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     

Near-Dirac–Hartree–Fock results for first-row atoms calculated with GTO basis sets

Relativistic basis sets for first-row atoms have been constructed by using the near-Hartree–Fock (nonrelativistic) eigenvectors calculated by Partridge. These bases generate results of near-Dirac–Hartree–Fock quality. Relativistic total and orbital energies, relativistic corrections to the total energy, and magnetic interaction energies for the first-row atoms have been presented. The smallest Gaussian expansions (13s8 p expansions) yield Dirac–Hartree–Fock total energies accurate through six significant digits, while the largest expansions (18s13p expansions) give these energies accurate through seven significant digits. These results are more accurate than some of the results reported earlier, particularly for the open-shell atoms, indicating that the basis employed is reasonably economical for relativistic calculations. © 1995 John Wiley & Sons, Inc.     

Pair-excitation MCSCF treatment of small molecules in an optimized Slater–Transform–Preuss basis set

Pair-excitation multiconfigurational self-consistent field (PEMCSCF ) treatment of 11 small molecules (LiH, BeH₂, BH₃, BF, CH₄, C₂H₄, C₂H₂, CH₂O, NH₃, H₂O, and HF) has been carried out in a minimum basis set of Slater Transform Preuss functions as fitted by six cartesian gaussians (STP -6G). The advantages of accuracy without using a split basis are shown by comparison to familiar 4-31G and 6-31G calculations using molecular geometries optimized with STO -6G basis sets. A benefit is shown for the use of minimum basis fitted to STP functions: they overemphasize long-tail radial dependence to achieve long range basis sensitivity without increasing the basis size at the AO -to-MO transformation step in the configuration interaction portion of the MCSCF algorithm. Fully optimized STP -6G parameters are given and appear to be transferable as shown for acrolein. A FORTRAN listing of the full least squares fitting algorithm is available* for in situ generation of STP -6G orbitals energetically superior to 4-31G, or a less accurate STP -6G 1S, 2S, and 2P basis may be scaled directly as if they were STO -6G functions, but with considerably lower energy that with an STO -6G basis.     

Highly accurate relativistic universal Gaussian basis set for Dirac–Fock–Breit calculations

Ion mobilities of H₂O⁺ drifting in helium are calculated and compared with experiment. These calculations employ global potential energy surfaces of the H₂O⁺–He complex, which in the present case were calculated ab initio at the unrestricted MP2 level of theory using a basis set of aug‐cc‐pVTZ quality, and treating the ion as a rigid body. Details are presented of the general characteristics of both the ground and first‐excited electronic states of the complex. Although only the ground‐state surface was used for the mobility calculations, the ab initio determination of the ground state necessitated the inclusion of the first‐excited state owing to the presence of a crossing between the two. This crossing is also described. Mobilities calculated from the global surfaces are in good agreement with experiment. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

On the evaluation of spin–orbit coupling matrix elements in a spin‐adapted basis

In the present article, we outline a simple scheme for generating configuration interaction matrix elements for spin–orbit interactions in molecules. The procedure leads to a close parallelism with spin‐free permutation‐group approaches. Unitary shift operators were successfully used on the orbital space to generate the matching permutations necessary to evaluate the required matrix elements. The procedure is adequately illustrated using examples. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 23–27, 1999     

A possible basis for structure–function relationship of estrogens

It is well known that a wide variety of molecules compete for binding to the estrogen receptor and act as estrogens and/or antiestrogens. These molecules such as estradiol, diethylstilbestrol, doisynolic acid, the triarylethylenes, and cyclofenyl apparently share little resemblance which could account for their interaction with a common estrogen binding site. Knowledge of the receptor binding of triarylethylene and cyclofenyl prototypes, in particular, relative to that of the other estrogens is critical for understanding their structure-function relationship. We have carried out a study on the receptor binding specificity of triarylethylene and cyclofenyl prototypes. This study has revealed that these molecular types share considerable resemblance in their receptor binding specificity and differ from estradiol and other similar molecules in some important respects. However, comparison of their substructural binding specificities reveals the possibility that the triarylethylene and estradiol prototypes may interact with at least some common regions of the estrogen binding site. Based on this reasoning the comparative receptor binding of estrogens has been rationalized on the basis of a subsite hypothesis for the estrogen binding site. According to this hypothesis, the composite estrogen binding site is composed of essentially five subsites, and that the structurally different estrogenic prototypes can interact with different set of subsites, and thus differ in their binding orientation. The essential difference in the activity profile of estradiol prototypes and the triarylethylene antiestrogens reveals the possibility of a causal relationship between the binding orientation of a ligand and its activity profile. This model for receptor site can thus serve as a working hypothesis to rationalize the structure-function relationship of estrogens.     

Biphenylene as a crosslinking unit in polyaromatic ether–ketone and ether–ketone–sulfone resins. XVI

Biphenylene units have been incorporated into polyaromatic ether–ketone and polyaromatic ether–ketone–sulfone resins as useful crosslinking sites. Crosslinking is achieved by heating the resins to 300–400°C. The keto polymers are soluble only in sulfuric acid before curing, but the sulfone polymers are soluble also in some aprotic solvents. Molded “I beams” of the cured keto polymer are stronger than those of the sulfone polymer. Both classes of polymer are quite thermally stable. Curing can be hastened by catalyzing with rhodium compounds.     

Compatibility of correlation‐consistent basis sets with a hybrid Hartree–Fock/density functional method

The present study examines the feasibility of combining the correlation‐consistent basis sets developed by Dunning and coworkers with the hybrid Hartree–Fock/density functional method B3LYP. Furthermore, extrapolation to the complete basis set (CBS) limit minimizes errors due to the presence of an incomplete basis set and can act as a rigorous test of the limitations of the B3LYP method. Equilibrium geometries, energies, and harmonic vibrational frequencies were determined for a series of well‐studied, yet computationally challenging, small inorganics and their respective ions. The results were then extrapolated to the CBS limit, where applicable, and compared to experiment. It was found that a union between the hybrid Hartree–Fock/density functional B3LYP method and Dunning's augmented correlation‐consistent basis sets gave results that were comparable to molecular orbital methods that explicitly account for electron correlation. Furthermore, the minimum basis set necessary to attain reasonable results for the systems studied was aug‐cc‐pVTZ. Upgrading to the aug‐cc‐pVQZ level and subsequent extrapolation to the CBS limit further improved the overall agreement with the experiment. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 207–216, 1999     

Compact contracted basis sets for third-row atoms: Ga–Kr

The (14s11p5d) primitive basis set of Dunning for the third-row main group atoms Ga-Kr has been contracted [6s4p1d]. The core functions have been relatively highly contracted while those which represent the valence region have been left uncontracted to maintain flexibility. Calculations with the [6s4p1d] contraction are reported for a variety of molecules involving third-row atoms. This basis set is found to satisfactorily reproduce experimental properties such as geometric configurations, dipole moments, and vibrational frequencies for a range of molecules. Comparisons are made with the performance of the uncontracted basis set. Polarization functions for the contracted basis set are reported and performance of the basis set with and without polarization functions is examined. A relaxation of the [6s4p1d] contraction to [9s6p2d] for higher level evergy calculations is also presented.     

Efficient diffuse function-augmented basis sets for anion calculations. III. The 3-21+G basis set for first-row elements,Li–F

The relatively small diffuse function-augmented basis set, 3-21+G, is shown to describe anion geometries and proton affinities adequately. The diffuse sp orbital exponents are recommended for general use to augment larger basis sets.     

Molecular structure–biological activity relationships on the basis of quantum-chemical calculations

Detailed quantum-chemical calculations by means of semiempirical all-valence electrons methods and a generalized (multivariable) rank correlation analysis are the fundamentals of a novel strategy of search for QSAR within homologous series of compounds. The set of molecular parameters (describing the electronic and conformational properties as well as potential interactions of the drugs) is calculated theoretically. Owing to the rank correlation method, no linear model (like LFER ) for the dependence of the biological activity upon the molecular parameters is presumed. The computed correlation coefficients are valued by carefully determined levels of statistical significance. Significant correlations are used to predict unknown activities in terms of ranks relative to the basic sample.     

Valence bond approach exploiting Clifford algebra realization of Rumer–Weyl basis

A detailed algorithm is described that enables an implementation of a general valence bond (VB ) method using the Clifford algebra unitary group approach (CAUGA ). In particular, a convenient scheme for the generation and labeling of classical Rumer–Weyl basis (up to a phase) is formulated, and simple rules are given for the evaluation of matrix elements of unitary group generators, and thus of any spin-independent operator, in this basis. The case of both orthogonal and nonrothogonal atomic orbital bases is considered, so that the proposed algorithm can also be exploited in molecular orbital configuration interaction calculations, if desired, enabling a greater flexibility for N-electron basis-set truncation than is possible with the standard Gel'fand–Tsetlin basis. Finally, an exploitation of this formalism for the VB method, based on semiempirical Pariser–Parr–Pople (PPP )-type Hamiltonian and nonorthogonal overlap-enhanced atomic orbital basis, and its computer implementation, enabling us to carry out arbitrarily truncated or full VB calculations, is described in detail.     

Light Energy Collection in a Porphyrin–Imide–Corrole Ensemble

An assembly consisting of three units, that is, a meso‐substituted corrole ( C3 ), 1,8 naphthaleneimide ( NIE ), and a Zn porphyrin ( ZnP ), has been synthesized. NIE is connected to C3 through a 1,3‐phenylene bridge and to the ZnP unit through a direct C? C bond. The convergent synthetic strategy includes the preparation of a trans‐A₂B‐corrole possessing the imide unit, followed by Sonogashira coupling with a meso‐substituted A₃B‐porphyrin. The photophysical processes in the resulting triad ZnP-NIE-C3 are examined and compared with those of the corresponding C3-NIE dyad and the constituent reference models C3 , NIE , and ZnP . Excitation of the NIE unit in C3-NIE leads to a fast energy transfer of 98 % efficiency to C3 with a rate k_en=7.5×10¹⁰ s^?1, whereas excitation of the corrole unit leads to a reactivity of the excited state identical to that of the model C3 , with a deactivation rate to the ground state k=2.5×10⁸ s^?1. Energy transfer to C3 and to ZnP moieties follows excitation of NIE in the triad ZnP-NIE-C3 . The rates are k_en=7.5×10¹⁰ s^?1 and k_en=2.5×10¹⁰ s^?1 for the sensitization of the C3 and ZnP unit, respectively. The light energy transferred from NIE to Zn porphyrin unit is ultimately funneled to the corrole component, which is the final recipient of the excitation energy absorbed by the different components of the array. The latter process occurs with a rate k_en=3.4×10⁹ s^?1 and 89 % efficiency. Energy transfer processes take place in all cases by a Förster (dipole–dipole) mechanism. The theory predicts quite satisfactorily the rate for the ZnP/C3 couple, where components are separated by about 23 Å, but results in calculated rates that are one to two orders of magnitude higher for the couples NIE/ZnP (D/A) and NIE/C3, which are separated by distances of about 14 and 10 Å, respectively.     

Auxiliary basis sets for density‐fitting second‐order Møller–Plesset perturbation theory: Weighted core‐valence correlation consistent basis sets for the 4d elements Y–Pd

Auxiliary basis sets (ABS) specifically matched to the cc‐pwCVnZ‐PP and aug‐cc‐pwCVnZ‐PP orbital basis sets (OBS) have been developed and optimized for the 4d elements Y‐Pd at the second‐order Møller‐Plesset perturbation theory level. Calculation of the core‐valence electron correlation energies for small to medium sized transition metal complexes demonstrates that the error due to the use of these new sets in density fitting is three to four orders of magnitude smaller than that due to the OBS incompleteness, and hence is considered negligible. Utilizing the ABSs in the resolution‐of‐the‐identity component of explicitly correlated calculations is also investigated, where it is shown that i‐type functions are important to produce well‐controlled errors in both integrals and correlation energy. Benchmarking at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations level indicates impressive convergence with respect to basis set size for the spectroscopic constants of 4d monofluorides; explicitly correlated double‐ζ calculations produce results close to conventional quadruple‐ζ, and triple‐ζ is within chemical accuracy of the complete basis set limit. © 2013 Wiley Periodicals, Inc.