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Register a new userModern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method
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Recent advances in selected CI, including the adaptive sampling configuration interaction (ASCI) algorithm and its heat bath extension, have made the ASCI approach competitive with the most accurate techniques available, and hence an increasingly powerful tool in solving quantum Hamiltonians. In this work, we show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques we present ASCI results applied to a large range of systems and basis sets in order to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double- and triple-zeta benchmark data for the G1 dataset. The largest of these calculations is Si$_{2}$H$_{6}$ which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets.
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We introduce a new selected configuration interaction plus perturbation theory algorithm that is based on a deterministic analog of our recent efficient heat-bath sampling algorithm. This Heat-bath Configuration Interaction (HCI) algorithm makes use of two parameters that control the tradeoff between speed and accuracy, one which controls the selection of determinants to add to a variational wavefunction, and one which controls the the selection of determinants used to compute the perturbative correction to the variational energy. We show that HCI provides an accurate treatment of both static and dynamic correlation by computing the potential energy curve of the multireference carbon dimer in the cc-pVDZ basis. We then demonstrate the speed and accuracy of HCI by recovering the full configuration interaction energy of both the carbon dimer in the cc-pVTZ basis and the strongly-correlated chromium dimer in the Ahlrichs VDZ basis, correlating all electrons, to an accuracy of better than 1 mHa, in just a few minutes on a single core. These systems have full variational spaces of 3x10^14 and 2x10^22 determinants respectively.
We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 12, 3674 (2016)], by introducing a semistochastic algorithm for performing multireference Epstein-Nesbet perturbation theory, in order to completely eliminate the severe memory bottleneck of the original method. The proposed algorithm has several attractive features. First, there is no sign problem that plagues several quantum Monte Carlo methods. Second, instead of using Metropolis-Hastings sampling, we use the Alias method to directly sample determinants from the reference wavefunction, thus avoiding correlations between consecutive samples. Third, in addition to removing the memory bottleneck, semistochastic HCI (SHCI) is faster than the deterministic variant for many systems if a stochastic error of 0.1 mHa is acceptable. Fourth, within the SHCI algorithm one can trade memory for a modest increase in computer time. Fifth, the perturbative calculation is embarrassingly parallel. The SHCI algorithm extends the range of applicability of the original algorithm, allowing us to calculate the correlation energy of very large active spaces. We demonstrate this by performing calculations on several first row dimers including F2 with an active space of (14e, 108o), Mn-Salen cluster with an active space of (28e, 22o), and Cr2 dimer with up to a quadruple-zeta basis set with an active space of (12e, 190o). For these systems we were able to obtain better than 1 mHa accuracy with a wall time of merely 55 seconds, 37 seconds, and 56 minutes on 1, 1, and 4 nodes, respectively.
Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the Full Configuration Interaction Quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself), and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems.
The recently developed semistochastic heat-bath configuration interaction (SHCI) method is a systematically improvable selected configuration interaction plus perturbation theory method capable of giving essentially exact energies for larger systems than is possible with other such methods. We compute SHCI atomization energies for 55 molecules which have been used as a test set in prior studies because their atomization energies are known from experiment. Basis sets from cc-pVDZ to cc-pV5Z are used, totaling up to 500 orbitals and a Hilbert space of $10^{32}$ Slater determinants for the largest molecules. For each basis, an extrapolated energy well within chemical accuracy (1 kcal/mol or 1.6 mHa/mol) of the exact energy for that basis is computed using only a tiny fraction of the entire Hilbert space. We also use our almost exact energies to benchmark coupled-cluster [CCSD(T)] energies. The energies are extrapolated to the complete basis set limit and compared to the experimental atomization energies. The extrapolations are done both without and with a basis-set correction based on density-functional theory. The mean absolute deviations from experiment for these extrapolations are 0.46 kcal/mol and 0.51 kcal/mol, respectively. Orbital optimization methods used to obtain improved convergence of the SHCI energies are also discussed.
We derive expressions for the quantum electromagnetic field in a dispersive and dissipative dielectric medium, treating the medium as a continuum. We compare the Langevin approach with the Fano diagonalization procedure for the coupled system composed of the electromagnetic field, the dielectric medium, and the reservoir. In particular, we show that the quantized electric and magnetic fields obtained in both methods have exactly the same form. More generally, in thermal equilibrium, correlation functions computed in both methods are identical.
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