Claudia Filippi

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters. II. The water hexamer and van der Waals interactions

Second order Møller-Plesset perturbation theory at the complete basis set limit and diffusion quantum Monte Carlo are used to examine several low energy isomers of the water hexamer. Both approaches predict the so-called prism to be the lowest energy isomer, followed by cage, book, and cyclic isomers. The energies of the four isomers are very similar, all being within 10-15 meV/H(2)O. These reference data are then used to evaluate the performance of several density-functional theory exchange-correlation (xc) functionals. A subset of the xc functionals tested for smaller water clusters [I. Santra et al., J. Chem. Phys. 127, 184104 (2007)] has been considered. While certain functionals do a reasonable job at predicting the absolute dissociation energies of the various isomers (coming within 10-20 meV/H(2)O), none predict the correct energetic ordering of the four isomers nor does any predict the correct low total energy isomer. All xc functionals tested either predict the book or cyclic isomers to have the largest dissociation energies. A many-body decomposition of the total interaction energies within the hexamers leads to the conclusion that the failure lies in the poor description of van der Waals (dispersion) forces in the xc functionals considered. It is shown that the addition of an empirical pairwise (attractive) C(6)R(-6) correction to certain functionals allows for an improved energetic ordering of the hexamers. The relevance of these results to density-functional simulations of liquid water is also briefly discussed.

Energy-consistent pseudopotentials for quantum Monte Carlo calculations.

The authors present scalar-relativistic energy-consistent Hartree-Fock pseudopotentials for the main-group elements. The pseudopotentials do not exhibit a singularity at the nucleus and are therefore suitable for quantum Monte Carlo (QMC) calculations. They demonstrate their transferability through extensive benchmark calculations of atomic excitation spectra as well as molecular properties. In particular, they compute the vibrational frequencies and binding energies of 26 first- and second-row diatomic molecules using post-Hartree-Fock methods, finding excellent agreement with the corresponding all-electron values. They also show their pseudopotentials give superior accuracy than other existing pseudopotentials constructed specifically for QMC. Finally, valence basis sets of different sizes (VnZ with n=D,T,Q,5 for first and second rows, and n=D,T for third to fifth rows) optimized for our pseudopotentials are also presented.

Multiconfiguration wave functions for quantum Monte Carlo calculations of first‐row diatomic molecules

We use the variance minimization method to determine accurate wave functions for first‐row homonuclear diatomic molecules. The form of the wave function is a product of a sum of determinants and a generalized Jastrow factor. One of the important features of the calculation is that we are including low‐lying determinants corresponding to single and double excitations from the Hartree–Fock configuration within the space of orbitals whose atomic principal quantum numbers do not exceed those occurring in the Hartree–Fock configuration. The idea is that near‐degeneracy correlation is most effectively described by a linear combination of low‐lying determinants whereas dynamic correlation is well described by the generalized Jastrow factor. All the parameters occurring in both the determinantal and the Jastrow parts of the wave function are optimized. The optimized wave functions recover 79%–94% of the correlation energy in variational Monte Carlo and 93%–99% of the correlation energy in diffusion Monte Carlo.

Mixed time-dependent density-functional theory/classical trajectory surface hopping study of oxirane photochemistry

We present a mixed time-dependent density-functional theory (TDDFT)/classical trajectory surface hopping (SH) study of the photochemical ring opening in oxirane. Previous preparatory work limited to the symmetric CC ring-opening pathways of oxirane concluded that the Tamm-Dancoff approximation (TDA) is important for improving the performance of TDDFT away from the equilibrium geometry. This observation is supported by the present TDDFT TDA/SH calculations which successfully confirm the main experimentally derived Gomer-Noyes mechanism for the photochemical CO ring opening of oxirane and, in addition, provide important state-specific information not easily accessible from experiments. In particular, we find that, while one of the lowest two excited states is photochemically relatively inert, excitation into the other excited state leads predominantly to rapid ring opening, cyclic-C(2)H(4)O-->(*)CH(2)CH(2)O(*). This is followed by hopping to the electronic ground state where hot (4000 K) dynamics leads to further reactions, namely, (*)CH(2)CH(2)O()-->CH(3)CHO-->(*)CH(3)+(*)CHO and CH(4)+CO. We note that, in the dynamics, we are not limited to following minimum energy pathways and several surface hops may actually be needed before products are finally reached. The performance of different functionals is then assessed by comparison of TDDFT and diffusion Monte Carlo potential energy curves along a typical TDDFT TDA/SH reaction path. Finally, although true (S(0),S(1)) conical intersections are expected to be absent in adiabatic TDDFT, we show that the TDDFT TDA is able to approximate a conical intersection in this system.

Mixed time-dependent density-functional theory/classical photodynamics study of oxirane photochemistry

We present a mixed time-dependent density-functional theory (TDDFT)/classical trajectory surface hopping (SH) study of the photochemical ring opening in oxirane. Previous preparatory work limited to the symmetric CC ring-opening pathways of oxirane concluded that the Tamm-Dancoff approximation (TDA) is important for improving the performance of TDDFT away from the equilibrium geometry. This observation is supported by the present TDDFT TDA/SH calculations which successfully confirm the main experimentally derived Gomer-Noyes mechanism for the photochemical CO ring opening of oxirane and, in addition, provide important state-specific information not easily accessible from experiments. In particular, we find that, while one of the lowest two excited states is photochemically relatively inert, excitation into the other excited state leads predominantly to rapid ring opening, cyclic-C(2)H(4)O-->(*)CH(2)CH(2)O(*). This is followed by hopping to the electronic ground state where hot (4000 K) dynamics leads to further reactions, namely, (*)CH(2)CH(2)O()-->CH(3)CHO-->(*)CH(3)+(*)CHO and CH(4)+CO. We note that, in the dynamics, we are not limited to following minimum energy pathways and several surface hops may actually be needed before products are finally reached. The performance of different functionals is then assessed by comparison of TDDFT and diffusion Monte Carlo potential energy curves along a typical TDDFT TDA/SH reaction path. Finally, although true (S(0),S(1)) conical intersections are expected to be absent in adiabatic TDDFT, we show that the TDDFT TDA is able to approximate a conical intersection in this system.

Absorption Spectrum of the Green Fluorescent Protein Chromophore: A Difficult Case for ab Initio Methods?

We perform a thorough comparative investigation of the excitation energies of the anionic and neutral forms of the green fluorescent protein (GFP) chromophore in the gas phase using a variety of first-principle theoretical approaches commonly used to access excited state properties of photoactive molecules. These include time-dependent density functional theory (TDDFT), complete-active-space second-order perturbation theory (CASPT2), equation-of-motion coupled cluster (EOM-CC), and quantum Monte Carlo (QMC) methods. We find that all approaches give roughly the same vertical excitation for the anionic form, while TDDFT predicts an excitation for the neutral chromophore significantly lower than the highly correlated methods. Our findings support the picture emerging from the extrapolation of the Kamlet-Taft fit of absorption experimental data in solution and indicate that the protein gives rise to a considerable bathochromic shift with respect to vacuum. These results also open some questions on the interpretation of photodestruction spectroscopy experiments in the gas phase as well as on the accuracy of previous theoretical calculations in the more complex protein environment.

Comparison of exact and approximate density functionals for an exactly soluble model

We consider a model, given by two interacting electrons in an external harmonic potential, that can be solved analytically for a discrete and infinite set of values of the spring constant. The knowledge of the exact electronic density allows us to construct the exact exchange–correlation potential and exchange–correlation energy by inverting the Kohn–Sham equation. The exact exchange–correlation potential and energy are compared with the corresponding quantities, obtained for the same densities, using approximate density functionals, namely the local density approximation and several generalized gradient approximations. We consider two values of the spring constant in order to study the system in the low correlation case (high value of the spring constant) and in the high correlation case (low value of the spring constant). In both cases, the exchange–correlation potentials corresponding to approximate density functionals differ from the exact one over the entire spatial range. The approximate correlation...

Energy and Variance Optimization of Many-Body Wave Functions

We present a simple, robust, and efficient method for varying the parameters in a many-body wave function to optimize the expectation value of the energy. The effectiveness of the method is demonstrated by optimizing the parameters in flexible Jastrow factors that include 3-body electron-electron-nucleus correlation terms for the NO2 and decapentaene (C10H12) molecules. The basic idea is to add terms to the straightforward expression for the Hessian of the energy that have zero expectation value, but that cancel much of the statistical fluctuations for a finite Monte Carlo sample. The method is compared to what is currently the most popular method for optimizing many-body wave functions, namely, minimization of the variance of the local energy. The most efficient wave function is obtained by optimizing a linear combination of the energy and the variance.

Electronic Excitations of Simple Cyanine Dyes: Reconciling Density Functional and Wave Function Methods

The simplest cyanine dye series [H2N(CH)nNH2](+) with n = 1, 3, 5, 7, and 9 appears to be a challenge for all theoretical excited-state methods since the experimental spectra are difficult to predict and the observed deviations cannot be easily explained with standard arguments. We compute here the lowest vertical excitation energies of these dyes using a variety of approaches, namely, complete active space second-order perturbation theory (CASPT2), quantum Monte Carlo methods (QMC), coupled cluster linear response up to third approximate order (CC3), and various flavors of time-dependent density functional theory (TDDFT), including the recently proposed perturbative correction scheme (B2PLYP). In our calculations, all parameters such as basis set, active space, and geometry dependence are carefully analyzed. We find that all wave function methods give reasonably close excitation energies, with CASPT2 yielding the lowest values, and that the B2PLYP scheme gives excitations in satisfactory agreement with CC3 and DMC, significantly improving on the generalized gradient and hybrid approximations. Finally, to resolve the remaining discrepancy between predicted excitation energies and experimental absorption spectra, we also investigate the effect of excited-state relaxation. Our results indicate that a direct comparison of the experimental absorption maxima and the theoretical vertical excitations is not possible due to the presence of nonvertical transitions. The apparent agreement of earlier CASPT2 calculations with experiments was an artifact of the choice of active space and the use of an older definition of the zero-order Hamiltonian.

Excitation energies from density functional perturbation theory

We consider two perturbative schemes to calculate excitation energies, each employing the Kohn-Sham Hamiltonian as the unperturbed system. Using accurate exchange-correlation potentials generated from essentially exact densities and their exchange components determined by a recently proposed method, we evaluate energy differences between the groundstate and excited states in first-order perturbation theory for the helium, ionized lithium and beryllium atoms. It was recently observed that the zeroth-order excitations energies, simply given by the difference of the Kohn-Sham eigenvalues, almost always lie between the singlet and triplet experimental excitations energies, corrected for relativistic and finite nuclear mass effects. The first-order corrections provide about a factor of two improvement in one of the perturbative schemes but not in the other. The excitation energies within perturbation theory are found to be more accurate than the excitations obtained within Delta SCF while, for a two-electron system, they coincide with the ones obtained in time-dependent density functional theory within the single-pole approximation using our accurate static exchange-correlation potential and the time-dependent optimized effective potential kernel. We find that the agreement between the experimental and the perturbative excitation energies deteriorates significantly if potentials from approximate functionals such as the local density approximation and the optimized effective potential method are employed instead of the true Kohn-Sham potential