应用Monte Carlo方法计算He原子包含电子相关作用的基态能量

应用Monte Carlo方法计算He原子包含电子相关波函数的基态能量,获得了与精确值非常接近的结果．实践表明,应用Monte Carlo方法有可能在多电子体系中直接采用包含任意2个电子间距离ry的函数作为变分函数来考虑电子相关作用．     

Rovibrationally averaged properties of H2 using Monte Carlo methods

Using variational Monte Carlo and a simple explicitly correlated wave function, we have computed 18 molecular properties of the hydrogen molecule (X¹∑) at 24 internuclear distances. These properties have been combined with rapidly convergent rovibrational wave functions to produce rovibrationally averaged properties for several of the lowest rotational and vibrational levels of this system. Our results are in very good agreement with previous values found in the literature. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

p-Difluorobenzene-argon ground state intermolecular potential energy surface

The ground state intermolecular potential energy surface for the p-difluorobenzene-Ar van der Waals complex is evaluated using the coupled cluster singles and doubles including connected triple excitations [CCSD(T)] model and the augmented correlation consistent polarized valence double-zeta basis set extended with a set of 3s3p2d1f1g midbond functions. The surface minima are characterized by the Ar atom located above and below the difluorobenzene center of mass at a distance of 3.5290 A. The corresponding binding energy is -398.856 cm(-1). The surface is used in the evaluation of the intermolecular level structure of the complex. The results clearly improve previously available data and show the importance of using a good correlation method and basis set when dealing with van der Waals complexes.     

A systematic investigation of the ground state potential energy surface of H3+

Based on different ab initio electronic structure calculations (CI-R12 and Gaussian Geminals) of the Born-Oppenheimer electronic energy E(BO) of H(3)(+) from high to highest quality, we build up a potential energy surface which represents a highly reliable form of the topology of the whole potential region, locally and globally. We use the CI-R12 method in order to get within reasonable CPU-time a relatively dense grid of energy points. We demonstrate that CI-R12 is good enough to give an accurate surface, i.e., Gaussian Geminals are not absolutely necessary. For different types of potential energy surface fits, we performed variational calculations of all bound vibrational states, including resonances above the dissociation limit, for total angular momentum J = 0. We clarify the differences between different fits of the energy to various functional forms of the potential surface. Small rms-values (<1 cm(-1)) of the fit do not provide precise information about the interpolatory behaviour of the fit functions.     

The chlorobenzene-argon ground state intermolecular potential energy surface

Using the coupled cluster singles and doubles including connected triple excitations model with the augmented correlation consistent polarized valence double zeta basis set extended with a set of 3s3p2d1f1g midbond functions, we evaluate the ground state intermolecular potential energy surface of the chlorobenzene-argon van der Waals complex. The minima of 420 cm(-1) are characterized by Ar atom position vectors of the length 3.583 A, forming an angle of 9.87 degrees with respect to the axis perpendicular to the chlorobenzene plane. These results are compared to those obtained for similar complexes and to the experimental data available. From the potential the three-dimensional vibrational eigenfunctions and eigenvalues are calculated and the results allow to correct and complete the experimental assignment.     

Monte Carlo free energy calculations using electronic structure methods

The molecular mechanics-based importance sampling function (MMBIF) algorithm [R. Iftimie, D. Salahub, D. Wei, and J. Schofield, J. Chem. Phys. 113, 4852 (2000)] is extended to incorporate semiempirical electronic structure methods in the secondary Markov chain, creating a fully quantum mechanical Monte Carlo sampling method for simulations of reactive chemical systems which, unlike the MMBIF algorithm, does not require the generation of a system-specific force field. The algorithm is applied to calculating the potential of mean force for the isomerization reaction of HCN using thermodynamic integration. Constraints are implemented in the sampling using a modification of the SHAKE algorithm, including that of a fixed, arbitrary reaction coordinate. Simulation results show that sampling efficiency with the semiempirical secondary potential is often comparable in quality to force fields constructed using the methods suggested in the original MMBIF work. The semiempirical based importance sampling method presented here is a useful alternative to MMBIF sampling as it can be applied to systems for which no suitable MM force field can be constructed.     

Ab initio potential energy surface for HeF2 in its ground electronic state

The ground state potential energy surface for He–F₂ has been generated using the coupled-cluster singles and doubles excitation approach with perturbative treatment of triple excitations [CCSD(T)] and multi-reference configuration interaction (MRCI) methodologies, with augmented correlation consistent quadruple zeta basis set and diffused functions. Both the CCSD(T) and MRCI surfaces are compared and the results analyzed. The CCSD(T) surface exhibits van der Waals minima at different distances for different orientations of He approaching F₂ and is adequate to describe accurately only in the region around the equilibrium bond distance of F₂. The MRCI surface, on the other hand, yields reliable results for a wider range of F–F bond distances leading to the correct asymptote. Davidson correction to the MRCI surface makes it purely repulsive over the regions investigated.     

Ab initio potential energy surface and excited vibrational states for the electronic ground state of Li2H

A 285-point multi-reference configuration-interaction involving single and double excitations (MRS-DCI) potential energy surface for the electronic ground state of Li₂H is determined by using 6-311G (2df, 2pd) basis set. A Simons-Parr-Finlan polynomial expansion is used to fit the discrete surface with a X² of 4.64 × 10^-6. The equilibrium geometry occurs at R_e =0.172 nm and <LiHLi =94.10. The dissociation energy for reaction Li₂H(²A)⇑ Li₂(¹⌆_g)+H(²S) is 243.910 kJ/mol. and that for reaction Li₂H(²A)⇑HLi(¹be)+Li(²S) is 106.445 kJ/mol. The inversion barrier height is 50.388 kJ/mol. The vibrational energy levels are calculated using the discrete variable representation (DVR) method. Project supported by the National Natural Science Foundation of China (grant No. 29673029) and by the Special Doctoral Research Foundation of the State Education Commission of China.     

Ab initio potential energy surface and excited vibrational states for the electronic ground state of Li_2H

A 285-pomt multi-reference configuration-interaction involving single and double excitations ( MRS DCI) potential energy surface for the electronic ground state of L12H is determined by using 6-311G (2df,2pd)basis set.A Simons-Parr-Finlan polynomial expansion is used to fit the discrete surface with a x2 of 4.64×106 The equn librium geometry occurs at Rc=0.172 nm and,LiHL1=94.10°.The dissociation energy for reaction I2H(2A)→L12(1∑g)+H(2S) is 243.910 kJ/mol,and that for reaction L12H(2A')→HL1(1∑) + L1(2S) is 106.445 kl/mol The inversion barrier height is 50.388 kj/mol.The vibrational energy levels are calculated using the discrete variable representation (DVR) method.     

A new analytical potential energy surface for the singlet state of He2H+

The analytic potential energy surface (APES) for the exchange reaction of HeH(+) (X(1)Σ(+)) + He at the lowest singlet state 1(1)A(∕) has been built. The APES is expressed as Aguado-Paniagua function based on the many-body expansion. Using the adaptive non-linear least-squares algorithm, the APES is fitted from 15 682 ab initio energy points calculated with the multireference configuration interaction calculation with a large d-aug-cc-pV5Z basis set. To testify the new APES, we calculate the integral cross sections for He + H(+)He (v = 0, 1, 2, j = 0) → HeH(+) + He by means of quasi-classical trajectory and compare them with the previous result in literature.     

The ground state potential energy surface of methyl fluoride dimer

Potential energy surface for methyl fluoride dimer has been studied theoretically with ab initio molecular orbital method, using a 4-31G basis set. Dimer dissociation energies, Mulliken electronic populations, and dipole moments were obtained.     

A six-dimensional H(2)-H(2) potential energy surface for bound state spectroscopy

We present a six-dimensional potential energy surface for the (H(2))(2) dimer based on coupled-cluster electronic structure calculations employing large atom-centered Gaussian basis sets and a small set of midbond functions at the dimer's center of mass. The surface is intended to describe accurately the bound and quasibound states of the dimers (H(2))(2), (D(2))(2), and H(2)-D(2) that correlate with H(2) or D(2) monomers in the rovibrational levels (v,j)=(0,0), (0,2), (1,0), and (1,2). We employ a close-coupled approach to compute the energies of these bound and quasibound dimer states using our potential energy surface, and compare the computed energies for infrared and Raman transitions involving these states with experimentally measured transition energies. We use four of the experimentally measured dimer transition energies to make two empirical adjustments to the ab initio potential energy surface; the adjusted surface gives computed transition energies for 56 experimentally observed transitions that agree with experiment to within 0.036 cm(-1). For 26 of the 56 transitions, the agreement between the computed and measured transition energies is within the quoted experimental uncertainty. Finally, we use our potential energy surface to predict the energies of another 34 not-yet-observed infrared and Raman transitions for the three dimers.     

Vibrational–rotational energies of all H2 isotopomers using Monte Carlo methods

Using variational Monte Carlo techniques, we have computed several of the lowest rotational–vibrational energies of all the hydrogen molecule isotopomers (H₂, HD, HT, D₂, DT, and T₂). These calculations do not require the excited states to be explicitly orthogonalized. We have examined both the usual Gaussian wave function form as well as a rapidly convergent Padé form. The high‐quality potential energy surfaces used in these calculations are taken from our earlier work and include the Born–Oppenheimer energy, the diagonal correction to the Born–Oppenheimer approximation, and the lowest‐order relativistic corrections at 24 internuclear points. Our energies are in good agreement with those determined by other methods. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

A new "spectroscopic" potential energy surface for formaldehyde in its ground electronic state

We report a new "spectroscopic" potential energy surface (PES) of formaldehyde (H(2)(12)C(16)O) in its ground electronic state, obtained by refining an ab initio PES in a least-squares fitting to the experimental spectroscopic data for formaldehyde currently available in the literature. The ab initio PES was computed using the CCSD(T)/aug-cc-pVQZ method at 30 840 geometries that cover the energy range up to 44 000 cm(-1) above equilibrium. Ro-vibrational energies of formaldehyde were determined variationally for this ab initio PES by means of the program TROVE [Theoretical ROtation-Vibration Energies; S. N. Yurchenko, W. Thiel, and P. Jensen, J. Mol. Spectrosc. 245, 126 (2007)]. The parameter values in the analytical representation of the PES were optimized in fittings to 319 ro-vibrational energies with J = 0, 1, 2, and 5. The initial parameter values in the fittings were those of the ab initio PES, the ro-vibrational eigenfunctions obtained from this PES served as a basis set during the fitting process, and constraints were imposed to ensure that the refined PES does not deviate unphysically from the ab initio one in regions of configuration space not sampled by the experimental data. The resulting refined PES, referred to as H(2)CO-2011, reproduces the available experimental J ≤ 5 data with a root-mean-square error of 0.04 cm(-1).     

The potential energy surface of the jahn-teller-distorted 2E' ground state of copper trimer

It is shown that the configuration interaction calculations of Walch and Laskowski for the ground ²E' state of Cu₃ are consistent with truncating the potential energy at second order in the distance from the D_3h conical intersection, which leads to a diabatic representation (the “quadratic coupling model”) containing three parameters. Fitting these parameters to three of the vibronic spacings of Rohlfing and Valentini leads to a reasonable explanation of their spectrum. The resulting potential energy surfaces show a Jahn-Teller stabilization energy of 221 cm⁻¹ and a pseudorotation barrier of 95 cm⁻¹.     

A benchmark quantum Monte Carlo study of the ground state chromium dimer

We report calculations of the ground state energy and binding curve of the chromium dimer using the variational and diffusion quantum Monte Carlo (VMC and DMC) methods. We examined various single‐determinant and multideterminant wavefunctions multiplied by a Jastrow factor as a trial/guiding wavefunction for VMC/DMC. The molecular orbitals in the single determinants were calculated using restricted or unrestricted Hartree–Fock or density functional theory (DFT) calculations where five commonly used local (SVWN5), semilocal (PW91 and BLYP), and hybrid (B1LYP and B3LYP) functionals were examined. The multideterminant expansions were obtained from the generalized valence bond and (truncated) unrestricted configuration interaction with single and double excitations (UCISD) methods. We also examined a UCISD wavefunction in which UCISD expansions were added to the UB3LYP single‐determinant reference, and their coefficients were optimized at the VMC level. In addition to the wavefunction dependence, the effects of pseudopotentials and backflow transformation were also investigated. The UB3LYP single‐determinant and multideterminant wavefunctions were found to give the variationally best DMC energies within the framework of single‐determinant and multideterminants, respectively, though both the DMC energies were higher than twice the DMC atomic energy. Some of the VMC binding curves show a flat or quite shallow well bottom, which gets recovered deeper by DMC. All the DMC binding curves have a minimum indicating a bound state, but the unrestricted ones overestimate the equilibrium bond length. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

A Monte Carlo error estimator for the expansion of rigid-rotor potential energy surfaces

The computation of rotational energy transfer in nonreactive molecular collisions requires expanding the orientation dependence of the interaction potential over an appropriate complete set of orthonormal functions. We show that the use of random grids for the sampling of the angular geometries combined with the Monte Carlo theorem allows to estimate the mean accuracy on each expansion term determined by a least squares fit. The interest of our approach is illustrated by an application to the H₂O–H₂ system, of great astrophysical interest.