Kohn-Sham Density Functional Calculations Research Articles

Radical Ions of α,α‘-Bis(diphenylamino)-capped Oligothiophenes: A Combined Spectroelectrochemical and Theoretical Study

A new homologous series of alpha,alpha'-bis(diphenylamino)-capped oligothiophenes, prepared by a palladium-catalyzed coupling reaction of stannylated 2-diphenylaminothiophenes with 2-mono- or 2,5-dibromothiophenes and their homologues, was studied by in situ ESR/UV-vis/NIR spectroelectrochemistry. In general, the oxidation potentials of these oligothiophenes were found to be proportional to the inverse number of thiophene units. However, the potential slope of the first oxidation is completely different from that of higher oxidation steps. Trication radicals were identified by electron spin resonance (ESR) for higher thiophene homologues in addition to monocation radicals (polarons). According to the ESR hyperfine structures, the unpaired electron is delocalized in the conjugated system. In contrast to the parent alpha,alpha'-bis(diphenylamino)-capped oligothiophenes, the UV-vis/NIR absorption maxima of the oxidized species strongly depend on the number of thiophene units. Spin-restricted and spin-unrestricted Kohn-Sham density functional calculations were used to explain and to understand these properties. Absorption wavelength and intensities were calculated by the time-dependent density functional response theory. Unrestricted density functional calculations of oligothiophene dications (bipolarons) with five or more thiophene rings result in spin-broken structures which may be considered as two-polaron biradicals (polaron pairs).

Orbital-free embedding applied to the calculation of induced dipole moments in CO2⋯X (X=He, Ne, Ar, Kr, Xe, Hg) van der Waals complexes

The orbital-free frozen-density embedding scheme within density-functional theory [T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050 (1993)] is applied to the calculation of induced dipole moments of the van der Waals complexes CO2...X (X = He, Ne, Ar, Kr, Xe, Hg). The accuracy of the embedding scheme is investigated by comparing to the results of supermolecule Kohn-Sham density-functional theory calculations. The influence of the basis set and the consequences of using orbital-dependent approximations to the exchange-correlation potential in embedding calculations are examined. It is found that in supermolecular Kohn-Sham density-functional calculations, different common approximations to the exchange-correlation potential are not able to describe the induced dipole moments correctly and the reasons for this failure are analyzed. It is shown that the orbital-free embedding scheme is a useful tool for applying different approximations to the exchange-correlation potential in different subsystems and that a physically guided choice of approximations for the different subsystems improves the calculated dipole moments significantly.

A density-functional approach to polarizable models: A Kim-Gordon response density interaction potential for molecular simulations

A combined linear-response-frozen electron-density model has been implemented in a molecular-dynamics scheme derived from an extended Lagrangian formalism. This approach is based on a partition of the electronic charge distribution into a frozen region described by Kim-Gordon theory [J. Chem. Phys. 56, 3122 (1972); J. Chem. Phys. 60, 1842 (1974)] and a response contribution determined by the instantaneous ionic configuration of the system. The method is free from empirical pair potentials and the parametrization protocol involves only calculations on properly chosen subsystems. We apply this method to a series of alkali halides in different physical phases and are able to reproduce experimental structural and thermodynamic properties with an accuracy comparable to Kohn-Sham density-functional calculations.

Accurate quantum-chemical prediction of enthalpies of formation of small molecules in the gas phase.

The coupled-cluster approach, including single and double excitations and perturbative corrections for triple excitations, is capable of predicting molecular electronic energies and enthalpies of formation of small molecules in the gas phase with very high accuracy (specifically, with error bars less than 5 kJmol-1), provided that the electronic wavefunction is dominated by the Hartree-Fock configuration. This capability is illustrated by calculations on molecules containing O-H and O-F bonds, namely OH, FO, H2O, HOF, and F2O. To achieve this very high accuracy, it is imperative to account for electron-correlation effects in a quantitative manner, either by using explicitly correlated two-particle basis functions (R12 functions) or by extrapolating to the limit of a complete basis. Besides taking into account harmonic zero-point vibrational energies, it is also necessary to account for anharmonic corrections to the zero-point vibrational energies, to include the core orbitals into the coupled-cluster calculations, and to account for spin-orbit corrections and scalar relativistic effects. These additional corrections constitute small but significant contributions in the range of 1-4 kJmol-1 to the enthalpies of formation of the aforementioned molecules. The highly accurate coupled-cluster results, obtained by employing R12 functions and by including various corrections, are compared with standard Kohn-Sham density-functional calculations as well as with the Gaussian-2 and complete-basis-set model chemistries.

Bond and atomization energies of C 60 and C 70 fullerenes

The bond (BE) and atomization energies ( E 0 at ) of C 60 and C 70 fullerenes are predicted by the theoretical BELE partitioning method which uses information derived from the electronic charge density at bond critical points and from the length of the curve of maximum charge density between two bonded atoms (bond path). The nuclear geometries and electronic charge densities are obtained from Kohn-Sham density functional calculations employing a TZP AO basis and the non-local BLYP exchange-correlation functional. The predicted atomization energies at 0 K of C 60 and C 70 are 9765 kcal mol −1 (exp.: 9762–9797 kcal mol −1) and 11437 kcal mol −1 (exp.: 11455 kcal mol −1), respectively. The BE values of the six-six ring and the five six ring bonds of c 60are 118.9 and 103.3 kcal mol −1. The C 70 molecule shows a broader BE distribution ranging from 97.5 to 120.3 kcal mol −1. The results of the fullerenes are compared with corresponding data of benzene (BE = 120.3 kcal mol −1) and C 5 H 5 − ( BE = 110.9 kcal mol −1) as aromatic model compounds. From the C 60 and C 70 data a linear BE bond lengths relationship in fullerenes is established.

Efficiency of algorithms for Kohn-Sham density functional theory

Recent developments in numerical methods for computing Kohn-Sham electronic structure have substantially increased the sizes of systems which can be studied. In addition to fast Car-Parinello and conjugate gradient algorithms, there have been several innovative proposals aimed at achieving order N scaling in computer time, where N is the number of atoms in the cell. These developments demand a better understanding of the convergence properties of different numerical approaches to Kohn-Sham density functional calculations. In particular the non-linearities of the Kohn-Sham equations lead to non-trivial dependence of convergence times on the system size. The number of iterations required to converge the self-consistent Kohn-Sham equations is shown to grow like N 2 3 for insulators and like N for metals. If each iteration can be carried out in order N time, the total computational effort to solve a given system will thus scale like N 5 3 or N 2 for insulators or metals respectively. A similar analysis of conjugate gradient minimization methods shows that, in the worst case, of order O(N 1 3 ) energy and gradient evaluations are needed to converge the energy. Only in insulating systems which are “Wannier representable” (WR) is the number of iterations of O(1), allowing true order N calculations. A different approach, based upon conjugate gradient minimization with respect to variations in the single particle potential rather than the wave functions, is also found to scale like N 1 3 for insulators and scales as N for metals. Slower scaling with N will also be found in systems in which one dimension of the unit cell is much longer than the others, or for metals where the Fermi energy lies close to a van Hove singularity. These results are quite independent of calculational details, such as choice of basis set, but simply follow from the scaling with N of the relevant Jacobian or Hessian matrices.

Structure of the ammonia dimer studied by density functional theory

AbstractSelf‐consistent Kohn–Sham density functional calculations have been carried out to study the structure of the ammonia dimer. The local‐density approximation yields unusually large binding energy and short internitrogen distance compared with the experimental and more accurate theoretical data. The results from the Becke–Perdew gradient‐corrected functionals are generally in good agreement with those at the SCF MP2 level when the geometry is fully optimized with various large basis sets. With our best estimation, the staggered quasi‐linear structure (Cs) is 0.6 kcal/mol lower in energy than the symmetric cyclic one (C2h). The hydrogen‐bonded N—H bond in the staggered quasi‐linear structure is found to be 0.008 Å longer than the N—H bond in ammonia. In our calculations, we could not find the minima on the energy surface corresponding to the two asymmetric cyclic structures suggested by microwave spectra and coupled pair functional calculations. © 1994 John Wiley & Sons, Inc.

Ab initio molecular dynamics with an orbital-free density functional

A scheme for ab initio simulations of extended systems, which involves the use of the electron density as the basic variable, is discussed. The form of the kinetic energy functional is chosen to incorporate several exact limits (uniform system, linear response and rapidly varying density) while the rest of the energy functional is exactly the same as in a Kohn-Sham density functional calculation with the local density approximation. The authors' show that for sodium the present scheme yields high-quality results in a fraction of the time required with an orbital-based functional. The electronic part of the algorithm scales linearly with system size. An analysis of the stability of the method is made, and leads to criteria for selecting the non-physical parameters in the calculation so as to maximize the computational efficiency.

Density-functional thermochemistry. II. The effect of the Perdew–Wang generalized-gradient correlation correction

In an earlier paper [A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], Kohn–Sham density-functional calculations of the total atomization energies of the 55 molecules of the Gaussian-1 database of Pople and co-workers [J. Chem. Phys. 90, 5622 (1989); 93, 2537 (1990)] were reported. We found that the local-spin-density exchange-correlation approximation with a ‘‘gradient correction’’ for exchange gave an average deviation from experiment of only 3.7 kcal/mol. In the present work we assess the role of gradient corrections for dynamical correlation, and we enlarge our earlier survey to include 42 atomic and molecular ionization potentials and 8 proton affinities as well. We conclude that gradient corrections for correlation do not improve atomization energies, but are vitally important in electron nonconserving processes such as ionization.