A Mean Field Platform for Excited State Quantum Chemistry

We present a mean field theory for excited states that is broadly analogous to ground state Hartree-Fock theory. Like Hartree-Fock, our approach is deterministic, state-specific, applies a variational principle to a minimally correlated ansatz, produces energy stationary points, relaxes the orbital basis, has a Fock-build cost-scaling, and can serve as the foundation for correlation methods such as perturbation theory and coupled cluster theory. To emphasize this last point, we pair our mean field approach with an excited state analogue of second order Moller-Plesset theory and demonstrate that in water, formaldehyde, neon, and stretched lithium fluoride, the resulting accuracy far exceeds that of configuration interaction singles and rivals that of equation of motion coupled cluster.Comment: 6 page

Correlated electrons in Fe-As compounds: a quantum chemical perspective

State-of-the-art quantum chemical methods are applied to the study of the multiorbital correlated electronic structure of a Fe-As compound, the recently discovered LiFeAs. Our calculations predict a high-spin, S=2, ground-state configuration for the Fe ions, which shows that the on-site Coulomb interactions are substantial. Also, orbital degeneracy in the (xz,yz) sector and a three-quarter filling of these levels suggest the presence of strong fluctuations and are compatible with a low metallic conductivity in the normal state. The lowest electron-removal states have As 4p character, in analogy to the ligand hole states in p-type cuprate superconductors

Ab initio quantum dynamics using coupled-cluster

The curse of dimensionality (COD) limits the current state-of-the-art {\it ab initio} propagation methods for non-relativistic quantum mechanics to relatively few particles. For stationary structure calculations, the coupled-cluster (CC) method overcomes the COD in the sense that the method scales polynomially with the number of particles while still being size-consistent and extensive. We generalize the CC method to the time domain while allowing the single-particle functions to vary in an adaptive fashion as well, thereby creating a highly flexible, polynomially scaling approximation to the time-dependent Schr\"odinger equation. The method inherits size-consistency and extensivity from the CC method. The method is dubbed orbital-adaptive time-dependent coupled-cluster (OATDCC), and is a hierarchy of approximations to the now standard multi-configurational time-dependent Hartree method for fermions. A numerical experiment is also given.Comment: 5 figure

R-matrix calculation of differential cross sections for low-energy electron collisions with ground and electronically excited state O2 molecules

Differential cross sections for electron collisions with the O$_2$ molecule in its ground ${X}^{3}\Sigma_g^-$ state, as well as excited ${a}^{1}\Delta_g$ and ${b}^{1}\Sigma_g^+$ states are calculated. As previously, the fixed-bond R-matrix method based on state-averaged complete active space SCF orbitals is employed. In additions to elastic scattering of electron with the O$_2$ ${X}^{3}\Sigma_g^-$, ${a}^{1}\Delta_g$ and ${b}^{1}\Sigma_g^+$ states, electron impact excitation from the ${X}^{3}\Sigma_g^-$ state to the ${a}^{1}\Delta_g$ and ${b}^{1}\Sigma_g^+$ states as well as '6 eV states' of ${c}^{1}\Sigma_u^{-}$, ${A'}^{3}\Delta_u$ and ${A}^{3}\Sigma_u^{+}$ states is studied. Differential cross sections for excitation to the '6 eV states' have not been calculated previously. Electron impact excitation to the ${b}^{1}\Sigma_g^+$ state from the metastable ${a}^{1}\Delta_g$ state is also studied. For electron impact excitation from the O$_2$ ${X}^{3}\Sigma_g^-$ state to the ${b}^{1}\Sigma_g^+$ state, our results agree better with the experimental measurements than previous theoretical calculations. Our cross sections show angular behaviour similar to the experimental ones for transitions from the ${X}^{3}\Sigma_g^-$ state to the '6 eV states', although the calculated cross sections are up to a factor two larger at large scattering angles. For the excitation from the ${a}^{1}\Delta_g$ state to the ${b}^{1}\Sigma_g^+$ state, our results marginally agree with the experimental data except for the forward scattering direction

Resolving the notorious case of conical intersections for coupled cluster dynamics

The motion of electrons and nuclei in photochemical events often involve conical intersections, degeneracies between electronic states. They serve as funnels for nuclear relaxation - on the femtosecond scale - in processes where the electrons and nuclei couple nonadiabatically. Accurate ab initio quantum chemical models are essential for interpreting experimental measurements of such phenomena. In this paper we resolve a long-standing problem in coupled cluster theory, presenting the first formulation of the theory that correctly describes conical intersections between excited electronic states of the same symmetry. This new development demonstrates that the highly accurate coupled cluster theory can be applied to describe dynamics on excited electronic states involving conical intersections.Comment: 8 pages and 3 figures and including supporting information (with corrections and improved notation

Optimization of quantum Monte Carlo wave functions by energy minimization

We study three wave function optimization methods based on energy minimization in a variational Monte Carlo framework: the Newton, linear and perturbative methods. In the Newton method, the parameter variations are calculated from the energy gradient and Hessian, using a reduced variance statistical estimator for the latter. In the linear method, the parameter variations are found by diagonalizing a non-symmetric estimator of the Hamiltonian matrix in the space spanned by the wave function and its derivatives with respect to the parameters, making use of a strong zero-variance principle. In the less computationally expensive perturbative method, the parameter variations are calculated by approximately solving the generalized eigenvalue equation of the linear method by a nonorthogonal perturbation theory. These general methods are illustrated here by the optimization of wave functions consisting of a Jastrow factor multiplied by an expansion in configuration state functions (CSFs) for the C$_2$ molecule, including both valence and core electrons in the calculation. The Newton and linear methods are very efficient for the optimization of the Jastrow, CSF and orbital parameters. The perturbative method is a good alternative for the optimization of just the CSF and orbital parameters. Although the optimization is performed at the variational Monte Carlo level, we observe for the C$_2$ molecule studied here, and for other systems we have studied, that as more parameters in the trial wave functions are optimized, the diffusion Monte Carlo total energy improves monotonically, implying that the nodal hypersurface also improves monotonically.Comment: 18 pages, 8 figures, final versio

On how good DFT exchange-correlation functionals are for H bonds in small water clusters: Benchmarks approaching the complete basis set limit

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Moeller Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the non-hybrid GGA functionals mPWLYP and PBE1W perform the best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.Comment: 9 pages including 4 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Two-boson Correlations in Various One-dimensional Traps

A one-dimensional system of two trapped bosons which interact through a contact potential is studied using the optimized configuration interaction method. The rapid convergence of the method is demonstrated for trapping potentials of convex and non-convex shapes. The energy spectra, as well as natural orbitals and their occupation numbers are determined in function of the inter-boson interaction strength. Entanglement characteristics are discussed in dependence on the shape of the confining potential.Comment: 5 pages, 3 figure

Fermiology of Cuprates from First Principles: From Small Pockets to the Luttinger Fermi surface

Fermiology, the shape and size of the Fermi surface, underpins the low-temperature physical properties of a metal. Recent investigations of the Fermi surface of high-Tc superconductors, however, show a most unusual behavior: upon addition of carriers, ``Fermi'' pockets appear around nodal (hole doping) and antinodal (electron doping) regions of the Brillouin zone in the ``pseudogap'' state. With progressive doping, p, these evolve into well-defined Fermi surfaces around optimal doping (p_opt), with no pseudogap. Correspondingly, various physical responses, including d-wave superconductivity, evolve from highly anomalous, up to p_opt, to more conventional beyond. Describing this evolution holds the key to understanding high-temperature superconductivity. Here, we present ab initio quantum chemical results for cuprates, providing a quantitative description of the evolution of the Fermi surface with doping. Our results constitute an ab initio justification for several, hitherto proposed semiphenomenological theories, offering an unified basis for understanding of various, unusual physical responses of doped cuprates