We here develop a fully quantum embedded version of initiator full configuration interaction quantum Monte Carlo ( i –FCIQMC) and apply it to study an ionic bond (lithium hydride, LiH) and a covalent bond (hydrogen flouride, HF) physisorbed to a benzene molecule. The embedding is performed using a recently developed Huzinaga projection operator approach, which affords good synergy with i –FCIQMC by minimizing the number of orbitals in the calculation. When considering the dissociation energy of these bonds into closed-shell ionic fragments, we find that i −FCIQMC embedded in density functional theory ( i −FCIQMC-in-DFT) delivers comparable accuracy with coupled cluster singles and doubles with perturbative triples embedded in density functional theory (CCSD(T)-in-DFT). In treating the bond dissociation energy curve of HF, i –FCIQMC-in-DFT has improved accuracy over CCSD(T)-in-DFT due to the presence of strong correlation. We discuss the implications of the new i –FCIQMC-in-DFT method as applied to bond breaking in catalysis.
We here develop a fully quantum embedded version of initiator full configuration interaction quantum Monte Carlo ( i –FCIQMC) and apply it to study an ionic bond (lithium hydride, LiH) and a covalent bond (hydrogen flouride, HF) physisorbed to a benzene molecule. The embedding is performed using a recently developed Huzinaga projection operator approach, which affords good synergy with i –FCIQMC by minimizing the number of orbitals in the calculation. When considering the dissociation energy of these bonds into closed-shell ionic fragments, we find that i −FCIQMC embedded in density functional theory ( i −FCIQMC-in-DFT) delivers comparable accuracy with coupled cluster singles and doubles with perturbative triples embedded in density functional theory (CCSD(T)-in-DFT). In treating the bond dissociation energy curve of HF, i –FCIQMC-in-DFT has improved accuracy over CCSD(T)-in-DFT due to the presence of strong correlation. We discuss the implications of the new i –FCIQMC-in-DFT method as applied to bond breaking in catalysis.
We present an embedded fragment approach for high-level quantum chemical calculations on local features in periodic systems. The fragment is defined as a set of localized orbitals (occupied and virtual) corresponding to a converged periodic Hartree-Fock solution. These orbitals serve as the basis for the in-fragment post-Hartree-Fock treatment. The embedding field for the fragment, consisting of the Coulomb and exchange potential from the rest of the crystal, is included in the fragment's one-electron Hamiltonian. As an application of the embedded fragment approach, we investigate the performance of full configuration interaction quantum Monte Carlo (FCIQMC) with the adaptive shift. As the orbital choice, we use the natural orbitals from the distinguishable cluster method with singles and doubles. FCIQMC is a stochastic approximation to the full CI method and can be routinely applied to much larger active spaces than the latter. This makes this method especially attractive in the context of open shell defects in crystals, where fragments of adequate size can be rather large. As a test case, we consider dissociation of a fluorine atom from a fluorographane surface. This process poses a challenge for high-level electronic structure models as both the static and dynamic correlations are essential here. Furthermore, the active space for an adequate fragment (32 electrons in 173 orbitals) is already quite large even for FCIQMC. Despite this, FCIQMC delivers accurate dissociation and total energies.
The full configuration interaction quantum Monte Carlo (FCIQMC) method, as well as its "initiator" extension (i-FCIQMC), is used to tackle the complex electronic structure of the carbon dimer across the entire dissociation reaction coordinate, as a prototypical example of a strongly correlated molecular system. Various basis sets of increasing size up to the large cc-pVQZ are used, spanning a fully accessible N-electron basis of over 10(12) Slater determinants, and the accuracy of the method is demonstrated in each basis set. Convergence to the FCI limit is achieved in the largest basis with only O[10(7)] walkers within random errorbars of a few tenths of a millihartree across the binding curve, and extensive comparisons to FCI, CCSD(T), MRCI, and CEEIS results are made where possible. A detailed exposition of the convergence properties of the FCIQMC methods is provided, considering convergence with elapsed imaginary time, number of walkers and size of the basis. Various symmetries which can be incorporated into the stochastic dynamic, beyond the standard abelian point group symmetry and spin polarisation are also described. These can have significant benefit to the computational effort of the calculations, as well as the ability to converge to various excited states. The results presented demonstrate a new benchmark accuracy in basis-set energies for systems of this size, significantly improving on previous state of the art estimates.
We demonstrate the feasibility of using a stochastic solver, full configuration interaction quantum Monte Carlo with the initiator approximation (i-FCIQMC), to converge fragment embedding calculations, namely bootstrap embedding (BE). We first propose and test a general protocol for converging BE-i-FCIQMC calculations and then suggest how the quality of the calculation compares against that of deterministic BE-FCI using different numbers of walkers. We then demonstrate that BE-i-FCIQMC can perform as well as BE-FCI in the large walker limit and how different factors, including the size of the Hilbert space of the fragments, the number of walkers, and the nature of the chemical system, affect the achievable matching error. We finally perform BE-FCI calculations in realistic systems like benzene and cyclohexane using a double-ζ basis set. This work demonstrates the potential of performing FCI quality calculations in realistic systems using BE.
The initiator full configuration interaction quantum Monte Carlo method (i-FCIQMC) is applied to the binding curve of N2 in Slater-determinant Hilbert spaces formed of both canonical restricted Hartree-Fock (RHF) and symmetry-broken unrestricted Hartree-Fock (UHF) orbitals. By explicit calculation, we demonstrate that the technique yields the same total energy for both types of orbital but that as the bond is stretched, FCI expansions expressed in unrestricted orbitals are substantially more compact than their restricted counterparts and more compact than those expressed in split-localized orbitals. These unrestricted Hilbert spaces, however, become nonergodic toward the dissociation limit, and the total wave function may be thought of as the sum of two weakly coupled, spin-impure, functions whose energies are nonetheless very close to the exact energy. In this limit, it is a challenge for i-FCIQMC to resolve a spin-pure wave function. The use of unrestricted natural orbitals is a promising remedy for this problem, as their expansions are more strongly weighted toward lower excitations of the reference, and they provide stronger coupling to higher excitations than do UHF orbitals.
The initiator full configuration interaction quantum Monte Carlo (i-FCIQMC) method has recently been developed as a highly accurate stochastic electronic structure technique. It has been shown to calculate the exact basis-set ground state energy of small molecules, to within modest stochastic error bars, using tractable computational cost. Here, we use this technique to elucidate an often troublesome series of first-row diatomics consisting of Be2, C2, CN, CO, N2, NO, O2, and F2. Using i-FCIQMC, the dissociation energies of these molecules are obtained almost entirely to within chemical accuracy of experimental results. Furthermore, the i-FCIQMC calculations are performed in a relatively black-box manner, without any a priori knowledge or specification of the wave function. The size consistency of i-FCIQMC is also demonstrated with regards to these diatomics at their more multiconfigurational stretched geometries. The clear and simple i-FCIQMC wave functions obtained for these systems are then compared and investigated to demonstrate the dynamic identification of the dominant determinants contributing to significant static correlation. The appearance and nature of such determinants is shown to provide insight into both the i-FCIQMC algorithm and the diatomics themselves.
By performing a stochastic dynamic in a space of Slater determinants, the full configuration interaction quantum Monte Carlo (FCIQMC) method has been able to obtain energies which are essentially free from systematic error to the basis set correlation energy, within small and systematically improvable error bars. However, the weakly exponential scaling with basis size makes converging the energy with respect to basis set costly and in larger systems, impossible. To ameliorate these basis set issues, here we use perturbation theory to couple the FCIQMC wavefunction to an explicitly correlated strongly orthogonal basis of geminals, following the [2](R12) approach of Valeev et al. The required one- and two-particle density matrices are computed on-the-fly during the FCIQMC dynamic, using a sampling procedure which incurs relatively little additional computation expense. The F12 energy corrections are shown to converge rapidly as a function of sampling, both in imaginary time and number of walkers. Our pilot calculations on the binding curve for the carbon dimer, which exhibits strong correlation effects as well as substantial basis set dependence, demonstrate that the accuracy of the FCIQMC-F12 method surpasses that of all previous FCIQMC calculations, and that the F12 correction improves results equivalent to increasing the quality of the one-electron basis by two cardinal numbers.