Generation of a basis set for the calculation of molecular magnetic properties

Completeness conditions have been applied in the theory of molecular magnetic properties to determine the best gauge for a given basis set. They can similarly be used to optimise the basis for a fixed gauge origin. Test results indicate that the gauge dependence of the calculated properties can be significantly reduced in this way.     

Features of the energy surface in Dirac-Fock discrete basis description as applied to the Be atom

The features of the Be atom's energy surface as a function of basis set exponents in the Slater-type basis have been examined for both “balanced” and “unbalanced” basis sets. The results clearly show that the “balanced” basis guarantees a minimum energy which is an upper bound to the numerical Dirac-Fock limit. The “unbalanced” basis, however, gives a minimum energy which is much lower than the numerical limit.     

Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model

The model of the full optimized reaction space describes the electronic structure of a molecule in terms of the best wave-function that can be obtained as a superposition of all those configurations which are generate possible occupancies and couplings from a “formal minimal basis” of valence, orbitals on the constituent atoms. These configurations span a “full reaction space”, and MC SCF optimization of the orbitals in terms of an extended set of quantitative basis orbitals determines the full optimized reaction space (FORS). Basic justifications, methodological specifics and sample applications are discussed.     

Calculation of magnetic properties of HF,H2O,NH3, and CH4 molecules using a longitudinal gauge for the vector potential

A transformation of the transverse Coulomb vector potential was implemented to calculate molecular magnetic properties via the random-phase approximation (RPA) within the framework of a “longitudinal gauge.” In this gauge, the diamagnetic contribution to magnetic susceptibility is a tensor with equal diagonal components as in atoms, irrespective of molecular symmetry, whereas diagonal and average diamagnetic contributions to the nuclear magnetic shielding are the same as in the Coulomb gauge. Near-Hartree–Fock magnetic susceptibility and nuclear magnetic shielding tensors were evaluated for a set of small molecules, HF, H₂O, NH₃, and CH₄, employing extended Gaussian basis sets. The peculiar features of the longitudinal gauge, and the fulfillment of a series of sum rules involving the virial operator, which must be satisfied to guarantee gauge invariance of total magnetic tensors, were exploited to check the degree of convergence of theoretical values and to estimate the corresponding Hartree–Fock limit for the properties. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 31–45, 1998     

Effective basis sets for calculations of exchange-repulsion energy

Usefulness of different Gaussian basis sets for reproducing the “tail” region of the SCF wavefunctions employed in calculations of the exchange-repulsion effect is investigated for the model He-He interaction. It has been shown that extension of the monomer-centered basis set in the scheme of regularized even-tempered basis sets [M. W. Schmidt and K. Ruedenberg, J. Chem. Phys. 71 , 3951 (1979)] can be more efficient than augmentation of the fully energy-optimized basis set with diffuse basis functions. It has been also found that Landshoff term vanishes and the “tail” region is well reproduced if monomer wavefunctions are calculated with the basis set of the dimer.     

SCF theory of intermolecular interactions without basis set superposition error

Special SCF LCAO MO type equations are derived, permitting “supermolecule” calculations for intermolecular interactions, excluding basis set superposition error (BSSE) from the beginning on the basis of the “chemical Hamiltonian approach”. (No additional “monomer” calculations are necessary to correct for BSSE.) The formalism excluding the BSSE results in a non-Hermitean Fock matrix; an algorithm is proposed to obtain the required molecular orbitals, in which no integral transformation is needed.     

On the improvement of the gauge invariance in finite basis set coupled hartree—fock calculations of molecular magnetic properties

Finite basis set coupled Hartree—Fock calculations of molecular magnetic susceptibilities and nuclear shielding constants show a very large gauge dependence (i.e., a dependence on the origin of the magnetic vector potential). The best agreement with experiment is expected for a gauge origin at the electronic centroid for which choice the so-called paramagnetic cotributions to the above properties are small. However, with a finite basis set agreement with experiment may be fortuitous and some estimate of the contribution of the unknown functions is required.A general scheme is presented for dealing with the above problems. The essence of the method is to apply an average energy approximation to the unknown functions and to determine this energy by enforcing the gauge invariance requirement. Consequently the technique can still be categorised as an ab initio method and a close approach to the Hartree—Fock limit is achieved without the need to employ very large basis sets with extensive optimisation. The method is applied to the hydrogen fluoride molecule which provides numerical justification of the proposed scheme.     

A new algebraic approach to the eigenvalue problems of linear differential operators without integrations

In this work, a new approximation scheme based on the evaluation of the pointwise expectation of the Hamiltonian (H) via a conveniently chosen basis set is proposed. This scheme does not necessitate integration; however, physical and mathematical considerations in choosing the basis set are considerably important when very precise and rapidly convergent results are desired. In this method, the best linear combination of “well-selected” basis functions are sought in a way such that H ψ / ψ is flat in the neighborhood of a conveniently chosen point in the domain of H. This yields an algebraic eigenvalue problem. Some concrete applications that have already been realized confirm the efficiency of this approach.     

Application of many-body perturbation methods in a discrete orbital basis

The many-body perturbation theory techniques used by Kelly to calculate “pair correlation energies” have been implemented in a discrete orbital basis using a set of coupled non-linear equations. The methodology differs from the usual “independent pair” methods in that the pairs are coupled by “rearrangement” effects. Some numerical results on BH are given to illustrate the utility of the method.     

Splicing I: Using mixed basis sets in ab initio calculations

The effect of mixing (or “splicing”) extended and minimal basis sets on molecular properties such as geometries, Mulliken charges, dipoles, and internal rotation barriers was studied for several test molecules. The effect is gauged by comparison with full extended basis set calculations. It is found that splicing improves most properties relative to full minimal basis set calculations, and little accuracy is lost if the splicing is done in a judicious manner.     

Multireference basis-set reduction

We review “Hilbert space basis-set reduction” (BSR) as an approach to reduce the computational effort of accurate correlation calculations for large basis sets. We partition the single-particle basis into a small “internal” and a large “external” set. We use the MRCI method for the calculation for that part of configuration space in which only internal orbitals are occupied and perturbatively correct for the remaining configurations using a method similar to Shavitt's B_k method. The present implementation approximates the MRCI result for the unpartitioned basis set, with a significantly reduced computational effort. To demonstrate the viability of the method, we present results for selected states of small molecules (Be₂, CH₂, O₃). For the examples investigated, we find that relative energy differences can be reproduced to an accuracy of approximately 1 kcal/mol with a significant computational saving. © 1996 John Wiley & Sons, Inc.     

A theoretical study of paths for decomposition and rearrangement of dihydroxycarbene

The transition states for fragmentation of dihydroxycarbene [C(OH)₂] to H₂ and CO₂ and for the rearrangement of this carbene to formic acid were located by ab initio calculations. The relative energies of the transition states were determined at several levels of theory and the basis set dependence of the energies is discussed. At the best level of theory; using a basis set of double-zeta quality augmented by polarization functions and with the inclusion of extensive CI, we found that the transition state for fragmentation was considerably higher in energy than that for rearrangement. This finding is at variance with the predictions of the Woodward--Hoffmann rules because fragmentation represents an “allowed” reaction, whereas rearrangement is “forbidden.” In conformity with the Woodward–Hoffman rules, the transition state for rearrangement was found to be close in energy to H· + ·CO₂H. The even higher energy of the transition state for concerted fragmentation to H₂ and CO₂ is attributed to the need for the latter fragment to remain substantially bent in order to permit H₂ formation while maintaining a modicum of OH bonding. Difficulties in locating the transition state for concerted fragmentation are discussed and a new method for finding transition states is proposed.     

Flexible protein‐protein docking based on Best‐First search algorithm

We developed a new high resolution protein‐protein docking method based on Best‐First search algorithm that loosely imitates protein‐protein associations. The method operates in two stages: first, we perform a rigid search on the unbound proteins. Second, we search alternately on rigid and flexible degrees of freedom starting from multiple configurations from the rigid search. Both stages use heuristics added to the energy function, which causes the proteins to rapidly approach each other and remain adjacent, while optimizing on the energy. The method deals with backbone flexibility explicitly by searching over ensembles of conformations generated before docking. We ran the rigid docking stage on 66 complexes and grouped the results into four classes according to evaluation criteria used in Critical Assessment of Predicted Interactions (CAPRI; “high,” “medium,” “acceptable,” and “incorrect”). Our method found medium binding conformations for 26% of the complexes and acceptable for additional 44% among the top 10 configurations. Considering all the configurations, we found medium binding conformations for 55% of the complexes and acceptable for additional 39% of the complexes. Introducing side‐chains flexibility in the second stage improves the best found binding conformation but harms the ranking. However, introducing side‐chains and backbone flexibility improve both the best found binding conformation and the best found conformation in the top 10. Our approach is a basis for incorporating multiple flexible motions into protein‐protein docking and is of interest even with the current use of a simple energy function. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Accurate thermochemistry from quantum chemical calculations?

The answer to the title question is definitely “yes” – at least for fairly small molecules. Computational procedures, namely the Weizmann (Wn) and Gaussian-3 (G3) family of methods, the complete basis set extrapolation scheme (CBS-x), the “high accuracy extrapolated ab initio thermochemistry” (HEAT) as well as the “correlation consistent composite approach” (ccCA), aimed at energies with chemical accuracy or even better (sub kJ?mol^?1) are described and several applications illustrating the level of accuracy that can be achieved are presented.     

Ab initio study of hydrogen bonding in the phenol–water system

Three hydrogen-bonded minima on the phenol-water, C₆H₅OH—H₂O, potential energy surface were located with 3–21G and 6–31G** basis sets at both Hartree–Fock and MP2 levels of theory. MP2 binding energies were computed using large “correlation consistent” basis sets that included extra diffuse functions on all atoms. An estimate of the effect of expanding the basis set to the triple-zeta level (multiple f functions on carbon and oxygen and multiple d functions on hydrogen) was derived from calculations on a related prototype system. The best estimates of the electronic binding energies for the three minima are –7.8, –5.0, and –2.0 kcal/mol. The consequences of uncertainties in the geometries and limitations in the level of correlation recovery are analyzed. It is suggested that our best estimates will likely underestimate the complete basis set, full CI values by 0.1–0.3 kcal/mol. Vibrational normal modes were determined for all three minima, including an MP2/6–31G** analysis for the most strongly bound complex. Computational strategies for larger phenol–water complexes are discussed. © John Wiley & Sons, Inc.     

Orbital Interaction and the Mulliken-Walsh Diagram for AH2 Systems

We define θ- (or R-) bonding (or antibonding) character of the molecular orbitals according to the slopes of the orbital energy curves when the internuclear angle (or internuclear distance) is varied. So far the slope of the orbital curve has only been accounted for by the qualitative argument based on two factors: the orbital overlap and the s-p mixing. We employ the bond orbitals instead of the usual atomic orbitals as the basis set to analysis the character of the molecular orbitals. The Fock matrix in the bond orbital basis can then quantitatively account for the effects of both the overlap and s-p mixing factors. Our analysis also show that a third factor, the orbital interaction, is essential to account for both the “typical” and “abnormal” behavior of the slopes.