Localized Molecular Orbital Basis Research Articles

Exploiting the nearsightedness principle within the framework of the anti‐Hermitian contracted Schrödinger equation

AbstractThis work exploits the Kohn nearsightedness principle in the algorithms arising from the anti‐Hermitian contracted Schrödinger equation. The procedure provides the implementation of approximations yielding a considerable saving of computational costs in descriptions of N‐electron molecular systems by means of that technique. We report energies, at correlated level, of linear hydrogen chains designed at different geometries, so that we can analyze the strength of the interactions between first‐, second‐, third‐, fourth‐, and so forth neighbor atoms. Using localized molecular orbital basis sets, we observe rapid decays in the values of the elements of the reduced‐density‐matrix cumulant matrices, beyond a cut‐off radius, which justify the proposed approximations. The results, in terms of energies and reduced density matrices, have been compared with those obtained from the full configuration interaction method, showing the usefulness of the nearsightedness principle in this methodology.

Density functional theory based generalized effective fragment potential method.

We present a generalized Kohn-Sham (KS) density functional theory (DFT) based effective fragment potential (EFP2-DFT) method for the treatment of solvent effects. Similar to the original Hartree-Fock (HF) based potential with fitted parameters for water (EFP1) and the generalized HF based potential (EFP2-HF), EFP2-DFT includes electrostatic, exchange-repulsion, polarization, and dispersion potentials, which are generated for a chosen DFT functional for a given isolated molecule. The method does not have fitted parameters, except for implicit parameters within a chosen functional and the dispersion correction to the potential. The electrostatic potential is modeled with a multipolar expansion at each atomic center and bond midpoint using Stone's distributed multipolar analysis. The exchange-repulsion potential between two fragments is composed of the overlap and kinetic energy integrals and the nondiagonal KS matrices in the localized molecular orbital basis. The polarization potential is derived from the static molecular polarizability. The dispersion potential includes the intermolecular D3 dispersion correction of Grimme et al. [J. Chem. Phys. 132, 154104 (2010)]. The potential generated from the CAMB3LYP functional has mean unsigned errors (MUEs) with respect to results from coupled cluster singles, doubles, and perturbative triples with a complete basis set limit (CCSD(T)/CBS) extrapolation, of 1.7, 2.2, 2.0, and 0.5 kcal/mol, for the S22, water-benzene clusters, water clusters, and n-alkane dimers benchmark sets, respectively. The corresponding EFP2-HF errors for the respective benchmarks are 2.41, 3.1, 1.8, and 2.5 kcal/mol. Thus, the new EFP2-DFT-D3 method with the CAMB3LYP functional provides comparable or improved results at lower computational cost and, therefore, extends the range of applicability of EFP2 to larger system sizes.

Many-body localized molecular orbital approach to molecular transport

An ab initio based theoretical approach to describe nonequilibrium many-body effects in molecular transport is developed. We introduce a basis of localized molecular orbitals and formulate the many-body model in this basis. In particular, the Hubbard-Anderson Hamiltonian is derived for single-molecule junctions with intermediate coupling to the leads. As an example we consider a benzenedithiol junction with gold electrodes. An effective few-level model is obtained, from which spectral and transport properties are computed and analyzed. Electron-electron interaction crucially affects transport and induces multiscale Coulomb blockade at low biases. At large bias, transport through asymmetrically coupled molecular edge states results in the occurrence of "anomalous" conductance features, i.e., of peaks with unexpectedly large/small height or even not located at the expected resonance energies.

Elongation-CIS method: Describing excited states of large molecular systems in regionally localized molecular orbital basis

The elongation methodology is extended towards description of excited states through the ab initio CIS expansions in regionally localized molecular orbital basis. The formalism and implementation of the elongation-CIS method are presented. The expected accuracy of the method in comparison to the conventional CIS approach is illustrated by the results of calculations for model systems.

Elongation cutoff technique at Kohn–Sham level of theory

AbstractThe elongation cutoff technique ELG/C belongs to fragmentation methods. It uses the concept of locality and takes into account the sparsity of Kohn–Sham (KS) matrix in regionally localized molecular orbital basis set. In this article, a linear‐scaling implementation of ELG/C method at Kohn–Sham (KS) level of theory is presented. Its efficiency and accuracy is discussed for model system. The ELG/C KS scheme is based on local exchange‐correlation space approximation. Such approximation improves efficiency of the method and does not introduce a significant error. The current analysis includes the overall CPU (central processing unit) time and its most time consuming steps. The obtained results indicate that the ELG/C is a very efficient and accurate computational scheme. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Noncovalent Metal−Metal Interactions: The Crucial Role of London Dispersion in a Bimetallic Indenyl System

The nature of the "heterodox" metal-metal bond in bimetallic indenyl systems is revealed by a new high-level electronic structure analysis procedure based on perturbation theory within a localized molecular orbital basis. Surprisingly strong metal-metal interactions are found, and their origin in London dispersion effects has been uncovered. The importance of intramolecular van der Waals interactions, even for quite small organometallic systems, is highlighted.

Local correlation methods with a natural localized molecular orbital basis†

Natural localized molecular orbitals (NLMOs) have been used in local correlation calculations. For a test set of 30 molecules it is shown that the results obtained with NLMOs and Pipek–Mezey localization are very similar. However, NLMOs are much less sensitive to the basis set, in particular when diffuse functions are used. Based on natural population analysis (NPA) a new method to determine the domains in local correlation methods is proposed. It is demonstrated that this yields domains that are very insensitive to the choice of the basis set. For all 30 molecules the same domains are obtained with six different basis sets ranging from cc-pVDZ to aug-cc-pVQZ. This allows one to define the local correlation methods more uniquely than with previous methods. †This work is dedicated to Professor Pĕter Pulay.

Theoretical studies on the role of π‐electron delocalization in determining the conformation of N‐benzylideneaniline with three types of LMO basis sets

To understand the role of pi-electron delocalization in determining the conformation of the NBA (Ph-N==CH-Ph) molecule, the following three LMO (localized molecular orbital) basis sets are constructed: a LFMO (highly localized fragment molecular orbital), an NBO (natural bond orbital), and a special NBO (NBO-II) basis sets, and their localization degrees are evaluated with our suggesting index D(L). Afterward, the vertical resonance energy DeltaE(V) is obtained from the Morokuma's energy partition over each of three LMO basis sets. DeltaE(V) = DeltaE(H) (one electron energy) + DeltaE(two) (two electron energy), and DeltaE(two) = DeltaE(Cou) (Coulomb) + DeltaE(ex) (exchange) + DeltaE(ec) (or SigmaDeltaE(n)) (electron correction). DeltaE(H) is always stabilizing, and DeltaE(Cou) is destabilizing for all time. In the case of the LFMO basis set, DeltaE(Cou) is so great that DeltaE(two) > |DeltaE(H)|. Therefore, DeltaE(V) is always destabilizing, and is least destabilizing at about the theta = 90 degrees geometry. Of the three calculation methods such as HF, DFT, and MPn (n = 2, 3, and 4), the MPn method provides DeltaE(V) with the greatest value. In the case of the NBO basis set, on the contrary, DeltaE(V) is stabilizing due to DeltaE(Cou) being less destabilizing, and it is most stabilizing at a planar geometry. The LFMO basis set has the highest localization degree, and it is most appropriate for the energy partition. In the NBA molecule, pi-electron delocalization is destabilization, and it has a tendency to distort the NBA molecular away from its planar geometry as far as possible.

Elongation method with cutoff technique for linear SCF scaling

AbstractThe elongation method uses the concept of locality and works in a regionally localized molecular orbital basis set. In this method the system is partitioned into several frozen fragments and an active one. If the coupling between a given frozen fragment and the active space is small enough, one can develop a cutoff scheme for effectively discarding the former in all further calculations. At the Hartree–Fock level many two‐electron integrals are thereby eliminated, leading to a reduction in self‐consistent field computation time. In test calculations on four polyglycine conformers, with an appropriate default threshold for coupling, the cutoff error is very small and/or comparable to that of a normal elongation calculation. On the other hand, the computation time for 20 residues is a factor of 5 less than that of a normal Hartree–Fock treatment and scales linearly (or even sublinearly) with the number of residues. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

A natural linear scaling coupled-cluster method

It is shown that using an appropriate localized molecular orbital (LMO) basis, one is able to calculate coupled-cluster singles and doubles (CCSD) wave functions and energies for very large systems by performing full CCSD calculations on small subunits only. This leads to a natural linear scaling coupled-cluster method (NLSCC), in which total correlation energies of extended systems are evaluated as the sum of correlation energy contributions from individual small subunits within that system. This is achieved by defining local occupied orbital correlation energies. These are quantities, which in the LMO basis become transferable between similar molecular fragments. Conventional small scale existing molecular CCSD codes are all that is needed, the local correlation effect being simply transmitted via the appropriate LMO basis. Linear scaling of electronic correlation energy calculations is thus naturally achieved using the NLSCC approach, which in principle can treat nonperiodic extended systems of infinite basis set size. Results are shown for alkanes and several polyglycine molecules and the latter compared to recent results obtained via an explicit large scale LCCSD calculation. (c) 2004 American Institute of Physics.

Integral transformation with low-order scaling for large local second-order M�ller-Plesset calculations

An algorithm is presented for the four-index transformation of electron repulsion integrals to a localized molecular orbital (MO) basis. Unlike in most programs, the first two indices are transformed in a single step. This and the localization of the orbitals allows the efficient neglect of small contributions at several points in the algorithm, leading to significant time savings. Thresholds are applied to the following quantities: distant orbital pairs, the virtual space before and after the orthogonalizing projection to the occupied space, and small contributions in the transformation. A series of calculations on medium-sized molecules has been used to determine appropriate thresholds that keep the truncation errors small (below 0.01% of the correlation energy in most cases). Benchmarks for local second-order Møller–Plesset perturbation theory (MP2; i.e., MP2 with a localized MO basis in the occupied subspace) are presented for several large molecules with no symmetry, up to 975 contracted basis functions, and 60 atoms. These are among the largest MP2 calculations performed on a single processor. The computational time (with constant basis set) scales with a somewhat lower than cubic power of the molecular size, and the memory demand is moderate even for large molecules, making calculations that require a supercomputer for the traditional MP2 feasible on workstations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1241–1254, 1998

Calculations of phase transition of polydiacetylenes using localized molecular orbitals by elongation method

Photoinduced phase transition models between two distinct structures (acetylene and butatriene types) of polydiacetylene were investigated by using an elongation method. The geometries of these oligomers were optimized with ab initio self-consistent field. The wave functions for the calculation of the excitation energies were obtained with complete neglect of differential overlap in spectroscopy (CNDO/S approximation) by the elongation method. The excitation energies were calculated by using the single excitation configuration interaction method on the basis of localized molecular orbitals. The energy diagram for the phase transition is plotted and the structural change associated with the photoinduced excitation is discussed.

Calculations of the excitation energies of all-trans and 11,12s-dicis retinals using localized molecular orbitals obtained by the elongation method

In the present article, the excitation energies of the all-trans and the 11,12s-dicis retinals were calculated by using the elongation method. The geometries of these molecules were optimized with the 4-31G basis set by using the GAUSSIAN 92 program. The wave functions for the calculation of the excitation energies were obtained with CNDO/S approximation by the elongation method, which enables us to analyze electronic structures of aperiodic polymers in terms of the exciton-type local excitation and the charge transfer-type excitation. The excitation energies were calculated by using the single excitation configuration interaction (SECI) on the basis of localized molecular orbitals (LMOs). The LMOs were obtained in the process of the elongation method. The configuration interaction (CI) matrices were diagonalized by Davidson’s method. The calculated results were in good agreement with the experimental data for absorption spectra. In order to consider the isomerization path from 11,12s-dicis to all-trans retinals, the barriers to the rotations about C11–C12 double and C12–C13 single bonds were evaluated.

On the use of spatial symmetry in ab initio calculations. Transformation of the two-electron integrals from atomic orbital to localized molecular orbital basis

Anm5-dependent integral transformation procedure from atomic orbital basis to localized molecular orbitals is described for spatially extended systems with some Abelian symmetry groups. It is shown that exploiting spatial symmetry, the number of non-redundant integrals for normal saturated hydrocarbons can be reduced by a factor of 2.5-3.5, depending on the size of the system and on the basis. Starting from a list of integrals over basis functions in canonical order, the number of multiplications of the four-index transformation is reduced by a factor of 2.8-3.5 as compared to that of Diercksen's algorithm. It is pointed out that even larger reduction can be achieved if negligible integrals over localized molecular orbitals are omitted from the transformation in advance.