Comparing ab initio density-functional and wave function theories: the impact of correlation on the electronic density and the role of the correlation potential

The framework of ab initio density-functional theory (DFT) has been introduced as a way to provide a seamless connection between the Kohn-Sham (KS) formulation of DFT and wave-function based ab initio approaches [R. J. Bartlett, I. Grabowski, S. Hirata, and S. Ivanov, J. Chem. Phys. 122, 034104 (2005)]. Recently, an analysis of the impact of dynamical correlation effects on the density of the neon atom was presented [K. Jankowski, K. Nowakowski, I. Grabowski, and J. Wasilewski, J. Chem. Phys. 130, 164102 (2009)], contrasting the behaviour for a variety of standard density functionals with that of ab initio approaches based on second-order M?ller-Plesset (MP2) and coupled cluster theories at the singles-doubles (CCSD) and singles-doubles perturbative triples [CCSD(T)] levels. In the present work, we consider ab initio density functionals based on second-order many-body perturbation theory and coupled cluster perturbation theory in a similar manner, for a range of small atomic and molecular systems. For comparison, we also consider results obtained from MP2, CCSD, and CCSD(T) calculations. In addition to this density based analysis, we determine the KS correlation potentials corresponding to these densities and compare them with those obtained for a range of ab initio density functionals via the optimized effective potential method. The correlation energies, densities, and potentials calculated using ab initio DFT display a similar systematic behaviour to those derived from electronic densities calculated using ab initio wave function theories. In contrast, typical explicit density functionals for the correlation energy, such as VWN5 and LYP, do not show behaviour consistent with this picture of dynamical correlation, although they may provide some degree of correction for already erroneous explicitly density-dependent exchange-only functionals. The results presented here using orbital dependent ab initio density functionals show that they provide a treatment of exchange and correlation contributions within the KS framework that is more consistent with traditional ab initio wave function based methods.     

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.     

Calculations of molecular properties in hybrid coupled-cluster and molecular mechanics approach

We report benchmark calculations obtained with our new coupled-cluster singles and doubles (CCSD) code for calculating the first- and second-order molecular properties. This code can be easily incorporated into combined [Valiev, M.; Kowalski, K. J. Chem. Phys. 2006, 125, 211101] classical molecular mechanics (MM) and ab initio coupled-cluster (CC) calculations using NWChem, enabling us to study molecular properties in a realistic environment. To test this methodology, we discuss the results of calculations of dipole moments and static polarizabilities for the Cl2O system in the CCl4 solution using the CCSD (CC with singles and doubles) linear response approach. We also discuss the application of the asymptotic extrapolation scheme (AES) [Kowalski, K.; Valiev, M. J. Phys. Chem. A 2006, 110, 13106] in reducing the numerical cost of CCSD calculations.     

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.     

Thermal rearrangements of 1-ethynyl-2-methylcyclopropane: a computational study

In this research, a comprehensive theoretical investigation of the thermal rearrangements of 1-ethynyl-2-methylcyclopropane is carried out employing density functional theory (DFT), with the B3LYP functional, and high-level ab initio methods, such as the complete active space self-consistent field (CASSCF), multireference second-order M?ller-Plesset perturbation theory (MRMP2), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)]. In all computations Pople's polarized triple-ζ split valence basis set, 6-311G(d,p), is utilized. The potential energy surface (PES) for the relevant system is explored to provide a theoretical account of the experiments by Hopf, Ellis and Frey, Huntsman et al., and Berson. The computational results herein on the target system show that the thermal aromatization reaction does not proceed via conversion of 1,2,5-hexatriene (2) to 1,3,5-hexatriene (10a) as proposed by Hopf. Indeed, the reaction proceeds via conversion of 5 and 6 to bicyclo[3.1.0]hexene (9) as suggested by Huntsman et al.     

Quantum master equation method based on the broken-symmetry time-dependent density functional theory: application to dynamic polarizability of open-shell molecular systems

A novel method for the calculation of the dynamic polarizability (α) of open-shell molecular systems is developed based on the quantum master equation combined with the broken-symmetry (BS) time-dependent density functional theory within the Tamm-Dancoff approximation, referred to as the BS-DFTQME method. We investigate the dynamic α density distribution obtained from BS-DFTQME calculations in order to analyze the spatial contributions of electrons to the field-induced polarization and clarify the contributions of the frontier orbital pair to α and its density. To demonstrate the performance of this method, we examine the real part of dynamic α of singlet 1,3-dipole systems having a variety of diradical characters (y). The frequency dispersion of α, in particular in the resonant region, is shown to strongly depend on the exchange-correlation functional as well as on the diradical character. Under sufficiently off-resonant condition, the dynamic α is found to decrease with increasing y and/or the fraction of Hartree-Fock exchange in the exchange-correlation functional, which enhances the spin polarization, due to the decrease in the delocalization effects of π-diradical electrons in the frontier orbital pair. The BS-DFTQME method with the BHandHLYP exchange-correlation functional also turns out to semiquantitatively reproduce the α spectra calculated by a strongly correlated ab initio molecular orbital method, i.e., the spin-unrestricted coupled-cluster singles and doubles.     

Ab initio many-body investigation of structure and stability of two-fold rings in silicates

In this paper we present ab initio many-body calculations on the strain energy of W silica, taken as a model system for edge-sharing tetrahedral SiO(2) systems with respect to corner-sharing ones as in alpha quartz. The mean-field results were obtained using the restricted Hartree-Fock approach, while the many-body effects were taken into account by the second-order M?ller-Plesset perturbation theory and the coupled-cluster approach. Correlation contributions are found to play an important role to determine the stability of edge-sharing units. The most sophisticated method used in our calculation, i.e., the coupled-cluster approach with single and double excitations, yields a strain energy of 0.0427 a.u. per Si(2)O(4) unit with respect to alpha quartz, which is even smaller than the value obtained by a previous density functional theory calculation.     

Structure and stability of the organo-noble gas molecules XNgCCX and XNgCCNgX (Ng = Kr, Ar; X = F, Cl)

Density functional theory (B3LYP) and ab initio theory [second-order M?ller-Plesset perturbation theory (MP2) and coupled-cluster theory including single, double, and quasiperturbative triple excitations (CCSD(T))] have been used in combination with the standard and augmented correlation consistent basis sets (cc-pVnZ and aug-cc-pVnZ, where n = D, T, and Q) to investigate potential new noble gas compounds. Two classes of molecules were studied: XNgCCNgX and XNgCCX, where Ng = Kr and Ar and X = F and Cl. These molecules were characterized by finding the ground-state structures and calculating the relative energies, charge distributions, and vibrational frequencies. In addition, transition-state structures were also determined and decomposition pathways were identified through intrinsic reaction coordinate calculations.     

Time-dependent density functional theory calculation of van der Waals coefficient of sodium clusters

In this paper we employ all-electron ab initio time-dependent density functional theory based method to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) C(6) of sodium atom clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder relation [Phys. Rev. 3, 360 (1948)]. The calculations are carried out with two different exchange-correlation potentials: (i) the asymptotically correct statistical average of orbital potential (SAOP) and (ii) Vosko-Wilk-Nusair representation [Can. J. Phys. 58, 1200 (1980)] of exchange-correlation potential within local density approximation. A comparison with the other theoretical results has been performed. We also present the results for the static polarizabilities of sodium clusters and also compare them with other theoretical and experimental results. These comparisons reveal that the SAOP results for C(6) and static polarizability are quite accurate and very close to the experimental results. We examine the relationship between volume of the cluster and van der Waals coefficient, and find that to a very high degree of correlation C(6) scales as the square of the volume. We also present the results for van der Waals coefficient corresponding to cluster-Ar atom and cluster-N(2) molecule interactions.     

A global investigation of excited state surfaces within time-dependent density-functional response theory

This work investigates the capability of time-dependent density functional response theory to describe excited state potential energy surfaces of conjugated organic molecules. Applications to linear polyenes, aromatic systems, and the protonated Schiff base of retinal demonstrate the scope of currently used exchange-correlation functionals as local, adiabatic approximations to time-dependent Kohn-Sham theory. The results are compared to experimental and ab initio data of various kinds to attain a critical analysis of common problems concerning charge transfer and long range (nondynamic) correlation effects. This analysis goes beyond a local investigation of electronic properties and incorporates a global view of the excited state potential energy surfaces.     

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.     

Orbital-dependent correlation energy in density-functional theory based on a second-order perturbation approach: success and failure

We have developed a second-order perturbation theory (PT) energy functional within density-functional theory (DFT). Based on PT with the Kohn-Sham (KS) determinant as a reference, this new ab initio exchange-correlation functional includes an exact exchange (EXX) energy in the first order and a correlation energy including all single and double excitations from the KS reference in the second order. The explicit dependence of the exchange and correlation energy on the KS orbitals in the functional fits well into our direct minimization approach for the optimized effective potential, which is a very efficient method to perform fully self-consistent calculations for any orbital-dependent functionals. To investigate the quality of the correlation functional, we have applied the method to selected atoms and molecules. For two-electron atoms and small molecules described with small basis sets, this new method provides excellent results, improving both second-order Moller-Plesset expression and any conventional DFT results significantly. For larger systems, however, it performs poorly, converging to very low unphysical total energies. The failure of PT based energy functionals is analyzed, and its origin is traced back to near degeneracy problems due to the orbital- and eigenvalue-dependent algebraic structure of the correlation functional. The failure emerges in the self-consistent approach but not in perturbative post-EXX calculations, emphasizing the crucial importance of self-consistency in testing new orbital-dependent energy functionals.     

Density-functional theory with effective potential expressed as a direct mapping of the external potential: applications to atomization energies and ionization potentials

In this paper the authors further develop and apply the direct-mapping density functional theory to calculations of the atomization energies and ionization potentials. Single-particle orbitals are determined by solving the Kohn-Sham [Phys. Rev. A. 140, 1133 (1965)] equations with a local effective potential expressed in terms of the external potential. A two-parametric form of the effective potential for molecules is proposed and equations for optimization of the parameters are derived using the exchange-only approximation. Orbital-dependent correlation functional is derived from the second-order perturbation theory in its Moller-Plesset-type zeroth-order approximation based on the Kohn-Sham orbitals and orbital energies. The total atomization energies and ionization potentials computed with the second-order perturbation theory were found to be in agreement with experimental values and benchmark results obtained with ab initio wave mechanics methods.     

Theoretical study of thermal rearrangements of 1-hexen-5-yne, 1,2,5-hexatriene, and 2-methylenebicyclo[2.1.0]pentane

In this research, a comprehensive theoretical investigation of the thermal rearrangements of 1-hexen-5-yne, 1,2,5-hexatriene, and 2-methylenebicyclo[2.1.0]pentane is carried out employing density functional theory (DFT) and high level ab initio methods, such as the complete active space self-consistent field (CASSCF), multireference second-order M?ller-Plesset perturbation theory (MRMP2), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)]. The potential energy surface (PES) for the relevant system is explored to provide a theoretical account of pyrolysis experiments by Huntsman, Baldwin, and Roth on the target system. The rate constants and product distributions are calculated using theoretical kinetic modelings. The rate constant for each isomerization reaction is computed using the transition state theory (TST). The simultaneous first-order ordinary-differential equations are solved numerically for the relevant system to obtain time-dependent concentrations, hence the product distributions at a given temperature. Our computed energy values (reaction energies and activation parameters) are in agreement with Roth's experiments and the product distributions of Huntsman's experiments at 340 and 385 °C with various reaction times, while simulated product fractions are in qualitative accordance with Baldwin's experiment.     

Ab initio studies of properties of small potassium clusters

We have studied the properties of various isomers of potassium clusters containing even number of atoms ranging from 2 to 20 at the ab initio level. The geometry optimization calculations of the isomers of each cluster are performed by using all-electron density functional theory with gradient corrected exchange-correlation functional. Using the optimized geometries of different isomers we investigate the evolution of binding energy, ionization potential, and static polarizability with the increasing size of the clusters. The polarizabilities are calculated by employing M?ller-Plesset perturbation theory and time-dependent density functional theory. The polarizabilities of dimer and tetramer are also calculated by employing large basis set coupled cluster theory with single and double excitations and perturbative triple excitations. The time-dependent density functional theory calculations of polarizabilities are carried out with two different exchange-correlation potentials: (i) an asymptotically correct model potential and (ii) within the local density approximation. A systematic comparison with the other available theoretical and experimental data for various properties of small potassium clusters mentioned above has been performed. These comparisons reveal that both the binding energy and the ionization potential obtained with gradient-corrected potential match quite well with the already published data. Similarly, the polarizabilities obtained with M?ller-Plesset perturbation theory and with model potential are quite close to each other and also close to experimental data.     

Molecular dynamics and metadynamics simulations of [2 + 2] photocycloaddition

Triplet state mechanism of [2 + 2] photocycloaddition forming a cyclobutane ring from two ethylenes is investigated in the context of photocatalysis. High‐level ab initio calculations are combined with ab initio adiabatic molecular dynamics and ab initio metadynamics for rare events modeling. In a photocatalytic scheme, a reactant reaches the triplet state either via intersystem crossing (ISC) or triplet sensitization. The model system adopts a biradical structure, which represents energy intersection with the ground state. The system either completes cyclization or undergoes fragmentation into two olefinic units. The potential and free energy surfaces of the cyclobutane/ethylenes system are mapped with multireference approaches describing possible reaction pathways. To obtain a full picture of a double bond photoreactivity, ab initio adiabatic dynamical calculations were used to estimate reaction yields and to model the effects of excess energy. The potential use of density functional theory based approaches for [2 + 2] photocycloaddition was investigated for future simulations and design of realistic photocatalytic systems. Dynamical aspects of [2 + 2] photocycloaddition via a triplet state manifold are investigated by combining ab initio multireference methods and ab initio molecular dynamics and metadynamics. The reaction pathways are studied for a model system of two ethylenes forming a cyclobutane ring to provide a basis for further studies on design of photocatalytic systems.     

The open-shell interaction of He with the B 3Piu(0+) state of Br2: an ab initio study and its comparison with a diatomics-in-molecule perturbation model

The interaction of He with Br2 in electronically excited B 3Piu state is investigated using spin-unrestricted single and double coupled-cluster approach with noniterative perturbative treatment of triple excitations. Internal electrons of the Br atom are described by effective core pseudopotentials. The validity of this approach is analyzed by comparing the lowest 2Sigma+ and 2Pi electronic states of the HeBr molecule with those obtained in all electron calculations [J. Chem. Phys. 115, 10438 (2001)]. In this context, we examine the performance of different basis sets and saturation with bond functions. The comparison of theoretical blue-shifts with the experiment provides confidence about the present ab initio calculations. In addition, He-Br results of ab initio calculations at the same level are used to obtain approximate He-Br2 (3Piu) interactions in the framework of the diatomics-in-molecule first order perturbation theory (IDIM-PT1) [J. Chem. Phys. 104, 9913 (1996)]. Overall, the IDIM-PT1 model results show a good agreement with the ab initio ones, being the main difference the sensitivity to the elongation of the Br-Br bond.