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.     

Interaction energies for the water dimer by supermolecular methods and symmetry-adapted perturbation theory: the role of bond functions and convergence of basis subsets

 Using a systematic series of basis sets in supermolecular and symmetry-adapted intermolecular perturbation theory calculations it is examined how interaction energies of various water dimer structures change upon addition and shifting of bond functions. Their addition to augmented double- and triple-zeta basis sets brings the sum of the electron correlation contributions to the second-order interaction energy nearly to convergence, while accurate first-order electrostatic and exchange contributions require better than augmented quadruple-zeta quality. A scheme which combines the different perturbation energy contributions as computed in different basis subsets performs uniformly well for the various dimer structures. It yields a symmetry-adapted perturbation theory value of −21.08 kJ/mol for the energy of interaction of two vibrationally averaged water molecules compared to −21.29 kJ/mol when the full augmented triple-zeta basis set is used throughout. Received: 4 November 1999 / Accepted: 8 February 2000 / Published online: 12 May 2000     

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.     

Simple preconditioning for time-dependent density functional perturbation theory

By far, the most common use of time-dependent density functional theory is in the linear-reponse regime, where it provides information about electronic excitations. Ideally, the linear-response equations should be solved by a method that avoids the use of the unoccupied Kohn-Sham states--such as the Sternheimer method--as this reduces the complexity and increases the precision of the calculation. However, the Sternheimer equation becomes ill-conditioned near and indefinite above the first resonant frequency, seriously hindering the use of efficient iterative solution methods. To overcome this serious limitation, and to improve the general convergence properties of the iterative techniques, we propose a simple preconditioning strategy. In our method, the Sternheimer equation is solved directly as a linear equation using an iterative Krylov subspace method, i.e., no self-consistent cycle is required. Furthermore, the preconditioner uses the information of just a few unoccupied states and requires simple and minimal modifications to existing implementations. In this way, convergence can be reached faster and in a considerably wider frequency range than the traditional approach.     

Searching of potential energy curves for the benzene dimer using dispersion-corrected density functional theory

The present work aims to establish the utility of dispersion-corrected density functional theory for potential energy curves of the benzene dimer, a problem that has received significant attention for a long time. The interaction energies of parallel-stacked, T-shaped and parallel-displaced benzene dimer configurations have been evaluated using both dispersion- and normal gradient-corrected Perdew-Burke-Ernzerhof functionals along with Dunning's augmented correlation-consistent polarized valence triple-zeta (aug-cc-pVTZ) basis functions and compared with explicit correlation methods. The potential energy curves for the parallel-stacked and parallel-displaced benzene dimers are in excellent agreement with highly accurate coupled cluster (CCSD(T)) results, while for the T-shaped benzene dimer the dispersion-corrected results show a distinct deviation, being closer in that case to the MP2 level of results. The overestimation of interaction energy in the T-shaped dimer may be attributed to the presence of a permanent dipole moment in this configuration and indicates a structural dependence of the dispersion-corrected density functional method.     

Spectra of water dimer from a new ab initio potential with flexible monomers

We report the definition and testing of a new ab initio 12-dimensional potential for the water dimer with flexible monomers. Using our recent accurate CCpol-8s rigid water pair potential [W. Cencek, K. Szalewicz, C. Leforestier, R. van Harrevelt, and A. van der Avoird, Phys. Chem. Chem. Phys. 10, 4716 (2008)] as a reference for the undistorted monomers' geometries, a distortion correction has been added, which was taken from a former flexible-monomer ab initio potential. This correction allows us to retrieve the correct binding energy D(e)=21.0 kJ mol(-1), and leads to an equilibrium geometry in close agreement with the one obtained from benchmark calculations. The kinetic energy operator describing the flexible-monomer water dimer has been expressed in terms of Radau coordinates for each monomer and a recent general cluster polyspherical formulation describing their relative motions. Within this formulation, an adiabatic scheme has been invoked in order to decouple fast (intramolecular) modes and slow (intermolecular) ones. Different levels of approximation were tested, which differ in the way in which the residual potential coupling between the intramolecular modes located on different monomers and the dependence of the monomer rotational constants on the dimer geometry are handled. Accurate calculations of the vibration-rotation-tunneling levels of (H(2)O)(2) and (D(2)O)(2) were performed, which show the best agreement with experiments achieved so far for any water potential. Intramolecular excitations of the two monomers were calculated within two limiting cases, to account for the lack of non-adiabatic coupling between intramolecular modes due to the intermolecular motion. In the first model, the excitation was assumed to stay either on the donor or the acceptor molecule, and to hop between the two moieties upon donor-acceptor interchange. In the second model, the excitation remains on the same molecule whatever is the dimer geometry. Marginal frequency differences, less than 2?cm(-1), were obtained for all modes, and the resulting infrared shifts are in good agreement with experiments.     

Application of symmetry-adapted perturbation theory to small ionic systems

The application of symmetry-adapted perturbation theory (SAPT) to small ionic systems was investigated in the context of the accuracy of calculated interaction energies for alkali halides. Two forms of alkali halides were considered: ion pairs M(+)X(-) (M = Li, Na, K, Rb, and X = F, Cl, Br, I) and dimers (MX)(2). The influence of the order of energy correction terms included in SAPT and the effect of the so-called hybrid approach to SAPT on the accuracy of the calculated energies (such as the interaction energies in the ion pairs and the binding energies in the dimers with respect to two free monomers) were studied. The effects of the size of basis sets, combined with SAPT, on the accuracy were also established.     

Steric effect: a quantitative description from density functional theory

The concepts of steric energy, steric potential, and steric charge are introduced within the density functional theory framework. The steric energy, representing a hypothetical state with all electrons packed into the lowest orbital and other effects entirely excluded, is a measure of the intrinsic space occupied by an electronic system. It is exclusive, repulsive, and extensive, and it vanishes for homogeneous electron gas. When Bader's zero-flux boundary condition is adopted, atoms in molecules are found to achieve balanced steric repulsion among one another with vanished steric energy density interfaces. A few molecular systems involving conformation changes and chemical reactions have been investigated to examine the relative contribution of the steric and other effects, providing insights for a few controversial topics from a different perspective.     

Breakdown of the single-exchange approximation in third-order symmetry-adapted perturbation theory

We report third-order symmetry-adapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the single-exchange approximation (SEA) employed to derive the third-order exchange-induction correction (E(exch-ind)((30))) fails to quench the attractive nature of the third-order induction (E(ind)((30))), leading to one-dimensional potential curves that become attractive rather than repulsive at short intermolecular separations. A scaling equation for (E(exch-ind)((30))), based on an exact formula for the first-order exchange correction, is introduced to approximate exchange effects beyond the SEA, and qualitatively correct potential energy curves that include third-order induction are thereby obtained. For induction-dominated systems, our results indicate that a "hybrid" SAPT approach, in which a dimer Hartree-Fock calculation is performed in order to obtain a correction for higher-order induction, is necessary not only to obtain quantitative binding energies but also to obtain qualitatively correct potential energy surfaces. These results underscore the need to develop higher-order exchange-induction formulas that go beyond the SEA.     

Degenerate symmetry-adapted perturbation theory of weak interactions between closed- and open-shell monomers: application to Rydberg states of helium hydride

Symmetry-adapted perturbation theory is extended to the (quasi) degenerate, open-shell case. The new formalism is tested in calculations of the interaction energies for a helium atom in the ground state interacting with an excited hydrogen atom. It is shown that the method gives satisfactory results if the coupling with higher Rydberg states of the dimer is small, as is the case for the A²Σ⁺,B²Π,E²Π,3²Π, and 1²Δ states of HeH. For the C²Σ⁺ state convergence of the method is very slow, but it can be improved by including the n=3 states in the model space. Received: 3 June 1998 / Accepted: 9 September 1998 / Published online: 7 December 1998     

Structure of the ammonia dimer studied by density functional theory

Self-consistent Kohn–Sham density functional calculations have been carried out to study the structure of the ammonia dimer. The local-density approximation yields unusually large binding energy and short internitrogen distance compared with the experimental and more accurate theoretical data. The results from the Becke–Perdew gradient-corrected functionals are generally in good agreement with those at the SCF MP 2 level when the geometry is fully optimized with various large basis sets. With our best estimation, the staggered quasi-linear structure (C_s) is 0.6 kcal/mol lower in energy than the symmetric cyclic one (C_2h). The hydrogen-bonded N—H bond in the staggered quasi-linear structure is found to be 0.008 Å longer than the N—H bond in ammonia. In our calculations, we could not find the minima on the energy surface corresponding to the two asymmetric cyclic structures suggested by microwave spectra and coupled pair functional calculations. © 1994 John Wiley & Sons, Inc.     

Intermolecular interaction energy of CH4 trimer by symmetry-adapted perturbation theory

The interaction energy for the cyclic CH₄ trimer is studied in terms of symmetry-adapted perturbation theory. The interaction energy around the van der Waals minimum is dominated by attractive dispersion energy, and the repulsive contribution at the smaller angle region is due to the first-order exchange energy. The total interaction energy is approximated by additive two-body components, because of a mutual cancellation between nonadditive three-body ones.     

Time-dependent density functional theory based on a noncollinear formulation of the exchange-correlation potential

In this study we have introduced a formulation of time-dependent density functional theory (TDDFT) based on a noncollinear exchange-correlation potential. This formulation is a generalization of conventional TDDFT. The form of this formulation is exactly the same as that of the conventional TDDFT for the excitation energies of transitions that do not involve spin flips. In addition, this noncollinear TDDFT formulation allows for spin-flip transitions. This feature makes it possible to resolve more fully excited state spin multiplets, while for closed-shell systems, the spin-flip transitions will result in singlet-triplet excitations and this excitation energy calculated from this formulation of TDDFT is exactly the same as that from ordinary TDDFT. This formulation is applied to the dissociation of H(2) in its (1)Sigma(g) (+) ground state and (1)Sigma(u) (+) and (3)Sigma(u) (-) excited states with (3)Sigma(u) (-) (M(s)=+1) as the reference state and the multiplets splitting of some atoms.     

Effective potential in density matrix functional theory

In the previous paper it was shown that in the ground state the diagonal of the spin independent second-order density matrix n can be determined by solving a single auxiliary equation of a two-particle problem. Thus the problem of an arbitrary system with even electrons can be reduced to a two-particle problem. The effective potential of the two-particle equation contains a term v(p) of completely kinetic origin. Virial theorem and hierarchy of equations are derived for v(p) and simple approximations are proposed. A relationship between the effective potential u(p) of the shape function equation and the potential v(p) is established.