A potential harmonic method for the three-body coulomb problem

A potential harmonic method that is suitable for the three-body coulomb systems is presented. This method is applied to solve the three-body Schroedinger equations for He and e ⁺ e ⁻ e ⁺ directly, and the calculations yield very good results for the energy. For example, we obtain a ground-state energy of −0.26181 hartrees for e ⁺ e ⁻ e ⁺, and −2.90300 hartrees for He with finite nuclear mass, in good agreement with the exact values of −0.26200 hartrees and −2.90330 hartrees. Compared with the full-set calculations, the errors in the total energy for ground and excited states of e ⁺ e ⁻ e ⁺ are very small, around −0.0001 hartrees. We conclude that the present method is one of the best PH methods for the three-body coulomb problem. Received: 5 September 1996 / Accepted: 14 July 1997     

Coefficient interrelatedness among polynomial potential functions of diatomic molecules

It is shown that the diatomic potential energy functions of Dunham, SPF and Ogilvie can be easily converted from one another when their coefficients are related. Through Maclaurin expansion and comparison of terms, the coefficients can be related by using the Pascal Triangle. In this paper, the coefficients were related up to the tenth order of δr/R for HX (X = H, Ga, Cl, I). Comparison of all three potential energy curves shows very good agreement for r ≤ 1.5R, thereby verifying the formulated relations. Observation of the plotted potential energy curves for r > 1.5R shows that the difference of the three potential function definitions is not reflected as any consistent trend arising from the related potential functions.     

Ground-state energy of an s-state model of the inhomogeneous electron liquid in relation to an exactly solvable model of He with additional radial correlation

Following Temkin’s proposal of the so-called s-wave model, Amovilli, Howard and March (AHM) displayed an exactly solvable model Hamiltonian in which an additional radial correlation is added. The ground-state wave function for this Hamiltonian, for modelling He-like atomic ions with nuclear charge Ze, is used here to compare and contrast with the Temkin Model. The differences only appear near the critical charges Z_ce at which one electron ionises, Z_c being precisely unity for the AHM model and having the value 0.948768 in Serra’s variational study of the s-wave model. These two models are then compared with He-like ions having the correct e²/r₁₂ interaction.     

Correlation-function potential-harmonic and generalized Laguerre function method for directly solving Schrodinger equations of atoms

The potential-harmonic and generalized Laguerre function method (PHGLF) was modified into the correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF). The eigenenergies for 21S, 31S and 41S states of helium-like systems from the CFPHGLF are much more accurate than those from the previous PHGLF, but the eigenenergy for the 11S is not as good as that from the PHGLF method. The results indicate that the electron-nucleus cusp plays more important role than the electron-electron cusp and the cluster structure for the loosely bound excited states, and that the electron-electron cusp is absolutely essential for the tightly bound ground state.     

Effect of available volumes on radial distribution functions

The traditional method of analyzing solution structuring properties of solutes using atom–atom radial distribution functions (rdfs) can give rise to misleading interpretations when the volume occupied by the solute is ignored. It is shown by using the examples of O(4) in α- and β-D-allose that a more reliable interpretation of rdfs can be obtained by normalising the rdf using the available volume, rather than the traditional volume of a spherical shell. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 363–367, 1998     

Application of renormalized coupled-cluster methods to potential function of water

The goal of this paper is to examine the performance of the conventional and renormalized single-reference coupled-cluster (CC) methods in calculations of the potential energy surface of the water molecule. A comparison with the results of the internally contracted multi-reference configuration interaction calculations including the quasi-degenerate Davidson correction (MRCI(Q)) and the spectroscopically accurate potential energy surface of water resulting from the use of the energy switching (ES) approach indicates that the relatively inexpensive completely renormalized (CR) CC methods with singles (S), doubles (D), and a non-iterative treatment of triples (T) or triples and quadruples (TQ), such as CR-CCSD(T), CR-CCSD(TQ), and the recently developed rigorously size extensive extension of CR-CCSD(T), termed CR-CC(2,3), provide substantial improvements in the results of conventional CCSD(T) and CCSD(TQ) calculations at larger internuclear separations. It is shown that the CR-CC(2,3) results corrected for the effect of quadruply excited clusters through the CR-CC(2,3)+Q approach can compete with the highly accurate MRCI(Q) data. The excellent agreement between the CR-CC(2,3)+Q and MRCI(Q) results suggests ways of improving the global potential energy surface of water resulting from the use of the ES approach in the regions of intermediate bond stretches and intermediate energies connecting the region of the global minimum with the asymptotic regions. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

Precise potential harmonic approach to directly solving Schrodinger equations of helium-like three-body systems

A complete potential harmonic scheme is presented,including the linked coupled hyperradial ordi nary differential equations and the secular equation of eigencnergy It has been used to directly solve the Scchrodinger equations of helium-like three-body systems (nuclear charge Z=1-9),and very accurate ground state eigonenergies as well as low-lying singlet excited state ones have been obtained     

Analytical potential energy function for the Van der Waals molecule He2Ne

A potential energy function has been derived for the two linear isomer structures He₂Ne⁺(X²Σ⁺) using ab initio calculations with the QCISD(T)/6–31++G(d,p) method. Because we use the reasonable dissociation limit (3) instead of the unacceptable one (1), our potential energy function represents considerable topographical features in detail, including the linear [He---Ne⁺---He] structure (R_HeNe = 1.4694 Å, R_He'Ne = 2.0069 Å HeNeHe = 180°) with two symmetric linear saddles (R_HeNe = R_He'Ne = 1.80 Å, HeNeHe = 180° and R_HeNe = 1.5 Å, R_He'Ne = 3.2 A°, HeNeHe = 180°), and the topographical minimum of the [He---He---Ne⁺] structure (R_HeHe = 2.2217 Å, R_HeNe = 1.4426 Å, HeHeNe = 180°), with a linear saddle (R_HeHe' = 3.0 Å, R_HeNe = 1.8 Å, HeHeNe = 180°).     

On construction of diatomic potential energy functions

The Clinton function α_n( R ) corresponding to the model potential energy function U_n( R ), is proposed as a test of applicability of U_n( R ). Such an analysis is given for some model potential energy functions.     

用θ-2θ型衍射仪测定溶液结构的新方法

叙述了θ－２θ型Ｘ射线衍射仪精确测定电解质溶液的结构的新实验技术。设计制作了具有慢温功能的最液体样品池，并建立了样品池窗口强度的校正方法，优化了液体Ｘ射线衍射数据和结构参数精细化的计算机程序，获得了非常令人满意的实验结果，由θ－２θ型Ｘ射线衍射仪精确测定的径向分布函数与θ－θ型衍射仪自由散射比较，表明ＤＲＦ分辨率有所提高。     

Precise potential harmonic approach to directly solving Schrödinger equations of helium-like three-body systems

A complete potential harmonic scheme is presented, including the linked coupled hyperradial ordinary differential equations and the secular equation of eigenenergy. It has been used to directly solve the Schrödinger equations of helium-like three-body systems (nuclear chargeZ = 1–9). and very accurate ground state eigenenergies as well as low-lying singlet excited state ones have been obtained.     

The sound velocities in dense fluids from distribution functions

The sound velocities and adiabatic compressibilities in dense fluids have been evaluated using three known analytical expressions for radial distribution functions (RDFs). Using such approach not only tests the power of distribution functions theory in predicting the sound velocities and adiabatic compressibilities, but also specifies better expressions in determining these properties. To calculate these quantities, the variation of RDF with density and temperature is required. Therefore, we should have analytical expressions which explicitly present RDF as a function of temperature, density and interparticle distance. It is shown that if an expression is used which properly presents RDFs as a function of interparticle distance, density and temperature, it is possible to calculate sound velocities and adiabatic compressibilities from distribution function theory.     

Degeneracy of confined D‐dimensional harmonic oscillator

Using the mathematical properties of the confluent hypergeometric functions, the conditions for the incidental, simultaneous, and interdimensional degeneracy of the confined D‐dimensional (D > 1) harmonic oscillator energy levels are derived, assuming that the isotropic confinement is defined by an infinite potential well and a finite radius R_c. Very accurate energy eigenvalues are obtained numerically by finding the roots of the confluent hypergeometric functions that confirm the degeneracy conditions. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

On the calculation of time correlation functions by potential scaling

We present and analyze a general method to calculate time correlation functions from molecular dynamics on scaled potentials for complex systems for which simulation is affected by broken ergodicity. Depending on the value of the scaling factor, correlations can be calculated for times that can be orders of magnitude longer than those accessible to direct simulations. We show that the exact value of the time correlation functions of the original system (i.e., with unscaled potential) can be obtained, in principle, using an action-reweighting scheme based on a stochastic path-integral formalism. Two tests (involving a bistable potential model and a dipeptide bond-vector orientational relaxation) are exemplified to showcase the strengths, as well as the limitations of the approach, and a procedure for the estimation of the time-dependent standard deviation error is outlined.     

Radial Functions of AIH X 1∑+ from Vibration-Rotational Spectra ana Spectral Properties of the Group 13 Hydrides

The coefficients C_j , j ≤ 9, defining the potential-energy V(z) and coefficients of two other radial functions related to adiabatic and nonadiabatic effects have been determined for AlH in the electronic ground state X ¹∑⁺ by a direct fit to the published frequencies and wavenumbers of vibration-rotational transitions of ²⁷Al¹H and ²⁷Al²H. The functions are valid in the range of internuclear distance/10^?10 m [1.24, 2.60]. Some trends in the spectral properties of the group 13 hydrides AlH, GaH, InH and TlH are discussed. The possibility of determining the rotational magnetogyric factor g_j from the available data of only wavenumbers of vibration-rotational transitions is considered; an approximate value g_j ～ ?2.25 is deduced for ²⁷Al¹H.     

用θ-2θ型衍射仪测定溶液结构的新方法

叙述了用θ－２θ型Ｘ射线衍射仪精确测定电解质溶液结构的新实验技术。设计制作了具有恒温功能的超厚液体样品池，并建立了样品池窗口强度的校正方法。优化了液体Ｘ射线衍射数据和结构参数精细化的计算机程序，获得了非常令人满意的实验结果。由θ－２θ型Ｘ射线衍射仪精确测定的径向分布函数与θ－θ型衍射仪自由散射比较，表明ＤＲＦ分辨率有所提高。     

用θ-2θ型粉末衍射仪精确测定溶液结构的新尝试

发展了用θ-2θ型衍射仪测定电解质水溶液结构的新方法.设计了具有恒温功能的超厚液体样品池并建议池窗口强度的校正规程.获得了令人非常满意的实验结果.θ-2θ型粉末衍射仪测定的径向分布函数与θ-θ型衍射仪的自由表面散射比较,表明径向分布函数分辨率有所提高.     

On the high accuracy of mp2-optimised geometmes and harmonic frequencies with large basis sets

An efficient procedure for the calculation of second derivatives of the energy at the closed-shell second-order Móller-Plesset (MP2) level of accuracy is described. The method is applied to H₂O, NH₃, H₂CO and HCN using large (TZ+2P or better) basis sets. For this set of molecules the accuracy of the optimised geometries is for single bonds ±0.002 Å, multiple bonds ±0.01 Å, angles ±0.2° and the mean error of the harmonic frequencies is 1.5%.     

On the number of spin functions in the first order interaction space

A proof is given that in a configuration interaction method the first-order interaction space contains at most only twice as many spin functions as the zeroth-order space. This allows for a dramatic reduction of the size of CI expansion. For most of the high-spin systems only two spin functions for each configuration are needed.