of the stationary phase.     

Generalized density functional theory for degenerate states

An extension of density functional theory is proposed for degenerate states. There are suitably selected basic variables beyond the subspace density. Generalized Kohn-Sham equations are derived. A direct method is proposed to ensure the fixed value of ensemble quantities. Then the Kohn-Sham equations are similar to the conventional Kohn-Sham equations. But the Kohn-Sham potential is different for different ensembles. A simple local expression is proposed for the correlation energy.     

Independent particle theory with electron correlation

We formulate an effective independent particle model where the effective Hamiltonian is composed of the Fock operator and a correlation potential. Within the model the kinetic energy and the exchange energy can be expressed exactly leaving the correlation energy functional as the remaining unknown. Our efforts concentrate on finding a correlation potential such that exact ionization potentials and electron affinities can be reproduced as orbital energies. The equation-of-motion coupled-cluster approach enables us to define an effective Hamiltonian from which a correlation potential can be extracted. We also make the connection to electron propagator theory. The disadvantage of the latter is the inherit energy dependence of the potential resulting in a different Hamiltonian for each orbital. Alternatively, the Fock space coupled-cluster approach employs an effective Hamiltonian which is energy independent and universal for all orbitals. A correlation potential is extracted which yields the exact ionization potentials and electron affinities and a set of associated molecular orbitals. We also describe the close relationship to Brueckner theory.     

New approach to the correlation problem: Electron interaction potential as a variable in solving the many-particle Schrödinger equation

The many-electron wave function is represented as the product of the wave function of the independent particles and the function that depends only on the value of the interelectron interaction potential. The function defines the electron correlation effects; a standard linear differential equation was derived to define the function. The equation depends on the functions of independent particles; a generalization of the Hartree-Fock equations including electron correlation was obtained for these functions. The total energy calculation of two-electron ions shows that even solving an ordinary differential equation for the function of independent particles represented by the functions of noninteracting electrons leads to higher accuracy than the one achieved in the Hartree-Fock theory.     

Does an exact local exchange potential exist?

In Kohn–Sham density functional theory, equations for occupied orbital functions of a model state are derived from the exact ground‐state energy functional of Hohenberg and Kohn. The exchange‐correlation potential in these exact Kohn–Sham equations is commonly assumed to be a local potential function rather than a more general linear operator. This assumption is tested and shown to fail for the exchange potential in a Hartree–Fock model for atoms, for which accurate solutions are known. This revised version was published online in July 2006 with corrections to the Cover Date.     

Tunneling molecular dynamics in the light of the corpuscular-wave dualism theory

This paper presents the experimental demonstration of the corpuscular-wave dualism theory. The correlation between the de Broglie wavelength related to the thermal motion and the potential barrier width and height is reported. The stochastic jumps of light atoms (hydrogen, deuterium) between two equilibrium sites A and B (identical geometry) occur via different pathways; one pathway is over the barrier (classical dynamics), and the other one is through the barrier (tunneling). On the over-the-barrier pathway, there are no obstacles for the de Broglie waves, and this pathway exists from high to low temperatures up to 0 K because the thermal energy is subjected to the Maxwell distribution and a certain number of particles owns enough energy for the hopping over the barrier. On the tunneling pathway, the particles pass through the barrier, or they are reflected from the barrier. Only particles with the energy lower than barrier heights are able to perform a tunneling hopping. The de Broglie waves related to these energies are longer than the barrier width. The Schr?dinger equation is applied to calculate the rate constant of tunneling dynamics. The Maxwell distribution of the thermal energy has been taken into account to calculate the tunneling rate constant. The equations for the total spectral density of complex motion derived earlier by us together with the expression for the tunneling rate constant, derived in the present paper, are used in analysis of the temperature dependence of deuteron spin-lattice relaxation of the ammonium ion in the deuterated analogue of ammonium hexachloroplumbate ((ND4)2PbCl6). It has been established that the equation CpTtun = EH (thermal energy equals activation energy), where Cp is the molar heat capacity (temperature-dependent, known from literature), determines directly the low temperature Ttun at which the de Broglie wavelength, lambdadeBroglie, related to the thermal energy, CpT, is equal to the potential barrier width, L. Above Ttun, the lambdadeBroglie wavelength related to the CpT energy is shorter than the potential barrier width and not able to overcome the barrier. The activation energy EH equals 7.5 kJ/mol, and therefore, the Ttun temperature for deuterons in ((ND4)2PbCl6 is 55.7 K. The agreement between the potential barrier width following from the simple geometrical calculations (L = 0.722 A) and de Broglie wavelength at Ttun (L = 0.752 A) is good. The temperature plots of the deuteron correlation times for (ND4)2PbCl6 reveal comparable values of the correlation times of the tunneling, (tau(T)), and over-the-barrier jumps (tau(H)) near 34.8 K. Matsuo, on the basis of the molar heat capacity study, found the first-order phase transition at this temperature.     

Is the enthalpy of fusion of tris(acetylacetonato)metal(III) complexes affected by their potential energy in the crystal state?

In this Article we present enthalpies of fusion and melting points obtained from new thermochemical measurements of tris(acetylacetonato)metal(III), M(acac)(3), complexes (M = Fe, Al, Cr, Mn, Co) using differential scanning calorimetry (DSC) and evaluate them in relation to their different values found in the literature. An enthalpy of fusion of 27.67 kJ mol(-)(1) was derived for Mn(acac)(3) from a symmetrical DSC thermogram captured for the first time. The enthalpy value was indirectly confirmed with the solubility measurements of Mn(acac)(3) in acetylacetone. A hypothesis has been stated that the enthalpy of fusion and the potential energy of M(acac)(3) in the crystal state may be related. To calculate molecular in-crystal potential energy, in this Article we proposed a molecular mechanics model for the M(acac)(3) class of compounds. Nine X-ray crystal structures of M(acac)(3) complexes (M = Fe, Al, V, Mn, Co, Cr, Sc) were included in the modeling. The conformational potential energy was minimized for a molecule surrounded by other molecules in the crystal lattice. The partial charges from two schemes, the electrostatic potential (ESP) fit and the natural population analysis (NPA), were used to construct two types of force fields to examine which force field type would yield a better fit with the experimental thermal properties. The final force fields were named FF-ESP and FF-NPA. Both force field sets reproduced well the experimental crystal data of nine M(acac)(3) complexes as well as of tris(3-methyl-2,4-pentanedionato-O,O')cobalt(III). Only in-crystal potential energies derived by FF-NPA yielded a significant correlation (correlation coefficient R = -0.71) with the measured enthalpies of fusion. The enthalpy of fusion for Co(acac)(3) could not be determined experimentally because of simultaneous decomposition and fusion, and it is predicted to be 33.2 kJ mol(-)(1) from the correlation regression line.     

Exact electronic properties in the classically forbidden region of a metal surface

We derive exact properties of the inhomogeneous electron gas in the asymptotic classically forbidden region at a metal–vacuum interface within the framework of local effective potential energy theory. We derive a new expression for the asymptotic structure of the Kohn–Sham density functional theory (KS‐DFT) exchange‐correlation potential energy v_xc(r) in terms of the irreducible electron self‐energy. We also derive the exact asymptotic structure of the orbitals, density, the Dirac density matrix, the kinetic energy density, and KS exchange energy density. We further obtain the exact expression for the Fermi hole and demonstrate its structure in this asymptotic limit. The exchange‐correlation potential energy is derived to be v_xc(z → ∞) = ?α_KS,xc/z, and its exchange and correlation components to be v_x(z → ∞) = ?α_KS,x/z and v_c(z → ∞) = ?α_KS,c/z, respectively. The analytical expressions for the coefficients α_KS,xc and α_KS,x show them to be dependent on the bulk‐metal Wigner–Seitz radius and the barrier height at the surface. The coefficient α_KS,c = 1/4 is determined in the plasmon‐pole approximation and is independent of these metal parameters. Thus, the asymptotic structure of v_xc(z) in the vacuum region is image‐potential‐like but not the commonly accepted one of ?1/4z. Furthermore, this structure depends on the properties of the metal. Additionally, an analysis of these results via quantal density functional theory (Q‐DFT) shows that both the Pauli W_x(z → ∞) and lowest‐order correlation‐kinetic W(z → ∞) components of the exchange potential energy v_x(z → ∞), and the Coulomb W_c(z → ∞) and higher‐order correlation‐kinetic components of the correlation potential energy v_c(z → ∞), all contribute terms of O(1/z) to the structure. Hence correlations attributable to the Pauli exclusion principle, Coulomb repulsion, and correlation‐kinetic effects all contribute to the asymptotic structure of the effective potential energy at a metal surface. The relevance of the results derived to the theory of image states and to KS‐DFT is also discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Ab initio and analytic intermolecular potentials for Ar-CF4

Ab initio calculations at the CCSD(T) level of theory were performed to characterize the Ar + CF4 intermolecular potential. Potential energy curves were calculated with the aug-cc-pVTZ basis set, and with and without a correction for basis set superposition error (BSSE). Additional calculations were performed with other correlation consistent basis sets to extrapolate the Ar-CF4 potential energy minimum to the complete basis set (CBS) limit. Both the size of the basis set and BSSE have substantial effects on the Ar + CF4 potential. Calculations with the aug-cc-pVTZ basis set, and with a BSSE correction, appear to give a good representation of the BSSE corrected potential at the CBS limit. In addition, MP2 theory is found to give potential energies in very good agreement with those determined by the much higher level CCSD(T) theory. Two model analytic potential energy functions were determined for Ar + CF4. One is a fit to the aug-cc-pVTZ calculations with a BSSE correction. The second was derived by fitting an average BSSE corrected potential, which is an average of the CCSD(T)/aug-cc-pVTZ potentials with and without a BSSE correction. These analytic functions are written as a sum of two-body potentials and excellent fits to the ab initio potentials are obtained by representing each two-body interaction as a Buckingham potential.     

A realistic potential model for N-H vector diffusion in proteins

A realistic model for the potential energy for the diffusion of N-H vectors in a protein is proposed, massively modifying the simplistic models currently used in the literature. In particular, a quantitative and analytical connection between the order parameter of the N-H vector diffusion in a protein and the number of potential minima is established, offering a significant insight into the longstanding question of how protein dynamics is affected by the potential-energy landscape. The largest number of potential minima in a protein is estimated to be no more than around 25. In addition, the conformational entropies derived from classical statistical mechanics and quantum statistical mechanics are proved to be identical. Based on the presented theoretical formula, the number of potential minima for each residue of five representative proteins is evaluated and shows a good correlation between local structural flexibility and the number of potential minima.     

An analysis of nonlocal density functionals in chemical bonding

In this work, we carry out an analysis of the gradient-corrected density functionals in molecules that are used in the Kohn–Sham density functional approach. We concentrate on the special features of the exchange and correlation energy densities and exchange and correlation potentials in the bond region. By comparing to the exact Kohn–Sham potential, it is shown that the gradient-corrected potentials build in the required peak in the bond midplane, but not completely correctly. The gradient-corrected potentials also exhibit wrong asymptotic behavior. Contributions from different regions of space (notably bond and outer regions) to nonlocal bonding energy contributions are investigated by integrating the exchange and correlation energy densities in various spatial regions. This provides an explanation of why the gradient corrections reduce the local density approximation (LDA ) overbinding of molecules. It explains the success of the presently used nonlocal corrections, although it is possible that there is a cancellation of errors, too much repulsion being derived from the bond region and too little from the outer region. © John Wiley & Sons, Inc.     

Density functionals from many-body perturbation theory: the band gap for semiconductors and insulators

Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the derivative discontinuity of the exchange-correlation functional. In practice for semiconductors and insulators the band gap calculated within any local or semilocal density approximations underestimates severely the experimental energy gap. On the other hand, calculations with an "exact" exchange potential derived from many-body perturbation theory via the optimized effective potential suggest that improving the exchange-correlation potential approximation can yield a reasonable agreement between the Kohn-Sham band gap and the experimental gap. The results in this work show that this is not the case. In fact, we add to the exact exchange the correlation that corresponds to the dynamical (random phase approximation) screening in the GW approximation. This accurate exchange-correlation potential provides band structures similar to the local density approximation with the corresponding derivative discontinuity that contributes 30%-50% to the energy gap. Our self-consistent results confirm substantially the results for Si and other semiconductors obtained perturbatively [R. W. Godby et al., Phys. Rev. B 36, 6497 (1987)] and extend the conclusion to LiF and Ar, a wide-gap insulator and a noble-gas solid.     

Exchange and correlation energy in density functional theory

Several different versions of density functional theory (DFT) that satisfy Hohenberg–Kohn theorems are characterized by different definitions of a reference or model state determined by an N‐electron ground state. A common formalism is developed in which exact Kohn–Sham equations are derived for standard Kohn–Sham theory, for reference‐state density functional theory, and for unrestricted Hartree–Fock (UHF) theory considered as an exactly soluble model Hohenberg–Kohn theory. A natural definition of exchange and correlation energy functionals is shown to be valid for all such theories. An easily computed necessary condition for the locality of exchange and correlation potentials is derived. While it is shown that in the UHF model of DFT the optimized effective potential (OEP) exchange satisfies this condition by construction, the derivation shows that this condition is not, in general, sufficient to define an exact local exchange potential. It serves as a test to eliminate proposed local potentials that are not exact for ground states. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 521–525, 2000     

A kinetic energy fitting metric for resolution of the identity second-order Møller-Plesset perturbation theory

A kinetic-energy-based fitting metric for application in the context of resolution of the identity second-order M?ller-Plesset perturbation theory is presented, which is derived from the Poisson equation. Preliminary tests of the applicability include the evaluation of the error in the correlation energy, compared to standard M?ller-Plesset perturbation theory, with respect to the auxiliary basis set employed. We comment on the potential merits of this fitting metric, compared to standard resolution of the identity second-order M?ller-Plesset perturbation theory, and discuss its scaling behavior in the limit of large molecules.     

PuN和PuN_2基态分子的结构与势能函数

用相对论有效原子实势和密度泛函理论方法对PuN和PuN_2分子的结构进行优化 ，得到了其平衡几何构型和谐振频率。采用最小二乘法拟合出PuN基态分子的 Murrell-Sorbie解析势能函数，在此基础上推导出光谱数据和力常数，并用多体展 式理论导出PuN_2基态分子的解析势能函数，正确地反映了其平衡构型特性。     

Universal density functional approach to the calculation of correlation energies of atoms

A new local density functional approach for the calculation of correlation energies of many-electron atomic systems is proposed by using the exact results for the correlation energy of a two-electron system bound by a harmonic oscillator external potential. This is motivated by the fact that the correlation energy is a universal functional of the electron density, and the form of this functional is independent of the external potential. The calculated numerical results for the correlation energies show very good agreement with the standard values reported in the literature. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 461–465, 1997