Ab initio density functional theory: the best of both worlds?

Density functional theory (DFT), in its current local, gradient corrected, and hybrid implementations and their extensions, is approaching an impasse. To continue to progress toward the quality of results demanded by today's ab initio quantum chemistry encourages a new direction. We believe ab initio DFT is a promising route to pursue. Whereas conventional DFT cannot describe weak interactions, photoelectron spectra, or many potential energy surfaces, ab initio DFT, even in its initial, optimized effective potential, second-order many-body perturbation theory form [OEP (2)-semi canonical], is shown to do all well. In fact, we obtain accuracy that frequently exceeds MP2, being competitive with coupled-cluster theory in some cases. Furthermore, this is accomplished within a relatively fast computational procedure that scales like iterative second order. We illustrate our results with several molecular examples including Ne2,Be2,F2, and benzene.     

RDX geometries, excited states, and revised energy ordering of conformers via MP2 and CCSD(T) methodologies: insights into decomposition mechanism

The geometries, harmonic frequencies, elec-tronic excitation levels, and energetic orderings of various conformers of RDX have been computed at the ab initio MP2 and CCSD(T) levels, providing more reliable results than have been previously obtained. We observe that the various local minimum-energy conformers are all competitive for being the absolute minimum and that, at reasonable temperatures, several conformers will appreciably contribute to the population of RDX. As a result, we have concluded that any mechanistic study to investigate thermal decomposition can reasonably begin from any one of the cyclohexane conformers of RDX. As such, it is necessary to consider the transition states for each RDX conformer to gauge what the activation energy is. Homolytic bond dissociation has long been speculated to be critical to detonation; we report here the most accurate estimates of homolytic BDEs yet calculated, likely to be accurate within 3 kcal mol(-1). The differences in energy for homolytic BDEs among all the possible RDR conformers are again small, such that most all of the conformers can reasonably be speculated as the next step in the mechanism starting from the RDR radical.     

External coupled-cluster perturbation theory: description and application to weakly interaction dimers. Corrections to the random phase approximation

The formalism for developing perturbation theory by using an arbitrary fixed (external) set of amplitudes as an initial approximation is presented in a compact form: external coupled-cluster perturbation theory (xCCPT). Nonperturbative approaches also fit into the formalism. As an illustration, the weakly interacting dimers Ne(2) and Ar(2) have been studied in the various ring-coupled-cluster doubles (CCD) approximations; ring, direct-ring, antisymmetrized ring, and antisymmetrized direct ring, and a second-order correction in the xCCPT approach is added. The direct approaches include the summation of just Coulomb terms with the intention of selectively summing the largest terms in the perturbation first. "Coulomb attenuation" is effected by taking the random phase approximation to define such amplitudes, whose results are then improved upon using perturbation theory. Interaction energies at the ring-CCD level are poor but the xCCPT correction employed predicts binding energies which are only a few percent from the coupled-cluster single double (triple) values for the direct ring-CCD variants. Using the MP2 amplitudes which neglect exchange, the initial Coulomb-only term, leads to very accurate Ne(2) and Ar(2) potentials. However, to accurately compute the Na(2) potential required a different initial wavefunction, and hence perturbation. The potential energy surfaces of Ne(2) and Ar(2) are much too shallow using linear coupled-cluster doubles. Using xCCPT(2) with these amplitudes as the initial wavefunction led to slightly worse results. These observations suggest that an optimal external set of amplitudes exists which minimizes perturbational effects and hence improve the predictability of methods.     

Parallel implementation of electronic structure energy, gradient, and Hessian calculations

ACES III is a newly written program in which the computationally demanding components of the computational chemistry code ACES II [J. F. Stanton et al., Int. J. Quantum Chem. 526, 879 (1992); [ACES II program system, University of Florida, 1994] have been redesigned and implemented in parallel. The high-level algorithms include Hartree-Fock (HF) self-consistent field (SCF), second-order many-body perturbation theory [MBPT(2)] energy, gradient, and Hessian, and coupled cluster singles, doubles, and perturbative triples [CCSD(T)] energy and gradient. For SCF, MBPT(2), and CCSD(T), both restricted HF and unrestricted HF reference wave functions are available. For MBPT(2) gradients and Hessians, a restricted open-shell HF reference is also supported. The methods are programed in a special language designed for the parallelization project. The language is called super instruction assembly language (SIAL). The design uses an extreme form of object-oriented programing. All compute intensive operations, such as tensor contractions and diagonalizations, all communication operations, and all input-output operations are handled by a parallel program written in C and FORTRAN 77. This parallel program, called the super instruction processor (SIP), interprets and executes the SIAL program. By separating the algorithmic complexity (in SIAL) from the complexities of execution on computer hardware (in SIP), a software system is created that allows for very effective optimization and tuning on different hardware architectures with quite manageable effort.     

Benchmark studies on the building blocks of DNA. 1. Superiority of coupled cluster methods in describing the excited states of nucleobases in the Franck-Condon region

Equation of motion excitation energy coupled-cluster (EOMEE-CC) methods including perturbative triple excitations have been used to set benchmark results for the excitation energy and oscillator strength of the building units of DNA, i.e., cytosine, guanine, adenine and thymine. In all cases the lowest twelve transitions have been considered including valence and Rydberg ones. Triple-ζ basis sets with diffuse functions have been used and the results are compared to CC2, CASPT2, TDDFT, and DFT/MRCI results from the literature. The results clearly show that it is only the EOMEE-CCSD(T) that is capable of providing accuracy of about 0.1 eV. EOMEE-CCSD systematically overshoots the energy of all types of transitions by 0.1-0.3 eV, whereas CC2 is surprisingly accurate for ππ* transitions but fails (often badly) for nπ* and Rydberg transitions. DFT and CASPT2 seem to give reliable results for the lowest transition, but the error increases fast with the excitation level. The differences in the excitation energies often change the energy ordering of the states, which should even influence the conclusions of excited state dynamics obtained with these approximate methods. The results call for further benchmark calculations on larger building blocks of DNA (nucleosides, basis pairs) at the CCSD(T) level.     

Molecular cluster perturbation theory. I. Formalism

We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wave functions in a coupled-cluster framework. This new MCPT(2) framework uses coupled-cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wave functions that are infinite order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/Aces4 parallel architecture, making use of the advanced dynamic memory control and fine-grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts, lattice site dipole moments, and harmonic vibrational frequencies via explicit calculation of the bulk system for the polar and non-polar polymorphs of solid hydrogen fluoride. The explicit lattice size (without using any periodic boundary conditions) was expanded up to 1000 HF molecules, with 32,000 basis functions and 10,000 electrons. Our obtained HF lattice site dipole moments and harmonic vibrational frequencies agree well with the existing literature.     

Ab initio density functional theory applied to quasidegenerate problems

Ab initio density functional theory (DFT), previously applied primarily at the second-order many-body perturbation theory (MBPT) level, is generalized to selected infinite-order effects by using a new coupled-cluster perturbation theory (CCPT). This is accomplished by redefining the unperturbed Hamiltonian in ab initio DFT to correspond to the CCPT2 orbital dependent functional. These methods are applied to the Be-isoelectronic systems as an example of a quasidegenerate system. The CCPT2 variant shows better convergence to the exact quantum Monte Carlo correlation potential for Be than any prior attempt. When using MBPT2, the semicanonical choice of unperturbed Hamiltonian, plays a critical role in determining the quality of the obtained correlation potentials and obtaining convergence, while the usual Kohn-Sham choice invariably diverges. However, without the additional infinite-order effects, introduced by CCPT2, the final potentials and energies are not sufficiently accurate. The issue of the effects of the single excitations on the divergence in ordinary OEP2 is addressed, and it is shown that, whereas their individual values are small, their infinite-order summation is essential to the good convergence of ab initio DFT.     

Theoretical study of the He-HF+ complex. I. The two asymptotically degenerate ground state potential energy surfaces

Two three-dimensional potential energy surfaces (PESs) are reported for the cationic complex He-HF+; they are degenerate for linear geometries of the complex and correlate with the doubly degenerate X2Pi ground state of the HF+monomer. The PESs are computed from the interaction energies of the neutral dimer and the ionization potentials of the He-HF complex and the HF molecule. Ionization potentials are obtained from the outer valence Green's function (OVGF) method, while the energies of the neutral species are computed by means of the single and double coupled-cluster method with perturbative triples [CCSD(T)]. For comparison, interaction energies of the ionic complex were computed also by the use of the partially spin-restricted variant of the CCSD(T) method. After asymptotic scaling of the OVGF results, good agreement is found between the two methods. A single global minimum is found in the PES, for the linear He-HF+ geometry. The well depth and equilibrium separation are 2.240 A and 1631.3 cm(-1), respectively, at an HF+ bond length r=1.0012 A, in rather good agreement with results of Schmelz and Rosmus [Chem. Phys. Lett. 220, 117 (1994)]. The well depth depends much more strongly on the internuclear H-F separation than in the neutral He-HF complex and the global minimum in a full three-dimensional PES occurs at r=1.0273 A.     

Jahn-Teller effect in van der Waals complexes; Ar-C6H6 + and Ar-C6D6 +

The two asymptotically degenerate potential energy surfaces of argon interacting with the X (2)E(1g) ground state benzene(+) cation were calculated ab initio from the interaction energy of the neutral Ar-benzene complex given by Koch et al. [J. Chem. Phys. 111, 198 (1999)] and the difference of the geometry-dependent ionization energies of the complex and the benzene monomer computed by the outer valence Green's function method. Coinciding minima in the two potential surfaces of the ionic complex occur for Ar on the C(6v) symmetry axis of benzene(+) (the z axis) at z(e)=3.506 A. The binding energy D(e) of 520 cm(-1) is only 34% larger than the value for the neutral Ar-benzene complex. The higher one of the two surfaces is similar in shape to the neutral Ar-benzene potential, the lower potential is much flatter in the (x,y) bend direction. Nonadiabatic (Jahn-Teller) coupling was taken into account by transformation of the two adiabatic potentials to a two-by-two matrix of diabatic potentials. This transformation is based on the assumption that the adiabatic states of the Ar-benzene(+) complex geometrically follow the Ar atom. Ab initio calculations of the nonadiabatic coupling matrix element between the adiabatic states with the two-state-averaged CAS-SCF(5,6) method confirmed the validity of this assumption. The bound vibronic states of both Ar-C(6)H(6) (+) and Ar-C(6)D(6) (+) were computed with this two-state diabatic model in a basis of three-dimensional harmonic oscillator functions for the van der Waals modes. The binding energy D(0)=480 cm(-1) of the perdeuterated complex agrees well with the experimental upper bound of 485 cm(-1). The ground and excited vibronic levels and wave functions were used, with a simple model dipole function, to generate a theoretical far-infrared spectrum. Strong absorption lines were found at 10.1 cm(-1) (bend) and 47.9 cm(-1) (stretch) that agree well with measurements. The unusually low bend frequency is related to the flatness of the lower adiabatic potential in the (x,y) direction. The van der Waals bend mode of e(1) symmetry is quadratically Jahn-Teller active and shows a large splitting, with vibronic levels of A(1), E(2), and A(2) symmetry at 1.3, 10.1, and 50.2 cm(-1). The level at 1.3 cm(-1) leads to a strong absorption line as well, which could not be measured because it is too close to the monomer line. The level at 50.2 cm(-1) gives rise to weaker absorption. Several other weak lines in the frequency range of 10 to 60 cm(-1) were found.