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.     

Effects of adiabatic, relativistic, and quantum electrodynamics interactions on the pair potential and thermophysical properties of helium

The adiabatic, relativistic, and quantum electrodynamics (QED) contributions to the pair potential of helium were computed, fitted separately, and applied, together with the nonrelativistic Born-Oppenheimer (BO) potential, in calculations of thermophysical properties of helium and of the properties of the helium dimer. An analysis of the convergence patterns of the calculations with increasing basis set sizes allowed us to estimate the uncertainties of the total interaction energy to be below 50 ppm for interatomic separations R smaller than 4 bohrs and for the distance R = 5.6 bohrs. For other separations, the relative uncertainties are up to an order of magnitude larger (and obviously still larger near R = 4.8 bohrs where the potential crosses zero) and are dominated by the uncertainties of the nonrelativistic BO component. These estimates also include the contributions from the neglected relativistic and QED terms proportional to the fourth and higher powers of the fine-structure constant α. To obtain such high accuracy, it was necessary to employ explicitly correlated Gaussian expansions containing up to 2400 terms for smaller R (all R in the case of a QED component) and optimized orbital bases up to the cardinal number X = 7 for larger R. Near-exact asymptotic constants were used to describe the large-R behavior of all components. The fitted potential, exhibiting the minimum of -10.996 ± 0.004 K at R = 5.608 0 ± 0.000 1 bohr, was used to determine properties of the very weakly bound (4)He(2) dimer and thermophysical properties of gaseous helium. It is shown that the Casimir-Polder retardation effect, increasing the dimer size by about 2 ? relative to the nonrelativistic BO value, is almost completely accounted for by the inclusion of the Breit-interaction and the Araki-Sucher contributions to the potential, of the order α(2) and α(3), respectively. The remaining retardation effect, of the order of α(4) and higher, is practically negligible for the bound state, but is important for the thermophysical properties of helium. Such properties computed from our potential have uncertainties that are generally significantly smaller (sometimes by nearly two orders of magnitude) than those of the most accurate measurements and can be used to establish new metrology standards based on properties of low-density helium.     

Removal of dependencies from nearly complete basis sets. Calculations on the helium dimer

A method is devised for dealing with almost linearly dependent basis sets that contain large sets of bond functions. Using the largest of such basis sets, LARSAT, the second-order Møller-Plesset polarization dispersion energy of the helium dimer is calculated to be - 17.08 K at R = 5.6 bohrs. MR-SDCI calculations, employing a set of 37 reference configurations, were performed for the helium dimer with several basis sets at 4.0 and 5.6 bohrs. Size-extensivity corrections were included to take into account the R dependency of the size-extensivity error in MR-SDCI calculations. The He₂ interaction energies computed with basis LARSAT are - 10.92 K at 5.6 bohrs and 295.1 K at 4.0 bohrs. The 37-MR-SDCI calculations with basis LARSAT almost reproduce the He₂ full configuration interaction (CI) interaction energies computed with the same basis, at notably smaller cost. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 805–815, 1997     

Analytic functions for the three-body potential of the helium trimer

The three-body potential for the ground state of the helium trimer is determined by an extended geminal model. The basis set for the calculation is an uncontracted (19s,7p,6d,5f,4g,2h) set of Gaussian-type functions. Three different types of configurations were considered: (i) equilateral triangles, (ii) linear configurations with R12=R23, and (iii) a set of pseudorandom configurations. The interatomic distances were selected within the interval [3.0,9.0] bohrs. The computed points have been fitted to global potential functions. The fit is characterized by a maximum absolute error equal to 0.69 microEh and a mean error equal to -0.018 microEh.     

Intermolecular potentials based on symmetry-adapted perturbation theory with dispersion energies from time-dependent density-functional calculations

Recently, three of us have proposed a method [Phys. Rev. Lett. 91, 33201 (2003)] for an accurate calculation of the dispersion energy utilizing frequency-dependent density susceptibilities of monomers obtained from time-dependent density-functional theory (DFT). In the present paper, we report numerical calculations for the helium, neon, water, and carbon dioxide dimers and show that for a wide range of intermonomer separations, including the van der Waals and short-range repulsion regions, the method provides dispersion energies with accuracies comparable to those that can be achieved using the current most sophisticated wave-function methods. If the dispersion energy is combined with (i) the electrostatic and first-order exchange interaction energies as defined in symmetry-adapted perturbation theory (SAPT) but computed using monomer Kohn-Sham (KS) determinants, and (ii) the induction energy computed using the coupled KS static response theory, (iii) the exchange-induction and exchange-dispersion energies computed using KS orbitals and orbital energies, the resulting method, denoted by SAPT(DFT), produces very accurate total interaction potentials. For the helium dimer, the only system with nearly exact benchmark values, SAPT(DFT) reproduces the interaction energy to within about 2% at the minimum and to a similar accuracy for all other distances ranging from the strongly repulsive to the asymptotic region. For the remaining systems investigated by us, the quality of the SAPT(DFT) interaction energies is so high that these energies may actually be more accurate than the best available results obtained with wave-function techniques. At the same time, SAPT(DFT) is much more computationally efficient than any method previously used for calculating the dispersion and other interaction energy components at this level of accuracy.     

Potential energy surface and second virial coefficient of methane-water from ab initio calculations

Six-dimensional intermolecular potential energy surfaces (PESs) for the interaction of CH4 with H2O are presented, obtained from ab initio calculations using symmetry-adapted perturbation theory (SAPT) at two different levels of intramonomer correlation and the supermolecular approach at three different levels of electron correlation. Both CH4 and H2O are assumed to be rigid molecules with interatomic distances and angles fixed at the average values in the ground-state vibration. A physically motivated analytical expression for each PES has been developed as a sum of site-site functions. The PES of the CH4-H2O dimer has only two symmetry-distinct minima. From the SAPT calculations, the global minimum has an energy of -1.03 kcal/mol at a geometry where H2O is the proton donor, HO-H...CH4, with the O-H-C angle of 165 degrees, while the secondary minimum, with an energy of -0.72 kcal/mol, has CH4 in the role of the proton donor (H3C-H...OH2). We estimated the complete basis set limit of the SAPT interaction energy at the global minimum to be -1.06 kcal/mol. The classical cross second virial coefficient B12(T) has been calculated for the temperature range 298-653 K. Our best results agree well with some experiments, allowing an evaluation of the quality of experimental results.     

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.     

Correlated intermolecular interaction components from asymptotically corrected Kohn-Sham orbitals

In these years there was considerable interest inunderstanding of intermolecular forces in energetic(explosive) systems[1—3]. The supermolecular approach(SM) is widely adopted for calculating ab initio in-termolecular interactions. Nevertheless, it is unable toprovide physically meaningful interaction contribu-tions such as electrostatic, induction, repulsion anddispersion energies. In contrast, the symmetry-adaptedperturbation theory (SAPT)[4—8] has the ability to de-rive these correlated…     

Accurate, two-state ab initio study of the ground and first-excited states of He2+, including exact treatment of all Born-Oppenheimer correction terms

Born-Oppenheimer (BO) potentials for the ground and first-excited electronic states of He2+ are determined using high level ab initio techniques for internuclear separations R of 1.2-100 bohrs and accurately fit to analytical functions. In the present formulation, the BO potentials are nuclear mass independent, and the corresponding BO approximation is obtained by ignoring four terms of the full rovibronic Hamiltonian. These four Born-Oppenheimer correction (BOC) terms are as follows: (1) mass polarization, (2) electronic orbital angular momentum, (3) first derivative with respect to R, and (4) second derivative with respect to R. In order to enable an exact rovibronic calculation, each of the four BOC terms are computed as a function of R, for the two electronic states and for their coupling, without any approximation or use of empirical parameters. Each of the BOC terms is found to make a contribution to the total energy over at least some portion of the range of R investigated. Interestingly, the most significant coupling contribution arises from the electronic orbital angular momentum term, which is evidently computed for the first time in this work. Although several BOC curves exhibit a nontrivial dependence on R, all are accurately fit to analytical functions. The resulting functions, together with the BO potentials, are used to compute exact rovibronic energy levels for 3He 3He+,3He 4He+) and 4He 4He+. Comparison to available high quality experimental data indicates that the present BOC potentials provide the most accurate representation currently available of both the low- and high-lying levels of the ground electronic state and the bound levels of the excited state.     

Ultra-low energy elastic scattering in a system of three He atoms

Differential Faddeev equations in total angular momentum representation are used for the first time to investigate ultra-low energy elastic scattering of a helium atom on a helium dimer. Six potential models of interatomic interaction are investigated. The results improve and extend the Faddeev equations based results known in literature. The employed method can be applied to investigation of different elastic and inelastic processes in three- and four-atomic weakly bounded systems below three-body threshold.     

Exchange polarization effects in the interaction of closed-shell systems

Explicit formulae for the calculation of the exchange polarization energy in the interaction of closed-shell atoms or molecules have been derived by assuming neglect of the electron correlation within the noninteracting systems. The dispersion part of the exchange polarization energy has been represented as a sum of contributions arising from the interaction of two, three or four orbitals at a time. Each of these contributions is given by an integral involving the orbitals engaged in the interaction and the pair functions describing the dispersion interaction between these orbitals. The numerical calculations for the interaction of two ground-state beryllium atoms show that the exchange dispersion energy is positive and quenches about 5 to 10 per cent of the dispersion term. This results in a decrease of the interaction energy, computed as a sum of the SCF and dispersion components, by 6 to 30 per cent for interatomic distances ranging from 10 to 7 bohrs.Simplified formulae for estimating the exchange dispersion energy in the interaction of larger systems are also proposed and their accuracy is discussed.     

The rotational spectrum and structure for the argon-cyclopentadienyl thallium van der Waals complex: experimental and computational studies of noncovalent bonding in an organometallic pi-complex

The rotational spectrum of a noble gas-organometallic complex was measured using a pulse molecular beam Fourier transform microwave spectrometer. Rotational transitions for the neutral argon-cyclopentadienyl thallium weakly bound complex were measured in the 4-9 GHz range. Analysis of the spectrum showed that the complex is a prolate symmetric-top rotor with C(5V) symmetry. The experimentally determined molecular parameters for Ar-C(5)H(5) (205)Tl are B=372.4479(3) MHz, D(J)=0.123(2) kHz, and D(JK)=0.45(2) kHz. For Ar-C(5)H(5) (203)Tl, B=373.3478(5) MHz, D(J)=0.113(3) kHz, and D(JK)=0.37(3) kHz. Using a pseudodiatomic model with Lennard-Jones potential yields an approximate binding energy of 339 cm(-1). The argon atom is located on the a-axis of the C(5)H(5)Tl monomer, directly opposite from the thallium metal atom. The measured separation distance between argon and the cyclopentadienyl ring is R=3.56 A. The overall size of the cluster is about 6 A, measuring from argon to thallium. Relatively small D(J) and D(JK) centrifugal distortion constants were observed for the complex, indicating that the structure of Ar-C(5)H(5)Tl is somewhat rigid. MP2 calculations were used to investigate the possible structures and binding energies of the argon-cyclopentadienyl thallium complex. Calculated, counterpoise corrected binding energies are evaluated at R=3.56 A for Ar-C(5)H(5)Tl range from 334 to 418 cm(-1). The experimental binding energy epsilon=339 cm(-1) for Ar-C(5)H(5)Tl falls within this range. The higher-level MP2/aug-cc-pVTZ-PP (thallium)/aug-cc-pVTZ(Ar, C, H) calculation with variable R yielded R(e)=3.46 A and binding energy of 535 cm(-1). Our estimated binding energy for argon-cyclopentadienyl thallium is very similar to the binding energy of argon-benzene. Calculations for the new van der Waals complexes, Ar(C(5)H(5)Tl)(2) and (C(5)H(5)Tl)(2), have been obtained, providing further information on the structures and bonding properties of previously observed cyclopentadienyl thallium polymer chains. The calculated intermolecular distance R(Tl-Cp)=3.05 A for the (CpTl)(2) chain subunit (Cp is cyclopentadienyl, C(5)H(5)) is slightly longer than the measured x-ray value R(M-Cp)(M=Tl)=2.75 A. The x-ray distance R(Tl-Tl)=5.5 A for the chain structure is almost identical to the calculated R(Tl-Tl)=5.51 A for the (C(5)H(5)Tl)(2) dimer.     

Accurate Heitler-London interaction energy for He2

A 75-term Gaussian geminal wave function for the helium atom that has a variational energy within 0.42 μhartree of the exact one is constructed. It predicts an electron density that agrees to better than 0.4% with the predictions of energetically superior Hylleraas wave functions to electron-nucleus distances as large as 6a₀. The first-order Heitler-London interaction energy E⁽¹⁾ between a pair of helium atoms was computed using an antisymmetrized product of this Gaussian geminal wave function for each of the atoms. This interaction energy is an essential component in the exchange-Coulomb model for the He₂ potential. Our E⁽¹⁾ is probably converged to within 0.03 μhartree for interatomic distances between 3.0a₀ and 7.5a₀. The Coulombic part of the interaction energy was checked by computations using even more accurate Hylleraas wave functions for the monomers. Comparison with an E⁽¹⁾ value computed from self-consistent-field atomic wave functions shows that intra-atomic correlation effects range between 4% and 9%.     

Collision-induced dipole polarizability of helium dimer from explicitly correlated calculations

Large expansions in basis sets of explicitly correlated Gaussian functions and the variation-perturbation technique were used to calculate the static dipole polarizability of the helium dimer at 16 different internuclear separations from 1.0 to 9.0 bohrs. The convergence towards the complete basis set limit was analyzed in order to estimate uncertainties of all the calculated values. The results are significantly more accurate than literature data. Asymptotically correct analytic fits for the trace and anisotropy of collision-induced polarizability were obtained.