We propose an approach to the electronic structure problem based on noninteracting electron pairs that has similar computational cost to conventional methods based on noninteracting electrons. In stark contrast to other approaches, the wave function is an antisymmetric product of nonorthogonal geminals, but the geminals are structured so the projected Schrödinger equation can be solved very efficiently. We focus on an approach where, in each geminal, only one of the orbitals in a reference Slater determinant is occupied. The resulting method gives good results for atoms and small molecules. It also performs well for a prototypical example of strongly correlated electronic systems, the hydrogen atom chain.

We present an efficient approach to the electron correlation problem that is well-suited for strongly interacting many-body systems, but requires only mean-field-like computational cost. The performance of our approach is illustrated for the one-dimensional Hubbard model for different ring lengths, and for the non-relativistic quantum chemical Hamiltonian exploring the symmetric dissociation of the H50 hydrogen chain.The accurate description of the electron-electron interaction at the quantum-mechanical level is a key problem in condensed matter physics and quantum chemistry. Since most of the quantum many-body problems are extraordinarily difficult to solve exactly, different approximation schemes emerged [5][6][7][8][9], among which the density matrix renormalization group (DMRG) algorithm [10][11][12] gained a lot of popularity in both condensed matter physics [11] and quantum chemistry [13][14][15][16][17][18][19][20] over the last decade. Since the DMRG algorithm optimizes a matrix product state wavefunction, it is optimally suited for one-dimensional systems; though DMRG studies on higher-dimensional and compact systems have been reported [14,17,19,21]. Yet, novel theoretical approaches are desirable that can accurately describe strong correlation effects between electrons where the dimension of the Hilbert space exceeds the present-day limit of DMRG or general tensor-network approaches [22] allowing approximately 100 sites or 60 (spatial) orbitals, respectively.Another promising approach, suitable for larger strongly-correlated electronic systems, uses geminals (two-electron basis functions) as building blocks for the wavefunction [23][24][25][26][27][28][29][30]. One of the simplest practical geminal approaches is the antisymmetric product of 1-reference-orbital geminals (AP1roG) [31][32][33]. Unique among geminal methods, AP1roG can be rewritten as a fully general pair-coupled-cluster doubles wavefunc- * ayers@mcmaster.ca † dimitri.vanneck@ugent.be tion [34], i.e.where a † pσ and a pσ (σ = ↓, ↑) are the fermionic creation and annihilation operators, and |Φ 0 is some independent-particle wavefunction (usually the HartreeFock determinant). Indices i and a correspond to virtual and occupied sites (orbitals) with respect to |Φ 0 , P and K denote the number of electron pairs (P = N/2 with N being the total number of electrons) and orbitals, respectively, and {c a i } are the geminal coefficients. This wavefunction ansatz is size-extensive and has mean-field scaling, O P 2 (K − P ) 2 for the projected Schrödinger equation approach [31].To ensure size-consistency, however, it is necessary to optimize the one-electron basis functions [31], where all non-redundant orbital rotations span the occupiedoccupied, occupied-virtual, and virtual-virtual blocks with respect to the reference Slater determinant |Φ 0 . We have implemented a quadratically convergent algorithm: we minimize the energy with respect to the choice of the one-particle basis functions, subject to the constraint that the projected Schrödinger equati...

We introduce new nonvariational orbital optimization schemes for the antisymmetric product of one-reference orbital geminal (AP1roG) wave function (also known as pair-coupled cluster doubles) that are extensions to our recently proposed projected seniority-two (PS2-AP1roG) orbital optimization method [ J. Chem. Phys. 2014 , 140 , 214114 )]. These approaches represent less stringent approximations to the PS2-AP1roG ansatz and prove to be more robust approximations to the variational orbital optimization scheme than PS2-AP1roG. The performance of the proposed orbital optimization techniques is illustrated for a number of well-known multireference problems: the insertion of Be into H2, the automerization process of cyclobutadiene, the stability of the monocyclic form of pyridyne, and the aromatic stability of benzene.

We present a new, non-variational orbital-optimization scheme for the antisymmetric product of one-reference orbital geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [L. Bytautas, T. M. Henderson, C. A. Jimenez-Hoyos, J. K. Ellis, and G. E. Scuseria, J. Chem. Phys. 135, 044119 (2011)]. A numerical analysis is performed for the C2 and LiF molecules, for the CH2 singlet diradical as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases.

The orbital dependence of closed-shell wavefunction energies is investigated by performing doublyoccupied configuration interaction (DOCI) calculations, representing the most general class of these wavefunctions. Different local minima are examined for planar hydrogen clusters containing two, four, and six electrons applying (spin) symmetry-broken restricted, unrestricted and generalized orbitals with real and complex coefficients. Contrary to Hartree-Fock (HF), restricted DOCI is found to properly break bonds and thus unrestricted orbitals, while providing a quantitative improvement of the energy, are not needed to enforce a qualitatively correct bond dissociation. For the beryllium atom and the BH diatomic, the lowest possible HF energy requests symmetry-broken generalized orbitals, whereas accurate results for DOCI can be obtained within a restricted formalism. Complex orbital coefficients are shown to increase the accuracy of HF and DOCI results in certain cases.The computationally inexpensive AP1roG geminal wavefunction is proven to agree very well with all DOCI results of this study.2