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...