Localized Hartree Fock Orbitals Research Articles

Multilevel CC2 and CCSD in Reduced Orbital Spaces: Electronic Excitations in Large Molecular Systems.

We present efficient implementations of the multilevel CC2 (MLCC2) and multilevel CCSD (MLCCSD) models. As the system size increases, MLCC2 and MLCCSD exhibit the scaling of the lower-level coupled cluster model. To treat large systems, we combine MLCC2 and MLCCSD with a reduced-space approach in which the multilevel coupled cluster calculation is performed in a significantly truncated molecular orbital basis. The truncation scheme is based on the selection of an active region of the molecular system and the subsequent construction of localized Hartree–Fock orbitals. These orbitals are used in the multilevel coupled cluster calculation. The electron repulsion integrals are Cholesky decomposed using a screening protocol that guarantees accuracy in the truncated molecular orbital basis and reduces computational cost. The Cholesky factors are constructed directly in the truncated basis, ensuring low storage requirements. Systems for which Hartree–Fock is too expensive can be treated by using a multilevel Hartree–Fock reference. With the reduced-space approach, we can handle systems with more than a thousand atoms. This is demonstrated for paranitroaniline in aqueous solution.

Helium and Argon Interactions with Gold Surfaces: Ab Initio-Assisted Determination of the He–Au Pairwise Potential and Its Application to Accommodation Coefficient Determination

Global potentials for the extremely weak interaction between the He atom and gold surfaces are determined from ab initio calculations and validated with experimental-based determinations of well depth values. Dispersionless density functional periodic calculations are combined with effective pairwise functional parameters for the dispersion. These parameters are obtained from time-dependent density functional theory response theory using localized Hartree–Fock orbitals, as applied on He–Aun clusters. This He–Au pairwise potential is used in molecular dynamics simulations of gas–gold surface collisions from which incident and reflected gas atom velocities allow the determination of energy and momentum accommodation coefficients. Boundary quantities such as slip velocity and thermal resistance are not only derived from these coefficients, but also from a new methodology based on a nonparametric kernel, avoiding the atomic description of the gold surface. Similar collision simulations are performed for Ar fo...

Local Hartree-Fock orbitals using a three-level optimization strategy for the energy

Using the three-level energy optimization procedure combined with a refined version of the least-change strategy for the orbitals--where an explicit localization is performed at the valence basis level--it is shown how to more efficiently determine a set of local Hartree-Fock orbitals. Further, a core-valence separation of the least-change occupied orbital space is introduced. Numerical results comparing valence basis localized orbitals and canonical molecular orbitals as starting guesses for the full basis localization are presented. The results show that the localization of the occupied orbitals may be performed at a small computational cost if valence basis localized orbitals are used as a starting guess. For the unoccupied space, about half the number of iterations are required if valence localized orbitals are used as a starting guess compared to a canonical set of unoccupied Hartree-Fock orbitals. Different local minima may be obtained when different starting guesses are used. However, the different minima all correspond to orbitals with approximately the same locality.

Molecular gradient for second-order Møller-Plesset perturbation theory using the divide-expand-consolidate (DEC) scheme

We demonstrate that the divide-expand-consolidate (DEC) scheme--which has previously been used to determine the second-order Møller-Plesset (MP2) correlation energy--can be applied to evaluate the MP2 molecular gradient in a linear-scaling and embarrassingly parallel manner using a set of local Hartree-Fock orbitals. All manipulations of four-index quantities (describing electron correlation effects) are carried out using small local orbital fragment spaces, whereas two-index quantities are treated for the full molecular system. The sizes of the orbital fragment spaces are determined in a black-box manner to ensure that the error in the DEC-MP2 correlation energy compared to a standard MP2 calculation is proportional to a single input threshold denoted the fragment optimization threshold (FOT). The FOT also implicitly controls the error in the DEC-MP2 molecular gradient as substantiated by a theoretical analysis and numerical results. The development of the DEC-MP2 molecular gradient is the initial step towards calculating higher order energy derivatives for large molecular systems using the DEC framework, both at the MP2 level of theory and for more accurate coupled-cluster methods.

Algebraic connectivity analysis in molecular electronic structure theory I: coulomb potential, tensor connectivity, ε-approximation

In this (first) paper we attempt to generalize the notion of tensor connectivity, subsequently studying how this property is affected in different tensorial operations. We show that the often implied corollary of the linked diagram theorem, namely individual size-extensivity of arbitrary connected closed diagrams, can be violated in Coulomb systems. In particular, the assumption of the existence of localized Hartree–Fock orbitals is generally incompatible with the individual size-extensivity of connected closed diagrams when the interaction tensor is generated by the true two-body part of the electronic Hamiltonian. Thus, in general, size-extensivity of a many-body method may originate in specific cancellations of super-extensive quantities, breaking the convenient one-to-one correspondence between the connectivity of arbitrary many-body equations and the size-extensivity of the expectation values evaluated by those equations (for example, when certain diagrams are discarded from the method). Nevertheless, assuming that many-body equations are evaluated for a stable many-particle system, it is possible to introduce a workaround, called the ε-approximation, which restores the individual size-extensivity of an arbitrary connected closed diagram, without qualitatively affecting the asymptotic behavior of the computed expectation values. No assumptions concerning the periodicity of the system and its strict electrical neutrality are made.

Fragment-Localized Kohn-Sham Orbitals via a Singles Configuration-Interaction Procedure and Application to Local Properties and Intermolecular Energy Decomposition Analysis.

As for generating localized Hartree-Fock orbitals, we propose a potentially linear-scaling singles-CI scheme to construct fragment-localized density functional theory (DFT) orbitals for molecular systems as water clusters. Due to the use of a deformation step instead of a localization step, the influence of the environment on each separate molecule can be studied in detail. The generated orbital set for the whole molecular system is strictly equivalent to a set of canonical orbitals and is a subsequent energy decomposition of intermolecular interactions into electrostatic, exchange repulsion, and orbital interaction, well beyond dimer systems. Beyond this, the correspondence of the individual orbitals to the initial monomer orbitals permits to assess how an interaction deforms an electron density. We show this for dipole moments, which may be decomposed into monomer contributions, polarization, and charge-transfer contribution. Applications to a water and an ammonia dimer and chains of water molecules show possible further developments toward multipolar expansions and other orbital-based schemes for parametrizing force fields.

Rydberg states with quantum Monte Carlo

Calculations on Rydberg states are performed using quantum Monte Carlo methods. Excitation energies and singlet-triplet splittings are calculated for two model systems, the carbon atom (3P and 1P) and carbon monoxide ((1Sigma and 3Sigma). Kohn-Sham wave functions constructed from open-shell localized Hartree-Fock orbitals are used as trial and guide functions. The fixed-node diffusion quantum Monte Carlo (FN-DMC) method depends strongly on the wave function's nodal hypersurface. Nodal artefacts are investigated for the ground state of the carbon atom. Their effect on the FN-DMC results can be analyzed quantitatively. FN-DMC leads to accurate excitation energies but to less accurate singlet-triplet splittings. Variational Monte Carlo calculations are able to reproduce the experimental results for both the excitation energies and the singlet-triplet splittings.

Multireference configuration interaction treatment of excited-state electron correlation in periodic systems: the band structure of trans-polyacetylene

A systematic method to account for electron correlation in periodic systems which can predict quantitatively correct band structures of non-conducting solids from first principles is presented. Using localized Hartree–Fock orbitals (both occupied and virtual ones), an effective Hamiltonian is built up whose matrix elements can easily be transferred from finite to infinite systems. To describe the correlation effects wave-function-based multireference configuration interaction (MRCI) calculations with singly and doubly excited configurations are performed. This way it is possible to generate, both, valence and conduction bands with all correlation effects taken into account. trans-polyacetylene is chosen as a test system.

Advantages and limitations of Kohn–Sham orbitals as single electron basis for multireference configuration interaction and multireference perturbation theory

In the present work we study the performance of orbitals from an effective exact exchange-only optimized potential method, the localized Hartree–Fock approach, in multireference ab initio methods. In the first part local Hartree–Fock orbitals are used to describe the excited states of carbon monoxide, formaldehyde, and acetone in multireference configuration interaction calculations. The local Hartree–Fock orbitals are compared with standard Hartree–Fock orbitals, and those from a gradient corrected and a hybrid density functional. This part mainly tries to analyze possible deficiencies of the local Hartree–Fock orbitals. In the second part of this work the above-mentioned orbitals are tested in multireference perturbation theory second-order. We test to which extent known deficiencies of single state perturbation theory second-order are eliminated in multireference approaches, and then study how well local Hartree–Fock orbitals perform in multireference perturbation theory second-order computations of excited states.

Analysis of the Quality of Kohn–Sham Orbitals for Subsequent MRSD-CI Calculations of Excitation Energies

Abstract In the present work we study the properties of Kohn–Sham orbitals used in subsequent CI methods for the computation of electronic excitation energies in terms of orbital relaxation, static and dynamical correlation effects. As model systems, we use the water and the ethene molecule. As sets of orbitals, we use orbitals from an effective exact exchange Kohn–Sham method, the localized Hartree–Fock (LHF) method, as well as BLYP and HF orbitals. Our study shows that the use of LHF orbitals leads to negligible static correlation effects and thus facilitates assignments of excitation spectra, but it also shows that the remaining correlation contributions have to be taken into account carefully since error cancellation is only found in some fortitious cases. The comparison of LHF and BLYP orbitals shows that the BLYP orbitals are less suited for the description of the cationic system and as a consequence for the computation of Rydberg states.

Oxygen in the MgO Crystal. A Local Approach

Noncanonical localized Hartree―Fock orbitals of the O2- ion in the MgO crystal are calculated with the help of a special variational procedure whose variational parameters are transferred from the wave function to the confining potential simulating the crystal environment. The cluster expansion for the crystal energy is employed, and summation over the crystal is performed up to convergence. This procedure makes it possible to naturally incorporate the interionic correlation. The cohesive characteristics of MgO calculated in the present paper are in good agreement with the experiment. Bibliography: 22 titles.

Dressed coupled-electron-pair-approximation methods for periodic systems

The techniques of matrix dressing for configuration-interaction (CI)-type or coupled-electron-pair-approximation (CEPA)-type correlation treatments are reviewed with respect to the application to periodic systems. All methods ranging from canonical second-order Moller–Plesset perturbation theory over CI of single and double excitation, CEPA-0 or the averaged-coupled-pair-functional to self-consistent size-consistent CI can be formulated completely equivalently as an eigenvalue problem or as a solution to a system of linear equations. The size consistency of each method is obtained in a natural way, and invariance under orbital rotations is clearly assessible. A remark on the size consistency of the Davidson correction is presented. Additionally, the direct generation of localized Hartree–Fock orbitals as basic ingredients for the correlation calculations are addressed, as well as selected results on ring molecules, polymers, and 3D cubic beryllium as a model crystal.

Obtaining Wannier functions of a crystalline insulator within a Hartree-Fock approach: Applications to LiF and LiCl

An ab initio Hartree-Fock approach aimed at directly obtaining the localized orthogonal orbitals (Wannier functions) of a crystalline insulator is described in detail. The method is used to perform all-electron calculations on the ground states of crystalline lithium fluoride and lithium chloride, without the use of any pseudopotentials or model potentials. Quantities such as total-energy, x-ray structure factors, and Compton profiles obtained using the localized Hartree-Fock orbitals are shown to be in excellent agreement with the corresponding quantities calculated using the conventional Bloch-orbital--based Hartree-Fock approach. Localization characteristics of these orbitals are also discussed in detail.

Direct determination of localized Hartree–Fock orbitals as a step toward N scaling procedures

A method is proposed for the solution of the self-consistent field equations that can lead to localized occupied and virtual molecular orbitals, avoiding the need for solving for the canonical molecular orbitals. The method starts with strongly localized “guess molecular orbitals”, it is nonperturbative and proceeds through the diagonalization of single configuration interaction matrices which may be rendered size-consistent through appropriate coupled electron pair approximation or coupled-cluster-type dressings. We see a potential utility for the method in applications to large systems where localized orbitals will improve the scaling of the computational resources required with increasing system size.

Some aspects of new orthonormality-constrained orbital optimisation technique

The performance of a orthonormality-constrained orbital optimisation procedure has been investigated in its one-configuration limit and compared with that of the traditional method of Roothaan. An intrinsic superiority of the method is manifested in the achievement of smooth and stable optimisation even in pathological cases where Roothaan's method fails to converge. A simple “scaling” technique, somewhat akin to the “damping” procedure of Saunders et al. is developed to enhance the rate of descent on the energy surface. The possibility of generating localized Hartree—Fock orbitals directly by using the new method has also been explored and successfully implemented.

Effects of exchange energy and orbital orthogonality on barriers to internal rotation

In order to determine the effect of the Pauli principle on internal rotation barriers, we have calculated exchange and orbital orthogonality contributions to barriers for a small group of molecules: ethane, methanol, acetaldehyde, and hydrogen peroxide. To evaluate exchange contributions it was necessary to formulate variation equations and to energy-optimize simple product wavefunctions of orthogonal orbitals (Hartree-product wavefunctions). The resulting orbitals resemble very closely the Edmiston–Ruedenberg localized Hartree–Fock orbitals. Our results indicate that exchange contributions to the barriers in ethane and acetaldehyde are quite small. For methanol and hydrogen peroxide, our calculated contributions are considerably larger and suggest that, at least in some molecules, exchange contributions cannot be ignored. For all of the molecules, however, the exchange contribution is greatly overshadowed by that of end-to-end orbital orthogonality.

Geminal Localization in the Separated-Pair π-Electronic Model of Benzene

A problem of the geminal ``localization'' in the separated-pair π-electronic model of benzene is studied for a wide range of a coupling constant using the Pariser—Parr—Pople-type Hamiltonian. The general form of the ``localized geminals'' leading to the separated-pair wavefunction of the C3h symmetry is found as a function of two free parameters. These geminals are used in the separated-pair model calculation, showing that the previously used localization corresponding to the equivalent orbitals (i.e., the localized Hartree—Fock orbitals) is not the best one from the separated-pair model viewpoint, except for vanishingly small coupling constants. The optimization is also carried out after the projection of the single antisymmetrized product of geminals function onto the totally symmetric subspace of the D6h point group. Finally, the general implications of the ``symmetry dilemma'' are briefly discussed for both independent-particle and separated-pair models.