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Notes: Local (multiplicative) effective exchange potentials obtained from the linear-combination- of-atomic-orbital (LCAO) optimized effective potential (OEP) method are frequently unrealistic in that they tend to exhibit wrong asymptotic behavior (although formally they should have the correct asymptotic behavior) and also assume unphysical rapid oscillations around the nuclei. We give an algebraic proof that, with an infinity of orbitals, the kernel of the OEP integral equation has one and only one singularity associated with a constant and hence the OEP method determines a local exchange potential uniquely, provided that we impose some appropriate boundary condition upon the exchange potential. When the number of orbitals is finite, however, the OEP integral equation is ill-posed in that it has an infinite number of solutions. We circumvent this problem by projecting the equation and the exchange potential upon the function space accessible by the kernel and thereby making the exchange potential unique. The observed numerical problems are, therefore, primarily due to the slow convergence of the projected exchange potential with respect to the size of the expansion basis set for orbitals. Nonetheless, by making a judicious choice of the basis sets, we obtain accurate exchange potentials for atoms and molecules from an LCAO OEP procedure, which are significant improvements over local or gradient-corrected exchange functionals or the Slater potential. The Krieger–Li–Iafrate scheme offers better approximations to the OEP method. © 2001 American Institute of Physics.

Notes: The finite-basis-set optimized effective potential (OEP) method is presented from an integral equation point of view. It is shown that the projection method for solving the OEP integral equation provides a consistent and convenient approach for including orbital-dependent functionals and potentials in the finite-basis-set implementations of the Kohn–Sham theory. Different finite-basis-set realizations of the OEP method are introduced and tested within the exchange-only approximation. An exact condition involving the local multiplicative exchange potential and the nonlocal Hartree–Fock exchange potential built from Kohn–Sham orbitals is incorporated in our schemes. Numerical results are presented. © 2002 American Institute of Physics.

Notes: Using the optimized effective potential (OEP) method in conjunction with an orbital-dependent correlation functional developed on the basis of second-order many-body perturbation theory [MBPT(2)], we perform ab initio correlated density functional calculations. Unlike other density functional methods, this offers the first correlation approximation in a converging series of approximations analogous to that in wave function theory. The OEP-MBPT(2) correlation potentials of the helium isoelectronic series and the neon atom are in excellent agreement with prior quantum Monte Carlo (QMC) results, while the widely used conventional approximate density functional theory correlation potentials have qualitatively incorrect behavior. Furthermore, the correlation energies, total energies, and the highest occupied orbital energies calculated by the OEP-MBPT(2) method are also remarkably accurate. Unlike QMC, our procedure can be applied to general molecules. © 2002 American Institute of Physics.

Notes: Exchange-only ab initio (parameter-free) time-dependent density functional calculations for the vertical excitation energies of atoms and polyatomic molecules are performed by employing optimized effective potentials (OEP's) and their corresponding adiabatic exchange kernels for the first time. Accurate OEP's are obtained by a novel linear-combination-of-atomic-orbital (LCAO) algorithm [R. Colle and R. K. Nesbet, J. Phys. B 34, 2475 (2001)] in which a potential is represented as a sum of a seed potential having the correct −1/r asymptotic behavior and a small and rapidly decaying correction, the latter being approximated accurately by a linear combination of Gaussian functions. The time-dependent OEP (TDOEP) methods with and without the Tamm–Dancoff approximation are implemented by using a trial-vector algorithm, which allows us to avoid the storage or manipulation of transformed two-electron integrals or the diagonalization of large matrices. No approximation is made to TDOEP, besides the adiabatic approximation to the exchange kernel, the LCAO expansion of the orbitals and potentials, and occasionally the Tamm–Dancoff approximation. The vertical excitation energies of the beryllium atom and the nitrogen and water molecules calculated by TDOEP are compared with those obtained from time-dependent density functional theory (TDDFT) employing conventional local or gradient-corrected functionals, configuration interaction singles (CIS), time-dependent Hartree–Fock (TDHF) theory, similarity-transformed equation-of-motion coupled-cluster with single and double substitutions, and experiments. TDOEP, which neglects electron correlation while treating the exchange contribution rigorously within the Kohn–Sham DFT framework, performs equally well as, or even appreciably better than, CIS or TDHF. The slightly better performance of TDOEP might be attributed to the local nature of the exchange potentials that allows the bare orbital energy differences to approximate excitation energies well. Nevertheless, TDDFT employing local or gradient-corrected functionals outperforms TDOEP for low-lying valence excited states, implying that the former somehow accounts for electron correlation effectively, whereas for high-lying and Rydberg excited states, the latter performs better than the former. By combining the desirable features of OEP and local or gradient-corrected exchange-correlation potentials, we arrive at a simple asymptotic correction scheme to the latter. TDDFT with the asymptotic correction yields uniformly accurate excitation energies for both valence and Rydberg excited states.© 2002 American Institute of Physics.

Notes: In this communication we present the exact, local, one-electron, second-order correlation potential for molecules, for use in density functional studies. The correlation potential is represented in a basis set, and when combined with the exact exchange potential, it provides an exchange–correlation potential that is derived exclusively from exact, orbital-dependent expressions. In this sense, such potentials provide an ab initio density functional theory (DFT) that permits convergence to the exact answer as higher order terms are introduced, just as is the case for ab initio correlated methods. Furthermore, this potential includes some dispersion effects that are missing from other DFT potentials. © 2001 American Institute of Physics.

Notes: The electronic and structural properties of the ground and excited states of infinite polydiacetylene chains in acetylenic (PDA) and butatrienic (PBT) structures are studied by a series of ab initio crystalline orbital and linear-combination-of-atomic-orbital periodic density functional theory methods. A complete geometry optimization is performed for PDA and PBT with analytical energy gradient techniques at the Hartree–Fock (HF) and Becke3-Lee-Yang-Parr (B3LYP) levels. The HF/6-31G* and B3LYP/6-31G* reproduce the experimental geometrical parameters of substituted polydiacetylenes with a PDA-like structure. We compute the relative stability and the potential energy curves along the structural transition between PDA and PBT at the HF, B3LYP, and second-order many-body perturbation theory [MBPT(2)] levels. All these calculations predict PDA to be more stable than PBT by 28–87 kJ mol−1. A minimum corresponding to the PBT-like structure is found at the HF level, but not at the B3LYP or MBPT(2) level. We report the frequencies of all the infrared- and Raman-active vibrational modes of PDA at the HF and B3LYP levels. The frequencies of the carbon backbone stretching modes calculated at the B3LYP/6-31G* level are within 60 cm−1 of the measured frequencies of resonance Raman bands, when the former values are scaled by a uniform scale factor of 0.96. The ionization potential (IP), electron affinity (EA), and fundamental band gap (Eg) of PDA are calculated at the HF and B3LYP levels and also at the MBPT(2) level employing the quasiparticle formalism. B3LYP/6-31G* provides the most reasonable IP, EA, and Eg, which are within 0.6 eV of the experimental results. Vertical excitation energies to the lowest singlet and triplet excitons of PDA are obtained by configuration interaction singles and by time-dependent density functional theory employing the B3LYP functional. These treatments properly account for the nonvanishing exciton binding energy. While the CIS/6-31G* excessively overestimates the singlet excitation binding energies, B3LYP/6-31G* provides a value (0.3 eV) that is in good agreement with experiment (0.4 eV). © 2001 American Institute of Physics.

Notes: Electron correlation corrections to the excitation energy of the lowest-lying singlet exciton state of polyethylene are evaluated with the aid of the quasiparticle energies obtained from second-order many-body perturbation theory and from the second-order inverse Dyson equation. A simple approximation is proposed to avoid the evaluation of the quasiparticle energies for high- and low-lying energy bands, which is particularly problematic in extended-system calculations. The inclusion of both the electron correlation effects and diffuse basis functions is important for the proper description of the exciton state. The electron correlation corrections calculated by this method appear to be too large, probably due to the neglect of the screening effects of the quasiparticle interactions. © 2000 American Institute of Physics.

Notes: Noniterative corrections to the coupled-cluster (CC) method with singles and doubles (CCSD) due to triple and higher excitations in the cluster operator are investigated. The derivation is based on the standard procedure for evaluating contributions coming from higher excitation rank cluster operators into the CC equations for singles and doubles. The noniterative nature of the approach leads to a direct modification of the CCSD energy through a posteriori corrections, however, unlike previous derivations, we take into account the coupling between the energy and cluster amplitudes in the CC equations. The coupling is not present in the fully iterative CC schemes due to the linked diagram theorem which makes the cluster amplitude equations energy independent. We show, however, that if the problem of unlinked contributions is re-examined in the context of noniterative approaches, then their complete cancellation does not occur. This leads to a partial restoration of the energy dependence. The energy dependence then gives the cluster amplitudes more flexibility in adjusting to the energy changes within the noniterative approach which is especially important in quasidegenerate situations when the standard energy corrections become large. The resulting modifications introduce disconnected contributions to the energy so size-extensivity is no longer preserved. This approach provides a new hierarchy of CC corrections in which the standard corrections, like CCSD[T] or CCSD(T), appear as a natural first step in the derivation. Some of the corrections can be easily identified as analogous to those recently proposed by Kowalski and Piecuch in the context of the method of moments of CC equations. We also suggest new approximations. © 2001 American Institute of Physics.

Notes: A semiclassical approach to the calculation of thermal rate constants, based on the flux–flux autocorrelation function method, is presented with its applications. The autocorrelation function is generated along classical trajectories using a classical interpretation of the Boltzmannized flux operator. The activation energies for considered reactions are calculated using the G2/MP2 procedure. The forces are generated using a new parametrization of the PM3 NDDO Hamiltonian optimized for accurate gradients. Thermal rate constants for hydrogen abstraction from ethane and haloethanes by hydroxyl radical serve as a first test of this approach. Calculated results are in good agreement with cumulative rate constants for all systems considered over a range of temperature including room temperature. The approach is able to distinguish between α and β abstraction with a result for fluoroethane at room temperature that is consistent with the available experiment and trends that are in line with those expected. © 2001 American Institute of Physics.

Notes: Abstract. This is a personal perspective on the paper of Jiri Číz˘ek that initiated the use of coupled-cluster (CC) theory in chemistry. As CC theory is now the method of choice for most highly accurate quantum chemical studies, its influence is profound.