Multimode wavelet basis calculations via the molecular self-consistent-field plus configuration-interaction method

Wavelets provide potentially useful quantum bases for coupled anharmonic vibrational modes in polyatomic molecules as well as many other problems. A single compact support wavelet family provides a flexible basis with properties of orthogonality, localization, customizable resolution, and systematic improvability for general types of one-dimensional and separable systems. While direct product wavelet bases can be used in coupled multidimensional problems, exponential scaling of basis size with dimensionality ultimately provides limits on the number of coupled modes that can be treated simultaneously in exact quantum calculations. The molecular self-consistent-field plus configuration-interaction method is used here in multimode wavelet calculations to reduce the basis size without sacrificing flexibility or the ability to systematically control errors. Both two-dimensional Cartesian coordinate and three-dimensional curvilinear coordinate systems are examined with wavelets serving as universal bases in each case. The first example uses standard Daubechies [Ten Lectures on Wavelets (SIAM, Philadelphia (1992)] wavelets for each mode and the second adapts symmlet wavelets to intervals for each of the curvilinear coordinates.     

Use of molecular symmetry in SCF calculations

A method is described whereby molecular symmetry properties may be used to reduce the numbers of one- and two-electron integrals that need to be calculated and stored in the course of a molecular SCF calculation. The method is a generalization of a previously reported procedure, extending the earlier work to cover those molecules belonging to point groups which have complex representations. The practical application of the method is discussed and an illustrative example given. The quite extensive tables of molecular symmetry properties which the method uses may be computer generated in a straightforward manner. A procedure for doing this using a minimum amount of input data is presented.     

Convergence of the Rayleigh—Ritz method in self-consistent-field and multiconfiguration self-consistent-field calculations

We investigate the analytical convergence of SCF and MCSCF calculations, when the dimension of the subspaces to which the orbitals are restricted tends to infinity. We show that the completeness only inL ²(R ³;C ²) of the orbital bases does not ensure the convergence of the Ritz-energy, neither in SCF nor in MCSCF calculations, but that this convergence — as well as the convergence of the Ritz-orbitals in SCF calculations — is on the contrary guaranteed if the orbital bases are complete in the Sobolev spaceW ^1,2(R ³;C ²). Some consequences on the choice of the orbital exponents of Slater and Gauss functions are also discussed.     

On the use of spatial symmetry in atomic-integral calculations: An efficient permutational approach

The minimal number of independent nonzero atomic integrals that occur over arbitrarily oriented basis orbitals of the form ?(r) · Y_lm(Ω) is theoretically derived. The corresponding method can be easily applied to any point group, including the molecular continuous groups C_∞v and D_∞h. On the basis of this (theoretical) lower bound, the efficiency of the permutational approach in generating sets of independent integrals is discussed. It is proved that lobe orbitals are always more efficient than the familiar Cartesian Gaussians, in the sense that GLO s provide the shortest integral lists. Moreover, it appears that the new axial GLO s often lead to a number of integrals, which is the theoretical lower bound previously defined. With AGLO s, the numbers of two-electron integrals to be computed, stored, and processed are divided by factors 2.9 (NH₃), 4.2 (C₅H₅), and 3.6 (C₆H₆) with reference to the corresponding CGTO s calculations. Remembering that in the permutational approach, atomic integrals are directly computed without any four-indice transformation, it appears that its utilization in connection with AGLO s provides one of the most powerful tools for treating symmetrical species.     

Algorithm for variational calculations of molecular symmetry in solving anharmonic vibrational problems

A universal program for variational calculations of molecular symmetry in solving anharmonic vibrational problems, realized by the author, is described. The program uses the group-theoretical method. Symmetrized basis wave functions are constructed with the aid of the generalized KJebsch-Gordan series suggested by the author. The method of constructing symmetrized basis wave functions and the program for adequate calculations of molecular symmetry were verified for many molecules of different symmetry groups: O_h, O, T_d, T_h, T, D_∞h, C_t8v, D_nd, D_nh, D_n, C_nv, C_nh, S_2n, C_n, C_i, C_s, and C₁ where 2 ≤n ≤6. It was confirmed that the program provides correct results and high-speed operation. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 6, pp. 1146–1153, November–December, 1997.     

Broken symmetry in valence molecular region within Hartree-Fock calculations

Symmetry restricted and unrestricted Hartree-Fock calculations at theab initio LCAO-MO-SCF level have been carried out on the ground, core and valence hole states of N₂ at various N-N distances. A one-particle criterion for symmetry breaking is discussed. Strong broken-symmetry effects in the inner valence molecular region of N₂ have been found at larger N-N distances. This breaking of symmetry accompanying the symmetry unrestricted Hartree-Fock calculations of the inner valence hole states at large internuclear separations can be considered to be a common phenomenon with all highly symmetric molecules. The outer valence broken-symmetry effects with N₂ have showed some deviations as compared with these effects in the inner valence and core molecular regions.     

On the use of pseudopotentials in molecular calculations

A series of tests was performed of the Kahn-Goddard-Melius-Topiol pseudopotentials in view of their utilization with small contracted basis sets in molecular computations. The effects of inner-shell separability and of basis set contraction are underlined. The utilizability of Topiol's valence least-squares fitted Gaussian basis sets is studied.     

MO self-consistent-field calculations of quinoline and its derivatives

The electronic spectra and electronic structures of quinoline, the hydroxy form of 8-hydroxyquinoline, and the zwitterion form of 8-hydroxyquinoline, and the 8-hydroxy-N-methylquinolinium ion were calculated by the MO self-consistent-field method within the CNDO (complete neglect of differential overlap) approximation.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1524–1528, November, 1976.     

A new algorithm for molecular fragmentation in quantum chemical calculations

In this study, we present a "black-box" method for fragmenting a molecule with a well-defined Kekulé or valence-bond structure into a significant number of smaller fragment molecules that are more amenable to high level quantum chemical calculations. By taking an appropriate linear combination of the fragment energies, we show that it is possible in many cases to obtain highly accurate total energies when compared to the total energy of the full molecule. Our method is derived from the approach reported by Deev and Collins, but it contains significant unique elements, including an isodesmic approach to the fragmentation process. Using a method such as that described in this work it is in principle possible to obtain very accurate total energies of systems containing hundreds, if not thousands, of atoms as the approach is subject to massive parallelization.     

The use of symmetry in direct Møller-Plesset second-order calculations

Summary An algorithm for utilising abelian point group symmetry in direct MP2 energy calculations is presented. This is based upon the direct MP2 method of Head-Gordon, Pople and Frisch. The method uses the petite atomic orbital integral list as in conventional transformations coupled with a symmetry adaption of the three quarter transformed integrals. Representative calculations for ethylene and benzene are presented which demonstrate the potential of the method.     

Treatment of symmetry in MO calculations. II. Numerical projection operators for molecular orbitals

This article describes the numerical application of projection operators to restore the symmetry of molecular orbitals in self-consistent field (SCF) calculations when the symmetry is lost because of degeneracy or near degeneracy. The application of projection operators is particularly useful in cases of near degeneracies of three or more molecular orbitals, where it is difficult to find an effective algorithm for restoring the symmetry of molecular orbitals by orthonormal transformations.     

An efficient molecular orbital approach for self-consistent calculations of molecular junctions

To model electron transport through a molecular junction, we propose an efficient method using an ab initio self-consistent nonequilibrium Green's function theory combined with density functional theory. We have adopted a model close to the extended molecule approach, due to its flexibility, but have improved on the problems relating to molecule-surface couplings and the long-range potential via a systematic procedure for the same ab initio level as that of Green's function. The resulting algorithm involves three main steps: (i) construction of the embedding potential; (ii) perturbation expansion of Green's function in the molecular orbital basis; and (iii) truncation of the molecular orbital space by separating it into inactive, active, and virtual spaces. The above procedures directly reduce the matrix size of Green's function for the self-consistent calculation step, and thus, the algorithm is suitable for application to large molecular systems.     

Uniform semiclassical self-consistent-field calculations of vibrational resonance energies and widths

Using the Breit—Wigner definition of a resonance, we calculate both resonance positions and widths for a model non-separable hamiltonian, using a uniform semiclassical self-consistent-field (SCF) method. Excellent agreement with recent complex-coordinate quantum SCF calculations is obtained.     

Standard bond lengths for use in ab initio molecular orbital calculations

Standard bond lengths are proposed for a wide variety of bond lengths involving first row elements. These were obtained as average values from a large number of calculations made at the ab initio molecular orbital 4-31G level with geometry optimization. It is shown that these are generally in good agreement with accurate experimental values, where available.     

On the use of orientational restraints and symmetry corrections in alchemical free energy calculations

Alchemical free energy calculations are becoming a useful tool for calculating absolute binding free energies of small molecule ligands to proteins. Here, we find that the presence of multiple metastable ligand orientations can cause convergence problems when distance restraints alone are used. We demonstrate that the use of orientational restraints can greatly accelerate the convergence of these calculations. However, even with this acceleration, we find that sufficient sampling requires substantially longer simulations than are used in many published protocols. To further accelerate convergence, we introduce a new method of configuration space decomposition by orientation which reduces required simulation lengths by at least a factor of 5 in the cases examined. Our method is easily parallelizable, well suited for cases where a ligand cocrystal structure is not available, and can utilize initial orientations generated by docking packages.     

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

Anm ⁵-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.     

Multiconfiguration self-consistent-field theory based upon the fragment molecular orbital method

The fragment molecular orbital (FMO) method was combined with the multiconfiguration self-consistent-field (MCSCF) theory. One- and two-layer approaches were developed, the former involving all dimer MCSCF calculations and the latter limiting MCSCF calculations to a small part of the system. The accuracy of the two methods was tested using the six electrons in six orbitals complete active space type of MCSCF and singlet spin state for phenol+(H(2)O)(n), n=16,32,64 (6-31G( *) and 6-311G( *) basis sets); alpha helices and beta strands of phenylalanine-(alanine)(n), n=4,8,16 (6-31G( *)). Both double-zeta and triple-zeta quality basis sets with polarization were found to have very similar accuracy. The error in the correlation energy was at most 0.000 88 a.u., the error in the gradient of the correlation energy was at most 6.x10(-5) a.u./bohr and the error in the correlation correction to the dipole moment was at most 0.018 D. In addition, vertical singlet-triplet electron excitation energies were computed for phenol+(H(2)O)(n), (n=16,32,64), 6-31G( *), and the errors were found to be at most 0.02 eV. Approximately linear scaling was observed for the FMO-based MCSCF methods. As an example, an FMO-based MCSCF calculation with 1262 basis functions took 98 min on one 3.0 GHz Pentium4 node with 1 Gbyte RAM.     

The use of quantum molecular calculations to guide a genetic algorithm: a way to search for new chemistry

The process of gene-based molecular evolution has been simulated in silico by using massively parallel density functional theory quantum calculations, coupled with a genetic algorithm, to test for fitness with respect to a target chemical reaction in populations of genetically encoded molecules. The goal of this study was the identification of transition-metal complexes capable of mediating a known reaction, namely the cleavage of N(2) to give the metal nitride. Each complex within the search space was uniquely specified by a nanogene consisting of an eight-digit number. Propagation of an individual nanogene into successive generations was determined by the fitness of its phenotypic molecule to perform the target reaction and new generations were created by recombination and mutation of surviving nanogenes. In its simplest implementation, the quantum-directed genetic algorithm (QDGA) quickly located a local minimum on the evolutionary fitness hypersurface, but proved incapable of progressing towards the global minimum. A strategy for progressing beyond local minima consistent with the Darwinian paradigm by the use of environmental variations coupled with mass extinctions was therefore developed. This allowed for the identification of nitriding complexes that are very closely related to known examples from the chemical literature. Examples of mutations that appear to be beneficial at the genetic level but prove to be harmful at the phenotypic level are described. As well as revealing fundamental aspects of molecular evolution, QDGA appears to be a powerful tool for the identification of lead compounds capable of carrying out a target chemical reaction.     

Fe and Ni AB initio effective potentials for use in molecular calculations

We present effective potentials to replace the Ar core electrons of Fe and Ni. These effective potentials are obtained from ab initio ground state wavefunctions of Fe and Ni and are tested by comparing with ab initio SCF calculations for excited states of Fe, Fe⁺, Fe²⁺, Fe³⁺, Ni, Ni⁺, Ni²⁺, and the FeH⁺ molecule.