A general second order complete active space self-consistent-field solver for large-scale systems

We present a new second order complete active space self-consistent field implementation to converge wavefunctions for both large active spaces and large atomic orbital (AO) bases. Our algorithm decouples the active space wavefunction solver from the orbital optimization in the microiterations, and thus may be easily combined with various modern active space solvers. We also introduce efficient approximate orbital gradient and Hessian updates, and step size determination. We demonstrate its capabilities by calculating the low-lying states of the Fe(\Roman{2})-porphine complex with modest resources using a density matrix renormalization group solver in a CAS(22,27) active space and a 3000 AO basis

Non-Hermitian Rayleigh-Schroedinger Perturbation Theory

We devise a non-Hermitian Rayleigh-Schroedinger perturbation theory for the single- and the multireference case to tackle both the many-body problem and the decay problem encountered, for example, in the study of electronic resonances in molecules. A complex absorbing potential (CAP) is employed to facilitate a treatment of resonance states that is similar to the well-established bound-state techniques. For the perturbative approach, the full CAP-Schroedinger Hamiltonian, in suitable representation, is partitioned according to the Epstein-Nesbet scheme. The equations we derive in the framework of the single-reference perturbation theory turn out to be identical to those obtained by a time-dependent treatment in Wigner-Weisskopf theory. The multireference perturbation theory is studied for a model problem and is shown to be an efficient and accurate method. Algorithmic aspects of the integration of the perturbation theories into existing ab initio programs are discussed, and the simplicity of their implementation is elucidated.Comment: 10 pages, 1 figure, RevTeX4, submitted to Physical Review

A Perturbative Density Matrix Renormalization Group Algorithm for Large Active Spaces

We describe a low cost alternative to the standard variational DMRG (density matrix renormalization group) algorithm that is analogous to the combination of selected configuration interaction plus perturbation theory (SCI+PT). We denote the resulting method p-DMRG (perturbative DMRG) to distinguish it from the standard variational DMRG. p-DMRG is expected to be useful for systems with very large active spaces, for which variational DMRG becomes too expensive. Similar to SCI+PT, in p-DMRG a zeroth-order wavefunction is first obtained by a standard DMRG calculation, but with a small bond dimension. Then, the residual correlation is recovered by a second-order perturbative treatment. We discuss the choice of partitioning for the perturbation theory, which is crucial for its accuracy and robustness. To circumvent the problem of a large bond dimension in the first-order wavefunction, we use a sum of matrix product states (MPS) to expand the first-order wavefunction, yielding substantial savings in computational cost and memory. We also propose extrapolation schemes to reduce the errors in the zeroth- and first-order wavefunctions. Numerical results for Cr 2 with a (28e,76o) active space and 1,3-butadiene with a (22e,82o) active space reveal that p-DMRG provides ground state energies of a similar quality to variational DMRG with very large bond dimensions, but at a significantly lower computational cost. This suggests that p-DMRG will be an efficient tool for benchmark studies in the future

Applying Monte Carlo configuration interaction to transition metal dimers: exploring the balance between static and dynamic correlation

We calculate potential curves for transition metal dimers using Monte Carlo configuration interaction (MCCI). These results, and their associated spectroscopic values, are compared with experimental and computational studies. The multireference nature of the MCCI wavefunction is quantified and we estimate the important orbitals. We initially consider the ground state of the chromium dimer. Next we calculate potential curves for Sc$_{2}$ where we contrast the lowest triplet and quintet states. We look at the molybdenum dimer where we compare non-relativistic results with the partial inclusion of relativistic effects via effective core potentials, and report results for scandium nickel.Comment: 9 pages and 8 figure

Recent advances in electronic structure theory and their influence on the accuracy of ab initio potential energy surfaces

Recent advances in electronic structure theory and the availability of high speed vector processors have substantially increased the accuracy of ab initio potential energy surfaces. The recently developed atomic natural orbital approach for basis set contraction has reduced both the basis set incompleteness and superposition errors in molecular calculations. Furthermore, full CI calculations can often be used to calibrate a CASSCF/MRCI approach that quantitatively accounts for the valence correlation energy. These computational advances also provide a vehicle for systematically improving the calculations and for estimating the residual error in the calculations. Calculations on selected diatomic and triatomic systems will be used to illustrate the accuracy that currently can be achieved for molecular systems. In particular, the F+H2 yields HF+H potential energy hypersurface is used to illustrate the impact of these computational advances on the calculation of potential energy surfaces