Matrix product states and their uses in quantum chemistry

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Longitudinal static optical properties of hydrogen chains: finite field extrapolations of matrix product state calculations

We have implemented the sweep algorithm for the variational optimization of SU(2) x U(1) (spin and particle number) invariant matrix product states (MPS) for general spin and particle number invariant fermionic Hamiltonians. This class includes non-relativistic quantum chemical systems within the Born-Oppenheimer approximation. High-accuracy ab-initio finite field results of the longitudinal static polarizabilities and second hyperpolarizabilities of one-dimensional hydrogen chains are presented. This allows to assess the performance of other quantum chemical methods. For small basis sets, MPS calculations in the saturation regime of the optical response properties can be performed. These results are extrapolated to the thermodynamic limit.Comment: Submitted to J. Chem. Phy

Measurement of the three-dimensional velocity distribution of Stark-decelerated Rydberg atoms

Abstract.: The full three-dimensional velocity distributions of decelerated and accelerated particles in a Stark decelerator for Rydberg atoms and molecules have been measured. In the experiment, argon atoms in a supersonic beam are excited to low-field and high-field seeking Stark states with principal quantum number in the range n=15 to 25 and are decelerated in a 3 mm long decelerator consisting of four electrodes on which time-dependent voltages are applied. The time dependence of the resulting inhomogeneous electric field is chosen such that the decelerating force acting on the high-field seeking states is maximized at each point along the trajectories. The three-dimensional velocity distribution of the atoms before and after the deceleration is determined by measuring times of flight and two-dimensional images of the atomic cloud on the detector. Under optimal deceleration conditions, the decrease in kinetic energy in the longitudinal dimension amounts to 1.0×10-21 J and the increase in mean kinetic energy in the transverse dimensions is only 1.0×10-23 J. The corresponding temperatures of 100 mK and 300 mK in the two transverse dimensions are sufficiently low that trapping can be envisaged. The possibility of focusing a Rydberg atom beam is demonstrated experimentall

Simple and inexpensive perturbative correction schemes for antisymmetric products of nonorthogonal geminals

A new multireference perturbation approach has been developed for the recently proposed AP1roG scheme, a computationally facile parametrization of an antisymmetric product of nonorthogonal geminals. This perturbation theory of second-order closely follows the biorthogonal treatment from multiconfiguration perturbation theory as introduced by Surjan et al., but makes use of the additional feature of AP1roG that the expansion coefficients within the space of closed-shell determinants are essentially correct already, which further increases the predictive power of the method. Building upon the ability of AP1roG to model static correlation, the perturbation correction accounts for dynamical electron correlation, leading to absolute energies close to full configuration interaction results. Potential surfaces for multiple bond dissociation in H2O and N-2 are predicted with high accuracy up to bond breaking. The computational cost of the method is the same as that of conventional single-reference MP2

The influence of orbital rotation on the energy of closed-shell wavefunctions

The orbital dependence of closed-shell wavefunction energies is investigated by performing doubly-occupied configuration interaction (DOCI) calculations, representing the most general class of these wavefunctions. Different local minima are examined for planar hydrogen clusters containing two, four, and six electrons applying (spin) symmetry-broken restricted, unrestricted, and generalised orbitals with real and complex coefficients. Contrary to Hartree-Fock (HF), restricted DOCI is found to properly break bonds and thus unrestricted orbitals, while providing a quantitative improvement of the energy, are not needed to enforce a qualitatively correct bond dissociation. For the beryllium atom and the BH diatomic, the lowest possible HF energy requests symmetry-broken generalised orbitals, whereas accurate results for DOCI can be obtained within a restricted formalism. Complex orbital coefficients are shown to increase the accuracy of HF and DOCI results in certain cases. The computationally inexpensive AP1roG geminal wavefunction is proven to agree very well with all DOCI results of this study

Projected seniority-two orbital optimization of the Antisymmetric Product of one-reference orbital Geminal

We present a new, non-variational orbital-optimization scheme for the Antisymmetric Product of one-reference orbital Geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [J. Chem. Phys., 135, 044119 (2011)]. A numerical analysis is performed for the C$_2$, LiF and CH$_2$ molecules as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases.Comment: 7 pages, 2 figure