NECI: N-Electron Configuration Interaction with an emphasis on state-of-the-art stochastic methods.

We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24 000 central processing unit cores. In this paper, we describe the core functionalities of NECI and its recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green's functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing us to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs, and it is licensed under GPL-3.0.

Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo.

Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation.

Symmetry Breaking and Broken Ergodicity in Full Configuration Interaction Quantum Monte Carlo.

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.

Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo.

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.

Taming the First-Row Diatomics: A Full Configuration Interaction Quantum Monte Carlo Study.

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.

The mechanism of transport by mitochondrial carriers based on analysis of symmetry.

The structures of mitochondrial transporters and uncoupling proteins are 3-fold pseudosymmetrical, but their substrates and coupling ions are not. Thus, deviations from symmetry are to be expected in the substrate and ion-binding sites in the central aqueous cavity. By analyzing the 3-fold pseudosymmetrical repeats from which their sequences are made, conserved asymmetric residues were found to cluster in a region of the central cavity identified previously as the common substrate-binding site. Conserved symmetrical residues required for the transport mechanism were found at the water-membrane interfaces, and they include the three PX[DE]XX[RK] motifs, which form a salt bridge network on the matrix side of the cavity when the substrate-binding site is open to the mitochondrial intermembrane space. Symmetrical residues in three [FY][DE]XX[RK] motifs are on the cytoplasmic side of the cavity and could form a salt bridge network when the substrate-binding site is accessible from the mitochondrial matrix. It is proposed that the opening and closing of the carrier may be coupled to the disruption and formation of the 2 salt bridge networks via a 3-fold rotary twist induced by substrate binding. The interaction energies of the networks allow members of the transporter family to be classified as strict exchangers or uniporters.