Helium Dimer Interaction Energies from Gaussian Geminal and Orbital Calculations

Generation of Basis Sets for Accurate Molecular Calculations: Application to Helium Atom and Dimer

A new approach for basis set generation is reported and tested in helium atom and dimer. The basis sets thus computed, named sigma, range from DZ to 5Z and consist of the same composition as Dunning basis sets but with a different treatment of contractions. The performance of the sigma sets is analyzed for energy and other properties of He atom and He dimer, and the results are compared with those obtained with Dunning and ANO basis sets. The sigma basis sets and their extended versions up to triple augmented provide better energy values than Dunning basis sets of the same composition, and similar values to those attained with the currently available ANO. Extrapolation to complete basis set of correlation energy is compared between the sigma basis sets and those of Dunning, showing the better performance of the former in this respect.

On the formation of (anionic) excited helium dimers in helium droplets

Metastable atomic and molecular helium anions exhibiting high-spin quartet configurations can be produced in helium droplets via electron impact. Their lifetimes allow detection in mass spectrometric experiments. Formation of atomic helium anions comprises collision-induced excitation of ground state helium and concomitant electron capture. Yet the formation of molecular helium anions in helium droplets has been an unresolved issue. In this work, we explore the interaction of excited helium atoms exhibiting high-spin triplet configurations with ground state helium using the equation-of-motion coupled-cluster method. Transition barriers in the energetically lowest He*–He and He*^––He interaction potentials prevent molecule formation at the extremely low temperatures present in helium droplets. In contrast, some excited states allow a barrier-free formation of molecular helium (anions). Moreover, we show that the necessary excitation energies pinpoint (higher) resonances in recently recorded mass spectra and emend the assignment of those resonances that have previously been assigned to electron-impact ionization of ground state helium necessitating subsequent double-electron capture. Embedding molecules or molecular clusters in helium droplets is a predestined experimental technique for the study of phenomena at very low temperatures. Profound knowledge about active processes in the helium environment is required for a proper assessment of experimental data.

Pair potential for helium from symmetry-adapted perturbation theory calculations and from supermolecular data

Symmetry-adapted perturbation theory (SAPT) was applied to the helium dimer for interatomic separations R from 3 to 12 bohrs. The first-order interaction energy and the bulk of the second-order contribution were obtained using Gaussian geminal basis sets and are converged to about 0.1 mK near the minimum and for larger R. The remaining second-order contributions available in the SAPT suite of codes were computed using very large orbital basis sets, up to septuple-zeta quality, augmented by diffuse and midbond functions. The accuracy reached at this level was better than 1 mK in the same region. All the remaining components of the interaction energy were computed using the full configuration interaction method in bases up to sextuple-zeta quality. The latter components, although contributing only 1% near the minimum, have the largest uncertainty of about 10 mK in this region. The total interaction energy at R=5.6 bohrs is -11.000+/-0.011 K. For R< or =6.5 bohrs, the supermolecular (SM) interaction energies computed by us recently turned out to be slightly more accurate. Therefore, we have combined the SM results for R< or =6.5 bohrs with the SAPT results from 7.0 to 12 bohrs to fit analytic functions for the potential and for its error bars. The potential fit uses the best available van der Waals constants C(6) through C(16), including C(11), C(13), and C(15), and is believed to be the best current representation of the Born-Oppenheimer (BO) potential for helium. Using these fits, we found that the BO potential for the helium dimer exhibits the well depth D(e)=11.006+/-0.004 K, the equilibrium distance R(e)=5.608+/-0.012 bohrs, and supports one bound state for (4)He(2) with the dissociation energy D(0)=1.73+/-0.04 mK, and the average interatomic separation R=45.6+/-0.5 A.

Electronic structure of the benzene dimer cation

The benzene and benzene dimer cations are studied using the equation-of-motion coupled-cluster model with single and double substitutions for ionized systems. The ten lowest electronic states of the dimer at t-shaped, sandwich, and displaced sandwich configurations are described and cataloged based on the character of the constituent fragment molecular orbitals. The character of the states, bonding patterns, and important features of the electronic spectrum are explained using qualitative dimer molecular orbital linear combination of fragment molecular orbital framework. Relaxed ground state geometries are obtained for all isomers. Calculations reveal that the lowest energy structure of the cation has a displaced sandwich structure and a binding energy of 20 kcal/mol, while the t-shaped isomer is 6 kcal/mol higher. The calculated electronic spectra agree well with experimental gas phase action spectra and femtosecond transient absorption in liquid benzene. Both sandwich and t-shaped structures feature intense charge resonance bands, whose location is very sensitive to the interfragment distance. Change in the electronic state ordering was observed between sigma and piu states, which correlate to the B and C bands of the monomer, suggesting a reassignment of the local excitation peaks in the gas phase experimental spectrum.

Three-Body Contribution to the Helium Interaction Potential

Two nonadditive three-body analytic potentials for helium were obtained: one based on three-body symmetry-adapted perturbation theory (SAPT) and the other one on supermolecular coupled-cluster theory with single, double, and noniterative triple excitations [CCSD(T)]. Large basis sets were used, up to the quintuple-zeta doubly augmented size. The fitting functions contain an exponentially decaying component describing the short-range interactions and damped inverse powers expansions for the third- and fourth-order dispersion contributions. The SAPT and CCSD(T) potentials are very close to each other. The largest uncertainty of the potentials comes from the truncation of the level of theory and can be estimated to be about 10 mK or 10% at trimer's minimum configuration. The relative uncertainties for other configurations are also expected to be about 10% except for regions where the nonadditive contribution crosses zero. Such uncertainties are of the same order of magnitude as the current uncertainties of the two-body part of the potential.

Accurate Pair Interaction Energies for Helium from Supermolecular Gaussian Geminal Calculations

Nonrelativistic clamped-nuclei pair interaction energy for ground-state helium atoms has been computed for 12 interatomic separations ranging from 3.0 to 9.0 bohr. The calculations applied the supermolecular approach. The major part of the interaction energy was obtained using the Gaussian geminal implementation of the coupled-cluster theory with double excitations (CCD). Relatively small contributions from single, triple, and quadruple excitations were subsequently included employing the conventional orbital coupled-cluster method with single, double, and noniterative triple excitations [CCSD(T)] and the full configuration interaction (FCI) method. For three distances, the single-excitation contribution was taken from literature Gaussian-geminal calculations at the CCSD level. The orbital CCSD(T) and FCI calculations used very large basis sets, up to doubly augmented septuple- and sextuple-zeta size, respectively, and were followed by extrapolations to the complete basis set limits. The accuracy of the total interaction energies has been estimated to be about 3 mK or 0.03% at the minimum of the potential well. For the attractive part of the well, the relative errors remain consistently smaller than 0.03%. In the repulsive part, the accuracy is even better, except, of course, for the region where the potential goes through zero. For interatomic separations smaller than 4.0 bohr, the relative errors do not exceed 0.01%. Such uncertainties are significantly smaller than the expected values of the relativistic and diagonal Born-Oppenheimer contributions to the potential.

Potential Energy Surface for the Benzene Dimer and Perturbational Analysis of π−π Interactions

We present a complete 6-dimensional potential energy surface for the benzene dimer obtained using symmetry-adapted perturbation theory (SAPT) of intermolecular interactions based on Kohn-Sham's description of monomers. Ab initio calculations were performed for 491 dimer geometries in a triple-zeta-quality basis set supplemented by bond functions. An accurate analytic fit to the ab initio results has been developed and low-energy stationary points on the potential energy surface have been found. We have determined that there are three minima on the surface. Two of them, the tilted T-shape and the parallel-displaced, are nearly isoenergetic with interaction energies of -2.77 and -2.74 kcal/mol, respectively. The third minimum, a twisted edge-to-edge conformation, is significantly less attractive, with the interaction energy equal to -1.82 kcal/mol. Both the T-shape and sandwich geometries, sometimes assumed to be minima, are shown to be only saddle points. The potential energy surface is extremely flat between the two lowest minima, the barrier being only 0.10 kcal/mol above the global minimum. The second-virial coefficient obtained with the new potential agrees well with experimental results over a wide range of temperatures. The SAPT approach rigorously decomposes the interaction energy into physical components. The relative importance of these components has been analyzed.

Radiative correction to the helium dimer interaction energy

The leading-order radiative correction to the helium-helium interaction energy at the equilibrium internuclear distance has been calculated for the first time. The result is -1.27(2) mK. The calculations were performed using a new technique of evaluating expectation values of singular operators in connection with the most accurate wave functions of He(2) available today-the exponentially correlated Gaussian functions.

Relativistic correction to the helium dimer interaction energy

The lowest-order relativistic correction to the helium-helium interaction energy has been calculated for the first time, using two independent methods based on expansions in explicitly correlated Gaussian functions. At the equilibrium interatomic distance of 5.6 bohr, this correction amounts to +15.4 +/- 0.6 mK. As a by-product, a new upper bound of -10.9985 K for the nonrelativistic Born-Oppenheimer interaction energy has been obtained.

Bounds for the scattering length of spin-polarized helium from high-accuracy electronic structure calculations

We developed a series of correlation-consistent, polarized multiple zeta basis sets optimized specifically for the energy of the 2 3S state of helium atom. These basis sets were subsequently augmented with diffuse functions optimized for the van der Waals constants C6 through C14 which determine the asymptotic behavior of the second-order dispersion interaction between 2 3S helium atoms at large interatomic separation R. The resulting bases were applied to compute the Born-Oppenheimer (BO) potential for the lowest 5Sigmag+ state of the helium dimer. The coupled cluster and the full configuration-interaction techniques were employed to account for the electron correlation effects. The cardinal number extrapolation technique was used to obtain the complete-basis-set limit V(R) for the interaction potential and to find its lower VL(R) and upper VU(R) bounds. The resulting potentials were fitted to an analytical function containing accurate van der Waals constants C6 through C12 (including C11). We found that the complete-basis-set BO potential has a well depth De=1048.24+/-0.36 cm-1. The highest rotationless vibrational level is bound by D14=90.2+/-4.7 MHz, much stronger than the previous most accurate estimation of 15.2 MHz. The error bounds for De and D14 were obtained using the VL(R) and VU(R) potentials. The S-wave scattering length computed using the VL(R), V(R), and VU(R) potentials (assuming atomic masses) is aL=7.41 nm, a=7.54 nm, and aU=7.69 nm, respectively. We also computed the adiabatic, relativistic, and quantum electrodynamics (QED) corrections to the BO potential. When these corrections are taken into account the values of D14 and of a (both computed assuming nuclear masses) are 87.4+/-6.7 MHz and 7.64+/-0.20 nm; the error bounds reflect now also the uncertainty of the included adiabatic, relativistic, and QED corrections. The value of the scattering length resulting from our investigation lies outside the error bounds of all experimental determinations based on the properties of Bose-Einstein condensate of spin-polarized helium atoms.

Symmetry-adapted perturbation-theory calculations of intermolecular forces employing density-functional description of monomers

A symmetry-adapted perturbation theory based on Kohn-Sham determinants [SAPT(KS)] and utilizing asymptotically corrected exchange-correlation potentials has been applied to the He2, Ne2, (H2O)2, and (CO2)2 dimers. It is shown that SAPT(KS) is able to recover the electrostatic, first-order exchange, second-order induction, and exchange-induction energies with an accuracy approaching and occasionally surpassing that of regular SAPT at the currently programmed theory level. The use of the asymptotic corrections is critical to achieve this accuracy. The SAPT(KS) results can be obtained at a small fraction of the time needed for regular SAPT calculations. The robustness of the SAPT(KS) method with respect to the basis set size is also demonstrated. A theoretical justification for high accuracy of SAPT(KS) predictions for the electrostatic, first-order exchange, and second-order induction energies has been provided.

Fluctuation-dissipation theorem density-functional theory

Using the fluctuation-dissipation theorem (FDT) in the context of density-functional theory (DFT), one can derive an exact expression for the ground-state correlation energy in terms of the frequency-dependent density response function. When combined with time-dependent density-functional theory, a new class of density functionals results that use approximations to the exchange-correlation kernel fxc as input. This FDT-DFT scheme holds promise to solve two of the most distressing problems of conventional Kohn-Sham DFT: (i) It leads to correlation energy functionals compatible with exact exchange, and (ii) it naturally includes dispersion. The price is a moderately expensive O(N6) scaling of computational cost and a slower basis set convergence. These general features of FDT-DFT have all been recognized previously. In this paper, we present the first benchmark results for a set of molecules using FDT-DFT beyond the random-phase approximation (RPA)-that is, the first such results with fxc not equal to 0. We show that kernels derived from the adiabatic local-density approximation and other semilocal functionals suffer from an "ultraviolet catastrophe," producing a pair density that diverges at small interparticle distance. Nevertheless, dispersion interactions can be treated accurately if hybrid functionals are employed, as is demonstrated for He2 and HeNe. We outline constraints that future approximations to fxc should satisfy and discuss the prospects of FDT-DFT.

Radiative corrections to the polarizability of helium

The complete alpha(3) QED correction to the helium atom polarizability is computed assuming an infinite nuclear mass and found to be equal to 0.000030666(3) a.u., with the contribution from the electric-field dependence of the Bethe logarithm amounting to 0.000000193(2) a.u. After including the alpha(2) and alpha(3) corrections for the nuclear recoil and the leading part of the alpha(4) QED correction, we find that the molar polarizability of 4He is 0.51725419(9)(4) cm(3)/mol. The first of the two error bounds is dominated by the uncertainty of alpha(4) and higher-order QED corrections and the second reflects the uncertainty of the Avogadro constant.