Parallel pseudospectral electronic structure: I. Hartree–Fock calculations

We present an outline of the parallel implementation of our pseudospectral electronic structure program, Jaguar, including the algorithm and timings for the Hartree–Fock and analytic gradient portions of the program. We also present the parallel algorithm and timings for our Lanczos eigenvector refinement code and demonstrate that its performance is superior to the ScaLAPACK diagonalization routines. The overall efficiency of our code increases as the size of the calculation is increased, demonstrating actual as well as theoretical scalability. For our largest test system, alanine pentapeptide [818 basis functions in the cc-pVTZ(-f) basis set], our Fock matrix assembly procedure has an efficiency of nearly 90% on a 16-processor SP2 partition. The SCF portion for this case (including eigenvector refinement) has an overall efficiency of 87% on a partition of 8 processors and 74% on a partition of 16 processors. Finally, our parallel gradient calculations have a parallel efficiency of 84% on 8 processors for porphine (430 basis functions). © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1017–1029, 1998     

Generator coordinate Hartree–Fock method applied to the choice of a contracted Gaussian basis for the second-row atoms

The generator coordinate Hartree–Fock (GCHF) method is employed as a criterion for the selection of a 18s12p Gaussian basis for the atoms Na–Ar. The role of the weight functions in the assessment of the numerical integration range of the GCHF equations is shown. The extended basis is then contracted to (10s6p) by a standard procedure and in combination with the previously contracted (7s5p) Gaussian basis for the atoms Li–Ne is enriched with polarization functions. This basis is tested for AlF, SiO, PN, BCl, and P₂. The properties of interest were HF total energies, MP2 dipolar moments, bond distances, and dissociation energies. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 927–934, 1997     

Hartree–Fock wave functions with a modified GTO basis for atoms

We have solved the atomic Hartree–Fock equations by using the algebraic approach, expanding the single-particle radial wave function in terms of a modified Gaussian type orbitals (GTOs) basis. Several atomic properties such as Kato's cusp condition for the electron density or the correct asymptotic behavior of the electron momentum density distribution are accurately verified. Additionally the energy of the atomic ground state can be obtained by using a smaller number of basis functions than in standard GTO expansions. This study has been performed for several atoms of the first three rows. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 59–64, 1997     

An instability condition for the Hartree–Fock solution of the infinite one‐dimensional system with two‐crossing bands. I. Singlet‐instability check of metallic carbon nanotube

An instability condition is derived for the Hartree–Fock solution so that it can be applied to the system in which the highest occupied and the lowest unoccupied bands cross at the in‐between point in the Brillouin zone. The instability check developed here is further applied to a metallic single‐walled carbon nanotube having the two‐crossing bands toward prediction of its instability. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 574–582, 2000     

The isomers of phenalene and their singlet and triplet states: A Hartree–Fock and density functional computational investigation

Each of the isomers of phenalene, 1H-, 2H-, 3aH-, and 9bH-phenalene, as well as the cation, neutral radical, and anion in the phenalenyl system, have been examined at the Hartree–Fock 6-31G(d) and the density functional B3LYP/6-31G(d) levels of theory. The structures and properties of the phenalenes were determined as both singlets and triplets. While the data indicate that both the 9bH- and the 1H-isomer will exist as ground state singlets, the 2H- and 3aH-phenalenes are predicted to exist as ground state triplets; only the synthesis of the 1H-isomer has been reported in the literature. Structurally, 1H- and 2H-phenalene are planar systems, 3aH- and 9bH-phenalene are non-planar systems puckered at the saturated carbon, and the cation, neutral radical, and anion of phenalenyl are planar D_3h systems.     

Complete one‐ and two‐center partitioning scheme for the total energy in the Hartree–Fock theory

We proposed a complete calculation scheme for attributing the total energy by the Hartree–Fock theory to atoms (E_A) and the region between two atoms (E_AB). It was pointed out that the conventional method using the Fock matrix includes a large amount of mutual contamination in both E_A and E_AB. The new scheme was derived from the basic expression of the total energy. Calculated results by the new scheme satisfy the theoretical requirements. The scaling effect on partitioned energies was also examined. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 35–46, 1999     

An improved generator coordinate Hartree–Fock method applied to the choice of contracted Gaussian basis sets for first‐row diatomic molecules

Accurate Gaussian basis sets (18s for Li and Be and 20s11p for the atoms from B to Ne) for the first‐row atoms, generated with an improved generator coordinate Hartree–Fock method, were contracted and enriched with polarization functions. These basis sets were tested for B₂, C₂, BeO, CN⁻, LiF, N₂, CO, BF, NO⁺, O₂, and F₂. At the Hartree–Fock (HP), second‐order Møller–Plesset (MP2), fourth‐order Møller–Plesset (MP4), and density functional theory (DFT) levels, the dipole moments, bond lengths, and harmonic vibrational frequencies were studied, and at the MP2, MP4, and DFT levels, the dissociation energies were evaluated and compared with the corresponding experimental values and with values obtained using other contracted Gaussian basis sets and numerical HF calculations. For all diatomic molecules studied, the differences between our total energies, obtained with the largest contracted basis set [6s5p3d1f], and those calculated with the numerical HF methods were always less than 3.2 mhartree. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 15–23, 2000     

The Hartree–Fock triplet instability: influence of conformation and substitution

The triplet Hartree–Fock (HF) instability is investigated through the examples of substituted ethylenes and the small linear conjugated systems butadiene, hexatriene, octatetraene. A statistical analysis is performed for several conformations of the latters. The second eigenvalue of the instability matrix appears to be able to discriminate the groups of unsaturated compounds. The HF instability is largely influenced by conjugation and mesomeric effects and thus by the geometry. The number of π electrons is also an important factor. The electronic correlation related to the HF instability is not quantified by the energy difference between the post-HF and HF levels.     

Analytical Hartree–Fock wave functions subject to cusp and asymptotic constraints: He to Xe,Li+ to Cs+, H− to I−

Analytical, variational approximations to Hartree–Fock wave functions are constructed for the ground states of all the neutral atoms from He to Xe, the cations from Li⁺ to Cs⁺, and the stable anions from H⁻ to I⁻. The wave functions are constrained so that each atomic orbital agrees well with the electron–nuclear cusp condition and has good long‐range behavior. Painstaking optimization of the exponents and principal quantum numbers of the Slater‐type basis functions allows us to reach this goal while obtaining total energies that, at worst, are a few microHartrees above the numerical Hartree–Fock limit values. The wave functions are freely available by anonymous ftp from okapi.chem.unb.ca or upon request to the authors. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 491–497, 1999     

Simple derivation of conditions for instability in the Hartree–Fock and projected Hartree–Fock schemes

The conditions for instability of solutions of Hartree–Fock and projected Hartree–Fock equations are derived in a form involving finite real symmetric matrices. These conditions are also expressed in terms of the Fock–Dirac density matrix, both at the spin–orbital and at the orbital level. The particular variations which give rise to the so-called singlet and triplet instabilities are described.     

Towards a complete basis set limit of Hartree–Fock method: correlation-consistent versus polarized-consistent basis sets

In this paper the convergence pattern of correlation-consistent (cc-pVxZ) and polarized-consistent (PC-n) hierarchies relative to the complete basis set limit have been considered in a small set of diatomic molecules. Using the sequence of these basis sets it was demonstrated that potential energy surfaces derived from basis-set-dependent solution of the Hartree–Fock equations achieves the exact numerical derived potential energy surfaces (PESs) in an ordered manner. So it was possible to compute the spectroscopic parameters in the complete basis set limit with considerable accuracy using the most extended members of both hierarchies. On the other hand, for the first time the detailed convergence patterns of total energies in three separate inter-nuclear distances have been considered in these molecules and it was demonstrated that the total energies arrive at microhartree accuracy at a considerable rate. Possible performance of extrapolation schemes is discussed and it was demonstrated that reliable extrapolation procedures indeed exist. A successful test of the proposed extrapolation method, using the three most extended members of polarized-consistent basis sets, has been accomplished on selected polyatomic molecules.     

Molecular structure and vibrational spectra of indole and 5-aminoindole by density functional theory and ab initio Hartree–Fock calculations

The molecular geometry and vibrational frequencies of indole and 5-aminoindole in the ground state have been calculated by using the Hartree–Fock and density functional method with 6-311++G(d,p) basis set. The optimized geometrical parameters obtained by DFT calculations are in good agreement with the experimental values. Comparison of the observed fundamental vibrational frequencies of indole and 5-aminoindole with the calculated results by density functional and Hartree–Fock methods indicates that B3LYP is superior to the scaled Hartree–Fock approach for molecular vibrational problems. The theoretical spectrograms for FT-IR spectrum of 5-aminoindole have been constructed.     

Second- and higher-order convergence in linear and nonlinear multiconfigurational Hartree–Fock theory

We discuss how the local convergence of Newton–Raphson and fixed Hessian MCSCF iterative models may be rationalized in terms of a total order of convergence in an error vector and a corresponding error term. We demonstrate that a sequence of N Newton–Raphson iterations has a total order of convergence of 2^N and that a sequence of N fixed Hessian iterations has a total order of convergence of N + 1. We derive the error terms of a Newton–Raphson and a fixed Hessian sequence of iterations. We discuss the implementation of the fixed Hessian and the Newton–Raphson approaches both when linear and nonlinear transformations of the variables are carried out. Sample calculations show that insight into the structure of the local convergence of Newton–Raphson and fixed Hessian models can be based on an order of convergence and an error term analysis.     

Structure and conformational stability of CH2CHCH2X (X=F, Cl and Br) molecules—post Hartree–Fock and density functional theory methods

The molecular structure and conformational stability of CH₂CHCH₂X (X=F, Cl and Br) molecules were studied using ab initio and density functional theory (DFT) methods. The molecular geometries of 3-fluoropropene were optimized employing BLYP and B3LYP levels of theory of DFT method implementing 6-311+G(d,p) basis set. The MP2/6-31G^*, BLYP and B3LYP levels of theory of ab initio and DFT methods were used to optimize the 3-chloropropene and 3-bromopropene molecules. The structural and physical parameters of the molecules are discussed with the available experimental values. The rotational potential energy surface of the above molecules were obtained at MP2/6-31G^* and B3LYP/6-311+G(d,p) levels of theory. The Fourier decomposition of the rotational potentials were analyzed. The HF/6-31G^* and MP2/6-31G^* levels of theory have predicted the cis conformer as the minimum energy structure for 3-fluoropropene, which is in agreement with the experimental values, whereas the BLYP/6-311+G(d,p) and B3LYP/6-311+G(d,p) levels of theory reverses the order of conformation. The ΔE values calculated for 3-chloropropene at MP2/6-31G^*, BLYP/6-311+G(d,p) and B3LYP/6-311+G(d,p) levels of theory show that the gauche form is more stable than the cis form, which is in agreement with the experimental value. The same levels of theory have also predicted that the gauche form is stable than cis for 3-bromopropene molecule. The maximum hardness principle has been able to predict the stable conformer of 3-fluoropropene at HF/6-31G^* level of theory, but the same level of theory reverses the conformational stability of 3-chloropropene and 3-bromopropene molecules and MP2/6-31G^* level of theory predicted the stable conformer correctly.     

Accurate Gaussian basis sets for the H2O molecule generated with the molecular improved generator coordinate Hartree–Fock method

The molecular improved generator coordinate Hartree–Fock (MIGCHF) method is used to generate accurate basis sets of primitive Gaussian-type functions for the H₂O molecule. Sequences of increasing size atom centered basis sets are employed to explore the accuracy that can be achieved with this method. Using the O(24s14p8d5f2g1h);H(22s9p5d2f1g) basis set, the HF and second-order electron correlation energies of the H₂O ground state at the experimental geometry are computed as −76.0674680 and −0.3491935 hartree, respectively. The HF energy is in error by 20 μhartree and the second-order correlation energy corresponds to 96.5% of an estimate of the limiting value. The relevance of the present calculations is to show the accuracy that can be achieved in studies of small polyatomic molecules with the MIGCHF method.     

A new partitioning scheme for molecular interacting systems within a multiconfigurational or monoconfigurational Hartree–Fock formalism

A new method, based on the spatial decomposition of the reduced‐density and pair‐density matrices and the indistinguishable integrals formalism, is introduced to partition the molecular and stabilization energies into meaningful fragments. These are defined as entirely flexible variable‐size entities, for example, atoms, group of atoms, ions, and interacting monomers. This new partitioning scheme is especially appropriated to study systems in which a directly bonded group‐transfer process occurs. In these cases, the stabilization energies are partitioned into an intrafragment component, associated with the difference of intrinsic affinity to the transferred group between the involved fragments, and an interfragment component, associated with the difference of the magnitude of the interaction between the fragments in the initial and final binding complexes. This method was applied to the study of the arginine–carboxylate interactions, allowing us to have insight into what really happens in this system. Two (zwitterionic and neutral) binding complexes can be considered. The main effects accountable for the preferential stabilizations of the binding complexes are determined to be basis‐set independent. The zwitterionic complex is favored by the interfragment component, while the neutral complex is favored by the larger intrinsic proton affinity of the acetate relatively to the methylguanidium. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 157–176, 1999