Local exchange-correlation approximations and first-row molecular dissociation energies

Recent Xα calculations of bond energies and other related properties of first-row diatomic molecules show very encouraging agreement with experiment. In the worst cases, however, the Xα dissociation energies overestimate the experimental values by almost 2 eV. Therefore, we have examined several refinements of the Xα theory and their effects on molecular bond lengths, bond energies, and vibrational frequencies. Among them, gradient corrections to the Xα exchange energy and also some variations of the local spin-density correlation energy approximation are considered. We find that a local exchange-correlation functional with gradient corrections gives dissociation energies in significantly better agreement with experiment than the Xα approximation.     

Calculation of exchange-correlation potentials with auxiliary function densities

The use of Hermite Gaussian auxiliary function densities from the variational fitting of the Coulomb potential for the calculation of exchange-correlation potentials is discussed. The basic working equations for the energy and gradient calculation are derived. The accuracy of this approximation for optimized structure parameters and bond energies are analyzed. It is shown that the quality of the approximation can be systematically improved by enlarging the auxiliary function set. Average errors of 0.5 kcal/mol are obtained with auxiliary function sets including f and g functions. The timings for a series of alkenes demonstrate a substantial performance improvement.     

Scaling factors for vibrational frequencies and zero-point vibrational energies of some recently developed exchange-correlation functionals

The scaling factors for the vibrational frequencies and zero-point vibrational energies evaluated at various combinations of recently developed exchange-correlation functionals and various basis sets are reported. The exchange-correlation functionals considered are B972, B98, HCTH, OLYP, O3LYP, G96LYP, PBE0 and VSXC functionals; the basis sets employed are 3-21G, 6-31G*, 6-31G**, 6-31+G, 6-311G*, 6-311G**, 6-311G(df,p), 6-311+G(df,p), cc-pVDZ and aug-cc-pVDZ. The experimental harmonic frequencies of 122 small molecules and the zero-point vibrational energies of 39 small molecules are used to determine the scaling factors through the least-square fitting procedure. It was found that the scaling factors do not depend significantly on the basis sets considered. The vibrational frequency scaling factors evaluated by using the B98 and PBE0 functionals are recommended on the basis of smallest root mean square error. The zero-point vibrational energy scaling factors evaluated from the B972 functional with Pople's double-zeta basis set and the HCTH functional with Pople's triple-zeta basis set are recommended on the basis of smallest root mean square error.     

Time-dependent four-component relativistic density-functional theory for excitation energies. II. The exchange-correlation kernel

We extend our previous formulation of time-dependent four-component relativistic density-functional theory [J. Gao, W. Liu, B. Song, and C. Liu, J. Chem. Phys. 121, 6658 (2004)] by using a noncollinear form for the exchange-correlation kernel. The new formalism can deal with excited states involving moment (spin)-flipped configurations which are otherwise not accessible with ordinary exchange-correlation functionals. As a first application, the global potential-energy curves of 16 low-lying omega omega-coupled electronic states of the AuH molecule have been investigated. The derived spectroscopic parameters, including the adiabatic and vertical excitation energies, equilibrium bond lengths, harmonic and anharmonic vibrational constants, fundamental frequencies, and dissociation energies, are grossly in good agreement with those of ab initio multireference second-order perturbation theory and the available experimental data.     

Optimized effective potentials yielding Hartree-Fock energies and densities

It is commonly believed that the exchange-only optimized effective potential (OEP) method must yield total energies that are above corresponding ground-state Hartree-Fock (HF) energies except for one- and two-electron systems. We present a simple procedure for constructing local (multiplicative) exchange potentials that reproduce exactly the HF energy and density in any finite basis set for any number of electrons. For any finite basis set, no matter how large, there exist infinitely many such OEPs, which questions their suitability for practical applications.     

Virial exchange energies from model exact-exchange potentials

It is shown by the example of Slater's averaged exchange potential that a poor approximation to the optimized effective potential (OEP) can yield a deceptively accurate energy via the conventional Kohn-Sham energy functional. For a trial exchange potential to be correct, its Kohn-Sham energy must coincide with the value obtained by the Levy-Perdew virial relation. Significant discrepancies between Kohn-Sham and the virial exchange energies are found for self-consistent Slater, Becke-Johnson, and effective local potentials (ELPs); their relative magnitudes are used to argue that, as approximations to the exact-exchange OEP, ELPs are the most accurate. Virial energy discrepancies vanish for Yang-Wu OEPs when the orbital and auxiliary basis sets are balanced, and remain surprisingly small for oscillatory OEPs obtained with unbalanced basis sets.     

Efficient computation of the exchange-correlation contribution in the density functional theory through multiresolution

A new algorithm is presented to improve the efficiency of the computation of exchange-correlation contributions, a major time-consuming step in a density functional theory (DFT) calculation. The new method, called multiresolution exchange correlation (mrXC), takes advantage of the variation in resolution among the Gaussian basis functions and shifts the calculation associated with low-resolution (smooth) basis function pairs to an even-spaced cubic grid. The cubic grid is much less dense in the vicinity of the nuclei than the atom-centered grid and the computation on the former is shown to be much more efficient than on the latter. MrXC does not alter the formalism of the current standard algorithm based on the atom-centered grid (ACG), but instead employs two fast and accurate transformations between the ACG and the cubic grid. Preliminary results with local density approximation have shown that mrXC yields three to five times improvement in efficiency with negligible error. The extension to DFT functionals with generalized gradient approximation is also briefly discussed.     

Assessment of recently developed exchange-correlation functionals for the description of torsion potentials in pi-conjugated molecules

Newly developed exchange-correlation functionals in density functional theory (DFT) have been applied to describe conjugation effects in organic molecules. The performance of the various approaches is assessed through the calculation of torsion energy profiles and their critical comparison with available experimental data. Our results indicate that the OPTX-B95 exchange-correlation functional as well as its corresponding hybrid versions perform better than the well-established BLYP or B3LYP schemes when dealing with pi-conjugated molecules. In contrast, the recently introduced VSXC functional is not as reliable as other DFT methods for the systems examined here.     

Aggregation energies of nonionic micelles calculated via pair potentials

The aggregation energies of two different forms of nonionic isolated micelles belonging to a binary oil-in-water system were calculated by using pairwise central potentials. One of the micelles is an elongated form (the spherocylinder); the other one is a flat form (the square tablet). The spherocylinder and the square tablet degenerate into the same spherical micelle at low aggregation numbers, whereas they form elongated cylinders and lamellae, respectively, at very high aggregation numbers. Both forms are of particular importance in some nematic systems involving a phase transition. The interaction energy among the polar heads of the amphiphilic molecules was calculated using a central Lennard-Jones potential. The interaction energy among the hydrocarbon chains in the micelle bulk was calculated via a phenomenological potential model. The calculations were performed considering a wide range of values of the parameters involved (i.e. polar head diameter, chain length). The entropic contribution to the aggregation free energy is similar for both micelles, and so their relative stability depends principally on the aggregation energy. The micelle aggregation energy depends strongly on the aggregation number and other geometrical parameters for both forms. The present results are consistent with those obtained using the surfactant parameter model, which permits the evaluation of the elastic bending energy of the micelle membrane for both forms. Received: 29 March 1999 Accepted in revised form: 28 June 1999     

Activation energies and potentials of mean force for water cluster evaporation

Activation energies for water cluster evaporation are of interest in many areas of chemical physics. We present the first computation of activation energies for monomer evaporation of small water clusters using the formalism of dynamical nucleation theory (DNT). To this end, individual evaporation rate constants are computed for water clusters (H(2)O)(i), where i=2-10 for temperatures ranging from 243 to 333 K. These calculations employ a parallel sampling technique utilizing a Global Arrays toolkit. The resulting evaporation rate constants for each cluster are then fitted to Arrhenius equations to obtain activation energies. We discuss DNT evaporation rate constants and their relation to potentials of mean force, activation energies, and how to account for nonseparability of the reaction coordinate in the reactant state partition function.     

Efficient and reliable mixture critical points calculation by global optimization

Multicomponent systems may exhibit several critical points or no critical point at all. Local methods can find only one critical point for a given initial guess. Recently, several global methods have been proposed for finding all the solutions of the problem. In the present work, we propose a gradient-based calculation method using global optimization, with temperature and molar volume as primary variables, and with analytical partial derivatives calculated from a two-parameter cubic equation of state. The Tunneling global optimization method is used for finding all the global minima. The implementation is based on a unique feature of the Tunneling method, which is able to find efficiently and reliably multiple minima at the same level. Several mixtures from binaries to petroleum reservoir fluids are used to test the proposed method. Numerical experiments proved the efficiency and reliability of the Tunneling method for finding all mixture critical points.     

Efficient linear-response method circumventing the exchange-correlation kernel: theory for molecular conductance under finite bias

An iterative approach for calculating the frequency domain linear response of molecular systems within time-dependent density-functional theory is presented. The method completely avoids computing the exchange-correlation kernel which is typically the most expensive step for large systems. In particular, virtual orbitals are not needed. This approach may be useful for treating the response of large systems. We give an outline of the theory and a demonstration on a jellium model of an elliptic gold cluster. A detailed theory is appended discussing the computation of conductance and ac impedance of molecular junctions under bias.     

The performance of time-dependent density functional theory based on a noncollinear exchange-correlation potential in the calculations of excitation energies

In the present work we have studied the accuracy of excitation energies calculated from spin-flip transitions with a formulation of time-dependent density functional theory based on a noncollinear exchange-correlation potential proposed in a previous study. We compared the doublet-doublet excitation energies from spin-flip transitions and ordinary transitions, calculated the multiplets splitting of some atoms, the singlet-triplet gaps of some diradicals, the energies of excited quartet states with a doublet ground state. In addition, we attempted to calculate transition energies with excited states as reference. We compared the triplet excitation energies and singlet-triplet separations of the excited state from spin-flip and ordinary transitions. As an application, we show that using excited quartet state as reference can help us fully resolve excited states spin multiplets. In total the obtained excitation energies calculated from spin-flip transitions agree quite well with other theoretical results or experimental data.     

Core ionization potentials from self-interaction corrected Kohn-Sham orbital energies

We propose a simple self-interaction correction to Kohn-Sham orbital energies in order to apply ground state Kohn-Sham density functional theory to accurate predictions of core electron binding energies and chemical shifts. The proposition is explored through a series of calculations of organic compounds of different sizes and types. Comparison is made versus experiment and the "DeltaKohn-Sham" method employing separate state optimizations of the ground and core hole states, with the use of the B3LYP functional and different basis sets. A parameter alpha is introduced for a best fitting of computed and experimental ionization potentials. It is found that internal parametrizations in terms of basis set expansions can be well controlled. With a unique alpha=0.72 and basis set larger than 6-31G, the core ionization energies (IPs) of the self-interaction corrected Kohn-Sham calculations fit quite well to the experimental values. Hence, self-interaction corrected Kohn-Sham calculations seem to provide a promising tool for core IPs that combines accuracy and efficiency.     

Bond energies in alloys determined from underpotential deposition potentials

A procedure is presented to determine bond energies between the metal (Me) and substrate (S) components of binary alloys from characteristic underpotential deposition (UPD) potentials. The bond energy between Me and S atoms is one of the factors governing the deposition kinetics and structure of Me-S alloy deposits. The proposed procedure is based on the determination of the UPD potential for formation of a condensed two-dimensional (2D) phase of the less noble metal Me (the UPD metal) on the more noble metal S (the substrate). Making reasonable approximations, the sublimation enthalpy of the condensed 2D Me phase is obtained from the corresponding formation underpotential. From this sublimation enthalpy the bond energy of an atom of the UPD metal in a kink site position of the 2D Me phase is calculated. This value is used to calculate the bond energy (_Me-S) between an Me atom and an S atom. The method is demonstrated using experimental data obtained in selected electrochemical UPD systems.     

Fast and reliable numerical methods to simulate complex chemical kinetic mechanisms

Models that simulate atmospheric photochemistry require the use of a stiff ordinary differential equations (ODEs) solver. Since the simulation of the chemical transformations taking place in the system takes up to 80 percent of the CPU time, the numerical solver must be computationally fast. Also, the residual error from the solver must be small. Because most accurate solvers are relatively slow, modelers continue to search for timely, yet accurate integration methods. Over the past years an extensive number of articles have been dedicated to this subject. One of the highly debated questions is whether one should construct specialized algorithms or instead use general methods for stiff ODEs. In the present article we use the second alternative. We apply three linearly (semi-)implicit methods from the classical stiff ODE literature which we modified to implement the sparse routines to solve the system of equations describing a complex kinetic mechanism. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 349–358, 1998     

Improving numerical integration through basis set expansion

Calculations are presented to assess a theorem presented by S.F. Boys [(1969) Proc. R. Soc. A. 309:195], regarding the accuracy of numerical integration in quantum chemical calculations. The theorem states that the error due to numerical integration can be made proportional to the error due to basis set truncation, and thus goes to zero in the limit of a complete basis. We test this theorem on the hydrogen atom, showing that with a solution-spanning basis, the numerically exact orbital energy can indeed be calculated with a small number of integration points. Moreover, tests for H and H₂⁺ demonstrate that even when only a near-complete basis is employed, Boys Theorem can significantly reduce integration error. However, for other systems, like the oxygen atom and the CO₂ molecule, the theorem yields no advantage for some occupied orbitals. It is concluded that the theorem would be most useful for calculations that demand large basis sets.     

Density scaling and exchange-correlation energy

The exchange-correlation energy is studied using the density scaling proposed by Chan and Handy [G. K.-L. Chan and N. C. Handy, Phys. Rev. A 59, 2670 (1999)]. It is shown that there exists a value of the scaling factor for which the correlation energy disappears. The optimized potential method and the Krieger-Li-Iafrate approach are generalized to incorporate correlation.     

Three-dimensional numerical integration for electronic structure calculations

Two three-dimensional numerical schemes are presented for molecular integrands such as matrix alements of one-electron operators occuring in the Fock operator and expectation values of one-electron operators describing molecular properties. The schemes are based on a judicious partitioning of space so that product-Gauss integration rules can be used in each region. Convergence with the number of integration points is such that very high accuracy (8–10 digits) may be obtained with obtained with a modest number of points. The use of point group symmetry to reduce the required number of points is discussed. Examples are given for overlap, nuclear potential, and electric field gradient integrals.