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.

By expressing the electronic wavefunction in an explicitly-correlated (Jastrow-factorised) form, a similarity-transformed effective Hamiltonian can be derived. The effective Hamiltonian is non-Hermitian and contains three-body interactions. The resulting ground-state eigenvalue problem can be solved projectively using a stochastic configuration-interaction formalism. Our approach permits use of highly flexible Jastrow functions, which we show to be effective in achieving extremely high accuracy, even with small basis sets. Results are presented for the total energies and ionisation potentials of the first-row atoms, achieving accuracy within a mH of the basis-set limit, using modest basis sets and computational effort. PACS numbers: Valid PACS appear hereMethods aiming to obtain high-accuracy solutions to the electronic Schrödinger equation must tackle two essential components of the problem, namely providing highly flexible expansions capable of resolving nonanalytic features of the wavefunction, including the Kato cusps[1] at electron coalesence points, as well as treatment of many-electron correlation at medium and long range. The combination of these two facets of the problem leads to overwhelming computational complexity, requiring large basis sets and high-order correlation methods, approximations to which can result in a significant loss of accuracy. The goal of achieving "chemical" accuracy remains extremely challenging for all but the simplest systems.In Fock space approaches, including the majority of quantum chemical methodologies based on configurational expansions, the first-quantised Schrödinger Hamiltonian is replaced by a second-quantised form, expressed in a one-electron basis. The passage from first quantisation to second is invoked primarily to impose antisymmetry on the solutions, via fermionic creation and annihilation operators of the orbital basis. However, this formulation loses the ability to explicitly include electron pair variables (such as electron-electron distances) into the wavefunction, which has long been known [2] to be crucial in obtaining an efficient description of electron correlation. Correlation effects are then indirectly obtained via superpositions of Slater determinants over the Fock space, as in configuration interaction, coupled-cluster and tensor-decomposition methods. These are computationally costly methods, especially with large basis sets. In quantum chemistry, explicitly-correlated methods usually proceed via the R12 formalism of Kutzelnigg [3], and its more modern F12 variants [4], in combination with perturbation theory [5] or coupled-cluster theory [6]. These methods augment the Fock-space (configurational) wavefunctions with strongly-orthogonal geminal terms with fixed amplitudes, imposing a first-order cusp condition. This approximation is suitable for systems whose ground state wavefunction is dominated by a single determinant. The inclusion of explicit correlation in strongly correlated, multi-determinantal, wavefunctions remains an open challenge.In this...

We suggest an efficient method to resolve electronic cusps in electronic structure calculations, through the use of an effective transcorrelated Hamiltonian. This effective Hamiltonian takes a simple form for plane wave bases, containing up to two-body operators only, and its use incurs almost no additional computational overhead compared to that of the original Hamiltonian. We apply this method in combination with the full configuration interaction quantum Monte Carlo (FCIQMC) method to the homogeneous electron gas. As a projection technique, the non-Hermitian nature of the [physics.comp-ph]

Similarity transformation of the Hubbard Hamiltonian using a Gutzwiller correlator leads to a non-Hermitian effective Hamiltonian, which can be expressed exactly in momentum-space representation, and contains three-body interactions. We apply this methodology to study the two-dimensional Hubbard model with repulsive interactions near half-filling in the intermediate interaction strength regime (U/t = 4). We show that at optimal or near optimal strength of the Gutzwiller correlator, the similarity transformed Hamiltonian has extremely compact right eigenvectors, which can be sampled to high accuracy using the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method, and its initiator approximation.Near-optimal correlators can be obtained using a simple projective equation, thus obviating the need for a numerical optimisation of the correlator. The FCIQMC method, as a projective technique, is well-suited for such non-Hermitian problems, and its stochastic nature can handle the 3-body interactions exactly without undue increase in computational cost. The highly compact nature of the right eigenvectors means that the initiator approximation in FCIQMC is not severe, and that large lattices can be simulated, well beyond the reach of the method applied to the original Hubbard Hamiltonian. Results are provided in lattice sizes up to 50 sites and compared to auxiliary-field QMC. New benchmark results are provided in the off half-filling regime, with no severe sign-problem being encountered. In addition, we show that methodology can be used to calculate excited states of the Hubbard model and lay the groundwork for the calculation of observables other than the energy. |e J − e ex | J = 0.0 J = -0.2 J = -0.25 σ 0.0 σ −0.2 σ −0.25 10 3 10 4 10 5 10 6 10 7 N w J = 0.0 J = -0.3 J = -0.5

We demonstrate how similarity-transformed full configuration interaction quantum Monte Carlo (FCIQMC) based on the transcorrelated Hamiltonian can be applied to make highly accurate predictions for the binding curve of the beryllium dimer, marking the first case study of a molecular system with this method. In this context, the non-Hermitian transcorrelated Hamiltonian, resulting from a similarity transformation with a Jastrow factor, serves the purpose to effectively address dynamic correlation beyond the used basis set and thus allows for obtaining energies close to the complete basis set limit from FCIQMC already with moderate basis sets and computational effort. Building on results from other explicitly correlated methods, we discuss the role of the Jastrow factor and its functional form, as well as potential sources for size consistency errors, and arrive at Jastrow forms that allow for high accuracy calculations of the vibrational spectrum of the beryllium dimer.