Energy of the ground state of Be

The contributions from the diagrams of the first two orders are calculated for the energy of the ground state of Be. The result is E₂= =–1.25 Z²+1.55927422 Z–0.8775, with E ₂ ^corr =–0.01172683 Z –0.0720. Perturbation theories for the ground-state energy of Be are compared for Hartree-Fock and hydrogen-type functions.     

Configuration interaction benchmark for Be ground state

A set of 432 energy-optimized Slater-type radial orbitals together with spherical harmonics up to ? = 30 is used to approximate the corresponding full configuration interaction (CI) expansion for Be ground state. An analysis of radial and angular patterns of convergence for the energy yields a basis set incompleteness error of 8.7 μhartree of which 85% comes from radial basis truncations for ? ≤ 30. Select-divide-and-conquer CI (Bunge in J Chem Phys 125:014107, 2006; Bunge and Carbó-Dorca in J Chem Phys 125:014108, 2006) produces an energy upper bound 0.02(1) μhartree above the full CI limit. The energy upper bound E = ?14.6673473 corrected with these two truncation energy errors yields E = ?14.6673560 a.u. (Be) in fair agreement with the latest explicitly correlated Gaussian results of E = ?14.66735646 a.u. (Be). The new methods employed are discussed. It is acknowledged that at this level of accuracy traditional atomic CI has reached a point of diminishing returns. Modifications of conventional (orbital) CI to seek for significantly higher accuracy without altering a strict one-electron orbital formalism are proposed.     

Reduced first order density matrix for the Be ground state

A reduced first order density matrix for the Be ground state is computed from an extensive configuration interaction (CI ) wave function. A sequence of increasingly accurate CI wave functions Φ_q converging towards the exact Ψ is used to assess the quality of the results which include approximate bounds for the overlaps 〈Φ_q|Ψ〉, electron–nuclear coalescence cusp data, Weinhold's overlap between density matrices, virial ratios, occupation number spectra, and some expectation values. The nuclear magnetic shielding constant and the molar diamagnetic susceptibility are determined with 2.0 and 1.5% of uncertainty, respectively.     

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.     

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.     

On the ground state of Pd13

First-principles electronic structure calculations within a gradient corrected density functional formalism have been carried out to investigate the electronic structure and magnetic properties of Pd(13) clusters. It is shown that a bilayer ground-state structure that can be regarded as a relaxed bulk fragment is most compatible with the experimental results from Stern-Gerlach measurements. An icosahedral structure, considered to be the ground state in numerous previous studies, is shown to be around 0.14 eV above the ground state. A detailed analysis of the molecular orbitals reveals the near degeneracy of the bilayer or icosahedral structures is rooted in the stabilization by p- or d-like cluster orbitals. The importance of low-lying spin states in controlling the electronic and magnetic properties of the cluster is highlighted.     

A slater-transform-preuss (STP) wavefunction for the ground state of Be

A class of integral transform functions previously applied to He and Li has been extended to the ground state of Be where an energy of −14.567553 au was obtained. Although the function is slightly less than double-zeta quality and requires numerical integration techniques, it is shown how the parameters of the function can be related to single-zeta screening constants while obtaining much improved minimal basis energies.     

On the stability of the autodissociative ground electronic state of BeH2+

It is shown that the mechanism of spontaneous infrared emission enhances substantially the stability of the long-lived ground electronic state of the exotic BeH²⁺, whose autodissociation becomes possible only via tunneling. The system, initially situated in any vibrational level (except the high-lying ones for which dissociation is predominate) and statistically distributed over all rotational states, reaches stability through a cascade of dipole emissions toward lower levels. The rapid spatial variation of the dipole moment results in fast radiative processes and might suggest experimental observations easier to perform. The methodology is based on a recently presented analytic discrete variable representation (DVR ) [D.T. Colbert and W.H. Miller, J. Chem. Phys. 96 , 1982 (1992)] that facilitates calculations. This might prove particularly useful to spectroscopists, allowing a check of the quality of potentials produced by inversion methods or the reliable calculation of spectrochemical quantities. © 1995 John Wiley & Sons, Inc.     

On the spin-orbit splitting of CuCl2 in its 2 Pi g ground state

The spin-orbit splitting of CuCl(2) in its ground X(2)Pi(g) state remains an unknown or, at best, poorly defined quantity. The electronic spectrum of CuCl(2) has been studied by Fourier transform resolved, laser-induced fluorescence between 602 and 587 nm, in an attempt to identify transitions to the upper spin component of the ground state. In order to provide a well-defined excitation process, the sample was cooled to rotational temperatures of about 10 K in a free-jet expansion. Observations from just two rotationally perturbed levels in the upper electronic state, one for (63)Cu(35)Cl(2) and the other for (65)Cu(35)Cl(37)Cl, have revealed an additional feature about 482 cm(-1) above the (2)Pi(3/2) state. The effective rotational constants associated with these levels (0.066 20 cm(-1) for (63)Cu(35)Cl(2)) are significantly larger than those for the ground (2)Pi(3/2) state (0.058 13 cm(-1)). Analysis of this feature as the (2)Pi(1/2) component leads to a value of -482.9 cm(-1) for the spin-orbit coupling constant A and of -0.0846 cm(-1) for the lambda-doubling parameter (p+2q) for (63)Cu(35)Cl(2). Several other previously unobserved levels are also identified within 2000 cm(-1) of the ground state. Many of these also have anomalously large rotational constants.     

Estimation of the ground state correlation energy for isoelectronic series of 2 to 20 electrons

Correlation energies for all isoelectronic sequences of 2 to 20 electrons andZ=2 to 25 are obtained by taking differences between theoretical total energies of Dirac-Fock calculations and experimental total energies. These are pure relativistic correlation energies because relativistic and QED effects are already taken care of. The theoretical as well as the experimental values are analysed critically in order to get values as accurate as possible. The correlation energies obtained show an essentially consistent behaviour fromZ=2 to 17. ForZ>17 inconsistencies occur indicating errors in the experimental values which become very large forZ>25.     

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.     

On the ground state and first excited state geometries of syn-sesquinorbornene

Extende Hückel calculations on the title compound ($\text{1}$) predict hinge-like bending of the double bond corresponding to interplanar angles of 167° for the ground state and 210° for the first excited state. The predictions are discussed in terms of hyperconjugative interactions.     

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.     

A ground state potential energy surface for H2 using Monte Carlo methods

Using variational Monte Carlo and a simple explicitly correlated wave function we have computed the Born-Oppenheimer energy of the H2 ground state (X 1Sigmag+) at 24 internuclear distances. We have also calculated the diagonal correction to the Born-Oppenheimer approximation and the lowest-order relativistic corrections at each distance using variational Monte Carlo techniques. The nonadiabatic values are evaluated from numerical derivatives of the wave function with respect to the nuclear coordinates. With this potential energy surface we have computed several of the lowest vibrational-rotational energies for this system. Our results are in good agreement with the best values found in the literature.     

Carbon-beryllium binding in CH2Be

Ab initio molecular orbital theory is used to study carbon-beryllium binding in the lowest singlet and triplet states of CH₂Be. When electron correlation is included, both singlet and triplet states are significantly bound relative to the ground states of CH₂ and Be fragments.     

Connection between the upper and lower energy regions of the potential energy surface of the ground electronic state of the HSO2 system

The importance of the HSO(2) system in atmospheric and combustion chemistry has motivated several works dedicated to the study of associated structures and chemical reactions. Nevertheless, controversy still exists about a possible connection between the upper and lower energy regions of the potential energy surface (PES) for the ground electronic state of the system. Very recently, a path to connect these regions was proposed based on studies at the CASPT2/aug-cc-pV(T+d)Z level of calculation but the small energy difference between some of the transitions states along that path suggested the necessity of calculations at a higher level of theory. In the present work, we report a CCSD(T)/aug-cc-pV(T+d)Z study of the stationary states associated to the proposed connection path, including assessment of the most reliable complete basis set (CBS) extrapolation scheme for the system. Among the new features, the present calculations show that there are no structures corresponding to the HSO(2)(b) minimum and the TS3 saddle point obtained at the CASPT2 level and that the connection path between the upper and lower energy regions of the PES for the ground electronic state involves only one transition state and most probably more than one electronic state.     

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.     

Error bounds for the nonrelativistic electronic ground state energy of molecular hydrogen

Upper and lower bounds are calculated for the nonrelativistic electronic ground state energy of the¹ _g ⁺ state of molecular hydrogen using the method of variance minimization with Hylleraas-CI functions. In order to solve the occurring new integrals centered interparticle coordinates were introduced.