Search

In this paper, we investigate the effects of full electronic correlation on the high harmonic generation in the helium atom subjected to laser pulses of extremely high intensity. To do this, we perform real-time propagations of the helium atom wavefunction using quantum chemistry methods coupled to Gaussian basis sets. The calculations are done within the real-time time-dependent configuration interaction framework, at two levels of theory: time-dependent configuration interation with single excitations (TD-CIS, uncorrelated method) and time-dependent full configuration interaction (TD-FCI, fully correlated method), and analyse obtained HHG spectra. The electronic wavefunction is expanded in Dunning basis sets supplemented with functions adapted to describing highly excited continuum states. We also compare the TD-CI results with grid-based propagations of the helium atom within the single-active-electron approximation. Our results show when including the dynamical electron correlation, a noticeable improvement to the description of HHG can be achieved, in terms of e.g. a more constant intensity in the lower energy part of the harmonic plateau. However, such effects can be captured only if the basis set used suffices to reproduce the most basic features, such as the HHG cutoff position, at the uncorrelated level of theory., Comment: 14 pages, 2 figures

We present a method for calculation of the second-order exchange-dispersion energy in the framework of the symmetry-adapted perturbation theory (SAPT) for weakly interacting monomers described with multiconfigurational wave functions. The proposed formalism is based on response properties obtained from extended random phase approximation (ERPA) equations and assumes the single-exchange (

We present a formulation of the multiconfigurational (MC) wave function symmetry-adapted perturbation theory (SAPT). The method is applicable to noncovalent interactions between monomers which require a multiconfigurational description, in particular when the interacting system is strongly correlated or in an electronically excited state. SAPT(MC) is based on one- and two-particle reduced density matrices of the monomers and assumes the single-exchange approximation for the exchange energy contributions. Second-order terms are expressed through response properties from extended random phase approximation (ERPA). The dispersion components of SAPT(MC) have been introduced in our previous works [HapkaM.J. Chem. Theory Comput.2019, 15, 1016−102730525591; HapkaM.J. Chem. Theory Comput.2019, 15, 6712–672331670950]. SAPT(MC) is applied either with generalized valence bond perfect pairing (GVB) or with complete active space self-consistent field (CASSCF) treatment of the monomers. We discuss two model multireference systems: the H2 ··· H2 dimer in out-of-equilibrium geometries and interaction between the argon atom and excited state of ethylene. Using the C2H4* ··· Ar complex as an example, we examine second-order terms arising from negative transitions in the linear response function of an excited monomer. We demonstrate that the negative-transition terms must be accounted for to ensure qualitative prediction of induction and dispersion energies and develop a procedure allowing for their computation. Factors limiting the accuracy of SAPT(MC) are discussed in comparison with other second-order SAPT schemes on a data set of small single-reference dimers.

A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schr\"odinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one- or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from $5 \times 10^{13}\:\rm W/cm^2$ to $5 \times 10^{14}\:\rm W/cm^2$. We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors., Comment: Minor changes in Sec. 1, 2 and 3

The second virial coefficient and the second acoustic virial coefficient for helium-4 and helium-3 are computed for a wide range of temperatures (0.5--1000 K) using a highly accurate nonrelativistic interaction potential [M. Przybytek et al., Phys. Rev. Lett. 119, 123401 (2017)] and recalculated relativistic and quantum-electrodynamic components. The effects of the long-range retardation and of the nonadiabatic coupling of the nuclear and electronic motion are also taken into account. The results of our calculations represent at least fivefold improvement in accuracy compared to the previous ab initio work. The computed virial coefficients agree well with the most accurate recent measurements but have significantly smaller uncertainty.

This work concerns \emph{ab initio} calculations of the complete potential energy curve and spectroscopic constants for the ground state $X^1\Sigma_g^+$ of the beryllium dimer, Be$_2$. High accuracy and reliability of the results is one of the primary goals of the paper. To this end we apply large basis sets of Slater-type orbitals combined with high-level electronic structure methods including triple and quadruple excitations. The effects of the relativity are also fully accounted for in the theoretical description. For the first time the leading-order quantum electrodynamics effects are fully incorporated for a many-electron molecule. Influence of the finite nuclear mass corrections (post-Born-Oppenheimer effects) turns out to be completely negligible for this system. The predicted well-depth ($D_e=934.5\pm2.5\,\mbox{cm}^{-1}$) and the dissociation energy ($D_0=808.0\,\mbox{cm}^{-1}$) are in a very good agreement with the most recent experimental data. We confirm the existence of the weakly bound twelfth vibrational level [Patkowski et al., Science 326, 1382 (2009)] and predict that it lies just about 0.5 $\mbox{cm}^{-1}$ below the onset of the continuum.

We propose a method for calculating a second-order dispersion energy for weakly interacting multireference systems in arbitrary electronic states. It is based on response properties obtained from extended random phase approximation equations. The introduced formalism is general and requires only one- and two-particle reduced density matrices of monomers. We combine the new method with either generalized valence bond perfect pairing (GVB) or complete active space (CAS) self-consistent field description of the interacting systems. In addition to a general scheme, three approximations, leading to significant reduction of the computational cost, are developed by exploiting Dyall partitioning of the monomer Hamiltonians. For model multireference systems (H2···H2 and Be···Be) the method is accurate, unlike its single-reference-based counterpart. Neither GVB nor CAS description of single-reference monomers improves the dispersion energy with respect to the Hartree-Fock-based results.

Methods of the explicitly correlated F12 approach are applied to the problem of calculating the uncoupled second-order dispersion energy in symmetry-adapted perturbation theory. The accuracy of the new method is tested for noncovalently bound complexes from the A24 data set [J. Řezac and P. Hobza, J. Chem. Theory Comput. 2013, 9, 2151] using standard orbital basis sets aug-cc-pVXZ supplemented with auxiliary aug-cc-pVXZ_OPTRI sets. For near equilibrium geometries, it is possible to recover the dispersion energy with average relative errors consistently smaller than 0.1% (with respect to the CBS extrapolated limit estimated from regular orbital calculations). This level of accuracy is achieved already in the basis set of a triple-ζ quality, when a Slater-type correlation factor exp(−0.9r12) is combined with variant C of the F12 approach. The explicitly correlated approach clearly outperforms regular orbital calculations in the basis set of quintuple-ζ quality (average relative errors of 1%).

We report theoretical determination of the dipole polarizability of the neon atom, including its frequency dependence. Corrections for the relativistic, quantum electrodynamics, finite nuclear mass, and finite nuclear size effects are taken into account. We obtain the value ${\ensuremath{\alpha}}_{0}=2.66080(36)$ for the static polarizability, and ${\ensuremath{\alpha}}_{2}=2.850(7)$ and ${\ensuremath{\alpha}}_{4}=4.932(14)$ for the first two polarizability dispersion coefficients (Cauchy moments); all values are in atomic units (a.u.). In the case of static polarizability, our result agrees with the best experimental determination, Gaiser et al. [Phys. Rev. Lett. 120, 123203 (2018)], but our estimated uncertainty is significantly larger. For the dispersion coefficients, the results obtained in this work appear to be the most accurate to date overall compared to published theoretical and experimental data. We also calculated the static magnetic susceptibility of the neon atom, needed to obtain the refractive index of gaseous neon. Our result, ${\ensuremath{\chi}}_{0}=\ensuremath{-}8.484(19)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ a.u., is about 9% larger in absolute value than the recommended experimental value, Rumble et al. [CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, FL, 2019)].

In this work we propose a novel composite method for accurate calculation of the energies of many-electron atoms. The dominant contribution to the energy (pair energies) are calculated by using explicitly correlated factorisable coupled cluster theory. Instead of the usual Gaussian-type geminals for the expansion of the pair functions, we employ two-electron Hylleraas basis set. This eliminates the need for massive optimisation of nonlinear parameters and the required three-electron integrals can now be calculated relatively easily. The remaining contributions to the energy are calculated within the algebraic approximation by using large one-electron basis sets composed of Slater-type orbitals. The method is tested for the beryllium atom where the accuracy better than $1\,$cm$^{-1}$ is obtained. We discuss in details possible sources of the error and estimate the uncertainty in each energy component. Finally, we consider possible strategies to improve the accuracy of the method by one to two orders of magnitude. The most important advantage of the method is that is does not suffer from an exponential growth of the computational costs with increasing number of electrons in the system and thus can be applied to heavier atoms preserving a similar level of accuracy.

The pair potential for helium is computed with accuracy improved by an order of magnitude relative to the best previous determination. For the well region, its uncertainties are now below 1 millikelvin. The main improvement is due to the use of explicitly correlated wave functions at the nonrelativistic Born-Oppenheimer (BO) level of theory. The diagonal BO and the relativistic corrections are obtained from large full configuration interaction calculations. Nonadiabatic perturbation theory is used to predict the properties of the halo state of the helium dimer. Its binding energy and the average value of the interatomic distance are found to be 138.9(5) neV and 47.13(8) Å. The binding energy agrees with its first experimental determination of 151.9(13.3) neV [Zeller et al., Proc. Natl. Acad. Sci. U.S.A. 113, 14651 (2016)PNASA60027-842410.1073/pnas.1610688113].

Formulas for the coefficients A6, A8, and A10 determining the long-range asymptotic behavior E ad ( R ) ∼ - A 6 R - 6 - A 8 R - 8 - A 10 R - 10 of the diagonal Born–Oppenheimer (adiabatic) correction E ad ( R ) to the potential energy of a diatomic molecule are derived using two standard definitions of E ad ( R ) . The first one is based on the explicit separation of the center-of-mass and rotational coordinates from the total Hamiltonian of a system, while the second definition uses the Born–Handy expression in a laboratory system of coordinates. Expressions for the asymptotic coefficients resulting from both definitions are proved to be equivalent. The obtained formulas are used to compute the asymptotics of the adiabatic correction for the ground state of the hydrogen molecule and for the helium dimer in the lowest quintet and singlet states. In the latter case basis sets up to 8-tuple zeta quality were used to adequately account for the electron correlation effects.

The dissociation energies from all rovibrational levels of H2 and D2 in the ground electronic state are calculated with high accuracy by including relativistic and quantum electrodynamics (QED) effects in the nonadiabatic treatment of the nuclear motion. For D2, the obtained energies have theoretical uncertainties of 0.001 cm(-1). For H2, similar uncertainties are for the lowest levels, while for the higher ones the uncertainty increases to 0.005 cm(-1). Very good agreement with recent high-resolution measurements of the rotational v = 0 levels of H2, including states with large angular momentum J, is achieved. This agreement would not have been possible without accurate evaluation of the relativistic and QED contributions and may be viewed as the first observation of the QED effects, mainly the electron self-energy, in a molecular spectrum. For several electric quadrupole transitions, we still observe certain disagreement with experimental results, which remains to be explained.

Coupled cluster (CC) calculations with Gaussian geminals rely heavily on extensive optimizations of nonlinear parameters (exponents and positions) defining the geminal basis functions. As the CC method is not a variational theory, it provides no functional for such an optimization. The nonlinear parameters must therefore be supplied by some other theory, giving pair functions that can be expected to be close to those of the CC method. The conventional approach thus far was to use the second-order many-body perturbation theory with Moller–Plesset partition of the Hamiltonian (MP2) for this purpose and to minimize the corresponding Hylleraas-type functional. We present a new functional, which goes beyond the second order, and can be applied in situations when the Moller–Plesset theory converges slowly. This functional does take a partial account of infinite-order terms in the MP theory, but neglects the interpair coupling in the spirit of the independent electron pair approximation approach. The pair functions minimizing this new functional include the most important infinite-order contributions from the point of view of the MP theory and are much closer to the CC pair functions than the first-order ones. The nonlinear parameters obtained using this infinite-order functional are then better suited for coupled cluster calculations than those obtained using the MP2 functional. The effectiveness of the new functional is demonstrated by performing coupled cluster doubles (CCD) calculations for the Be atom and Li− ion. The obtained energies are much better than those based on the MP2 optimizations and represent the most accurate CCD energies for these systems obtained thus far. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

The odd-order dispersion coefficients C 11 , C 13 , C 15 appearing in the third order of perturbation theory, and the even-order ones C 12 , C 14 , C 16 with contributions from the second and fourth order were calculated for binary interactions among helium atoms in the lowest singlet and triplet S states. The computations were carried out in the determinant based full configuration interaction approach using specially optimized Gaussian basis sets. The sum-over-pseudostates technique was employed to construct the reduced resolvent. The results of our calculations show a limited accuracy of the extrapolation formulas used thus far to compute these higher-order coefficients.

The dissociation energy of molecular hydrogen is determined theoretically with a careful estimation of error bars by including nonadiabatic, relativistic, and quantum electrodynamics (QED) corrections. The relativistic and QED corrections were obtained at the adiabatic level of theory by including all contributions of the order α(2) and α(3) as well as the major (one-loop) α(4) term, where α is the fine-structure constant. The computed α(0), α(2), α(3), and α(4) components of the dissociation energy of the H2 isotopomer are 36 118.7978(2), -0.5319(3), -0.1948(2), and -0.0016(8) cm(-1), respectively, while their sum amounts to 36 118.0695(10) cm(-1), where the total uncertainty includes the estimated size (±0.0004 cm(-1)) of the neglected relativistic nonadiabatic/recoil corrections. The obtained theoretical value of the dissociation energy is in excellent agreement with the most recent experimental determination 36 118.0696(4) cm(-1) [J. Liu et al. J. Chem. Phys. 2009, 130, 174 306]. This agreement would have been impossible without inclusion of several subtle QED contributions which have not been considered, thus far, for molecules. A similarly good agreement is observed for the leading vibrational and rotational energy differences. For the D2 molecule we observe, however, a small disagreement between our value 36 748.3633(9) cm(-1) and the experimental result 36 748.343(10) cm(-1) obtained in a somewhat older and less precise experiment [Y. P. Zhang et al. Phys. Rev. Lett. 2004, 92, 203003]. The reason of this discrepancy is not known.

The properties of a balanced two-component Fermi gas in a one-dimensional harmonic trap are studied by means of the coupled cluster method. For few fermions we recover the results of exact diagonalization, yet with this method we are able to study much larger systems. We compute the energy, the chemical potential, the pairing gap, and the density profile of the trapped clouds, smoothly mapping the crossover between the few-body and many-body limits. The energy is found to converge surprisingly rapidly to the many-body result for every value of the interaction strength. Many more particles are instead needed to give rise to the non-analytic behavior of the pairing gap, and to smoothen the pronounced even-odd oscillations of the chemical potential induced by the shell structure of the trap., 6 pages, 4 figures

Recently proposed time-independent coupled cluster theory of the polarization propagator [R. Moszynski, P. S. Żuchowski, and B. Jeziorski, Collect. Czech. Chem. Commun. 70, 1109, 2005] has been implemented at the single and double excitations (CCSD) level. The performance of the new approach was investigated by carrying out calculations of static and dynamic electric dipole polarizabilities for various molecules and by making a comparison with values obtained from other ab initio methods, including the full configuration interaction (FCI) technique. Our results show that the polarizabilities computed with the new approach are in a good agreement with the time-dependent CCSD and (when available) FCI values. The isotropic C 6 dispersion coefficients for several benchmark van der Waals complexes, e.g. dimers of helium, argon, water, and benzene, are also reported. They compare very well with existing experimental and best theoretical data. The new propagator, implemented already in the MOLPRO package, is com...

The convergence behavior of symmetry-adapted perturbation theory (SAPT) expansions is investigated for an interacting system involving an excited, open-shell monomer. By performing large-order numerical calculations for the interaction of the lowest, 1s2s, triplet state of helium with the ground state of the hydrogen atom we show that the conventional polarization and symmetrized Rayleigh-Schrödinger expansions diverge in this case. This divergence is attributed to the continuum of intruder states appearing when the hydrogen electron is falling on the helium 1s orbital and the 2s electron is ejected from the interacting system. One of the dimer states resulting from the interaction becomes then a resonance, which presents a hard case to treat by a perturbation theory. We show that the SAPT expansions employing the strong symmetry-forcing procedure, such as the Eisenschitz-London- Hirschfelder-van der Avoird or the Amos-Musher theories, can cope with this situation and lead to convergent series when the permutational symmetry of the bound, quartet state is forced. However, these theories suffer from a wrong asymptotic behavior of the second- and higher-order energies when the interatomic distance R grows to infinity, which makes them unsuitable for practical applications. We show that by a suitable regularization of the Coulomb potential and by treating differently the regular, long-range and the singular, short-range parts of the interatomic electron-nucleus attraction terms in the Hamiltonian one obtains a perturbation expansion which has the correct asymptotic behavior in each order and which converges fast for a wide range of interatomic distances.

In this paper we present results of ab initio calculations for the beryllium dimer with a basis set of Slater-type orbitals (STOs). Nonrelativistic interaction energy of the system is determined using the frozen-core full configuration interaction calculations combined with high-level coupled-cluster correction for inner-shell effects. We have developed STO basis sets, ranging in quality from double to sextuple $\ensuremath{\zeta}$, which are used in these computations. Principles of their construction are discussed and several atomic benchmarks are presented. Relativistic effects of order ${\ensuremath{\alpha}}^{2}$ are calculated perturbatively by using the Breit-Pauli Hamiltonian and are found to be significant. We also estimate the leading-order QED effects. Influence of the adiabatic correction is found to be negligible. Finally, the electronic binding energy of the beryllium dimer is determined to be $929.0\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0.16em}{0ex}}1.9\phantom{\rule{0.16em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$, in a very good agreement with the recent experimental value.

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.

Two 4He atoms form a diatomic molecule with a significant vibrational wave function amplitude at interatomic separations R>100 A, where the retardation switches the London R(-6) decay of the potential to the Casimir-Polder R(-7) form. It has been assumed that this effect of retardation on the long-range part of the potential is responsible for the 2 A (4%) increase of the bond length of 4He2. We show that is, unexpectedly, insensitive to the potential at R>20 A and its increase is due to quantum electrodynamics effects computed by us from expressions valid at short R--beyond the validity range of Casimir-Polder theory--that seamlessly extend this theory to distances relevant for properties of long molecules.

The helium pair potential was computed including relativistic and quantum electrodynamics contributions as well as improved accuracy adiabatic ones. Accurate asymptotic expansions were used for large distances R. Error estimates show that the present potential is more accurate than any published to date. The computed dissociation energy and the average R for the (4)He(2) bound state are 1.62+/-0.03 mK and 47.1+/-0.5 A. These values can be compared with the measured ones: 1.1(-0.2)(+0.3) mK and 52+/-4 A [R. E. Grisenti, Phys. Rev. Lett. 85, 2284 (2000)].

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.