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Register a new useriCISCF: An Iterative Configuration Interaction-based Multiconfigurational Self-consistent Field Theory for Large Active Spaces
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An iterative configuration interaction (iCI)-based multiconfigurational self-consistent field (SCF) theory, iCISCF, is proposed to handle systems that require large complete active spaces (CAS). The success of iCISCF stems from three ingredients: (1) efficient selection of individual configuration state functions spanning the CAS, meanwhile maintaining full spin symmetry; (2) the use of Jacobi rotation for the optimization of active orbitals, in conjunction with a quasi-Newton algorithm for the core/active-virtual and core-active orbital rotations; (3) a second-order perturbative treatment of the residual space left over by the selection procedure (i.e., iCISCF(2)). Just like selected iCI being a very accurate approximation to CASCI, iCISCF(2) is a very accurate approximation to CASSCF. Several examples that go beyond the capability of CASSCF are taken as showcases to reveal the performances of iCISCF and iCISCF(2).
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An iterative orbital interaction (iOI) approach is proposed to solve, in a bottom-up fashion, the self-consistent field problem in quantum chemistry. While it belongs grossly to the family of fragment-based quantum chemical methods, iOI is distinctive in that (1) it divides and conquers not only the energy but also the wave function, and that (2) the subsystems sizes are automatically determined by successively merging neighboring small subsystems until they are just enough for converging the wave function to a given accuracy. Orthonormal occupied and virtual localized molecular orbitals are obtained in a natural manner, which can be used for all post-SCF purposes.
Full Configuration Interaction Quantum Monte Carlo (FCIQMC) has been effectively applied to very large configuration interaction (CI) problems, and was recently adapted for use as an active space solver and combined with orbital optimisation. In this work, we detail an approach within FCIQMC to allow for efficient sampling of fully internally-contracted multireference perturbation theories within the same stochastic framework. Schemes are described to allow for the close control over the resolution of stochastic sampling of the effective higher-body intermediates within the active space. It is found that while CASPT2 seems less amenable to a stochastic reformulation, NEVPT2 is far more stable, requiring a similar number of walkers to converge the NEVPT2 expectation values as to converge the underlying CI problem. We demonstrate the application of the stochastic approach to the computation of NEVPT2 within a (24,24) active space in a biologically relevant system, and show that small numbers of walkers are sufficient for a faithful sampling of the NEVPT2 energy to chemical accuracy, despite the active space already exceeding the limits of practicality for traditional approaches. This raises prospects of an efficient stochastic solver for multireference chemical problems requiring large active spaces, with an accurate treatment of external orbitals.
Even when starting with a very poor initial guess, the iterative configuration interaction (iCI) approach can converge from above to full CI very quickly by constructing and diagonalizing a small Hamiltonian matrix at each macro/micro-iteration. However, iCI scales exponentially with respect to the numbers of electrons and orbitals. The problem can be mitigated by observing that a vast number of configurations have little weights in the wave function and do not contribute to the correlation energy. The real questions are then (a) how to identify important configurations in the early stage of the calculation and (b) how to account for the residual contributions of those unimportant configurations. It is generally true that if a high-quality yet compact variational space can be determined for describing the static correlation, a low-order treatment of the residual dynamic correlation would be sufficient. While this is common to all selected CI schemes, the `iCI with selection scheme presented here has the following distinctive features: (1) Full spin symmetry is maintained. (2) Although the selection is performed on individual CSFs, it is orbital configurations (oCFG) that are used as the organizing units. (3) Given a coefficient pruning-threshold, the selection of important oCFGs/CSFs is performed iteratively until convergence. (4) At each iteration for the growth of wave function, the first-order interacting space is decomposed into disjoint subspaces to reduce memory requirement and facilitate parallelization. (5) Upper bounds for the interactions between oCFG pairs are used to screen each first-order interacting subspace before the first-order coefficients of individual CSFs are evaluated. (6) Upon termination of the selection, dynamic correlation is estimated by using the ENPT2 theory. The efficacy of the iCIPT2 scheme is demonstrated numerically by taking several examples.
We report an efficient algorithm using density fitting for the relativistic complete active space self-consistent field (CASSCF) method, which is significantly more stable than the algorithm previously reported by one of the authors [J. E. Bates and T. Shiozaki, J. Chem. Phys. 142, 044112 (2015)]. Our algorithm is based on the second-order orbital update scheme with an iterative augmented Hessian procedure, in which the density-fitted orbital Hessian is directly contracted to the trial vectors. Using this scheme, each microiteration is made less time consuming than one Dirac-Hartree-Fock iteration, and macroiterations converge quadratically. In addition, we show that the CASSCF calculations with the Gaunt and full Breit interactions can be efficiently performed by means of approximate orbital Hessians computed with the Dirac-Coulomb Hamiltonian. It is demonstrated that our algorithm can also be applied to systems under an external magnetic field, for which all of the molecular integrals are computed using gauge-including atomic orbitals.
Fragmentation methods applied to multireference wave functions constitute a road towards the application of highly accurate ab initio wave function calculations to large molecules and solids. However, it is important for reproducibility and transferability that a fragmentation scheme be well-defined with minimal dependence on initial orbital guesses or user-designed ad hoc fragmentation schemes. One way to improve this sort of robustness is to ensure the energy obeys a variational principle; i.e., that the active orbitals and active space wave functions minimize the electronic energy in a certain ansatz for the molecular wave function. We extended the theory of the localized active space self-consistent field, LASSCF, method (JCTC 2019, 15, 972) to fully minimize the energy with respect to all orbital rotations, rendering it truly variational. The new method, called vLASSCF, substantially improves the robustness and reproducibility of the LAS wave function compared to LASSCF. We analyze the storage and operation cost scaling of vLASSCF compared to orbital optimization using a standard CASSCF approach and we show results of vLASSCF calculations on some simple test systems. We show that vLASSCF is energetically equivalent to CASSCF in the limit of one active subspace, and that vLASSCF significantly improves upon the reliability of LASSCF energy differences, allowing for more meaningful and subtle analysis of potential energy curves of dissociating molecules. We also show that all forms of LASSCF have a lower operation cost scaling than the orbital-optimization part of CASSCF.
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