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Register a new useriOI: an Iterative Orbital Interaction Approach for Solving the Self-Consistent Field Problem
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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.
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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).
We introduce an iterative scheme to prove the Yamabe problem $ - aDelta_{g} u + S u = lambda u^{p-1} $, firstly on open domain $ (Omega, g) $ with Dirichlet boundary conditions, and then on closed manifolds $ (M, g) $ by local argument. It is a new proof, which solves the Yamabe problem for $ n geqslant 3 $ in a uniform argument, beyonds the traditional analysis with respect to the minimization of functionals.
Employing a local formula for the electron-electron interaction energy, we derive a self-consistent approximation for the total energy of a general $N$-electron system. Our scheme works as a local variant of the Thomas-Fermi approximation and yields the total energy and density as a function of the external potential, the number of electrons, and the chemical potential determined upon normalization. Our tests for Hookes atoms, jellium, and model atoms up to $sim 1000$ electrons show that reasonable total energies can be obtained with almost a negligible computational cost. The results are also consistent in the important large-$N$ limit.
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.
We present a first principles molecular dynamics approach that is based on time-reversible ex- tended Lagrangian Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 100, 123004 (2008)] in the limit of vanishing self-consistent field optimization. The optimization-free dynamics keeps the computational cost to a minimum and typically provides molecular trajectories that closely follow the exact Born-Oppenheimer potential energy surface. Only one single diagonalization and Hamiltonian (or Fockian) costruction are required in each integration time step. The proposed dy- namics is derived for a general free-energy potential surface valid at finite electronic temperatures within hybrid density functional theory. Even in the event of irregular functional behavior that may cause a dynamical instability, the optimization-free limit represents an ideal starting guess for force calculations that may require a more elaborate iterative electronic ground state optimization. Our optimization-free dynamics thus represents a flexible theoretical framework for a broad and general class of ab initio molecular dynamics simulations.
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