Coupled Cluster Valence Bond Method: Efficient Computer Implementation and Application to Multiple Bond Dissociations and Strong Correlations in the Acenes

Geminal-based electronic structure methods in quantum chemistry. Toward a geminal model chemistry

In this review, we discuss the recent progress in developing geminal-based theories for challenging problems in quantum chemistry. Specifically, we focus on the antisymmetrized geminal power, generalized valence bond, antisymmetrized product of strongly orthogonal geminals, singlet-type orthogonal geminals, the antisymmetric product of 1-reference orbital geminal, also known as the pair coupled cluster doubles ansatz, and geminals constructed from Richardson-Gaudin states. Furthermore, we review various corrections to account for the missing dynamical correlation effects in geminal models and possible extensions to target electronically excited states and open-shell species. Finally, we discuss some numerical examples and present-day challenges for geminal-based models, including a quantitative and qualitative analysis of wave functions, and software availability.

Resolving the π-assisted U-N σf-bond formation using quantum information theory

We model the potential energy profiles of the UO₂ (NCO)Cl₂^- → NUOCl₂^- + CO₂ reaction pathway [Y. Gong, V. Vallet, M. del Carmen Michelini, D. Rios and J. K. Gibson, J. Phys. Chem. A, 2014, 118, 325-330] using different pair coupled-cluster doubles (pCCD) methods. Specifically, we focus on pCCD and pCCD-tailored coupled cluster models in predicting relative energies for the various intermediates and transition states along the reaction coordinate. Furthermore, we augment our study on energetics with an orbital-pair correlation analysis of the complete reaction pathway that features two distinct paths. Our analysis of orbital correlations sheds new light on the formation and breaking of respective bonds between the uranium, oxygen, and nitrogen atoms along the reaction coordinates where the "yl" bond is broken and a nitrido compound formed. Specifically, the strengthening of the U-N σ_f-bond is assisted by a π-type interaction that is delocalized over the C-N-U backbone of the UO₂ (NCO)Cl₂^- complex.

Non-iterative Method for Constructing Valence Antibonding Molecular Orbitals and a Molecule-adapted Minimum Basis

While bonding molecular orbitals exhibit constructive interference relative to atomic orbitals, antibonding orbitals show destructive interference. When full localization of occupied orbitals into bonds is possible, bonding and antibonding orbitals exist in 1:1 correspondence with each other. Antibonding orbitals play an important role in chemistry because they are frontier orbitals that determine orbital interactions, as well as much of the response of the bonding orbital to perturbations. In this work, we present an efficient method to construct antibonding orbitals by finding the orbital that yields the maximum opposite spin pair correlation amplitude in second order perturbation theory (AB2) and compare it with other techniques with increasing the size of the basis set. We conclude the AB2 antibonding orbitals are a more robust alternative to the Sano orbitals as initial guesses for valence bond calculations, due to having a useful basis set limit. The AB2 orbitals are also useful for efficiently constructing an active space, and work as good initial guesses for valence excited states. In addition, when combined with the localized occupied orbitals, and relocalized, the result is a set of molecule-adapted minimal basis functions that is built without any reference to atomic orbitals of the free atom. As examples, they are applied to population analysis of halogenated methane derivatives, H-Be-Cl, and \ce{SF6} where they show some advantages relative to good alternative methods.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Block-Localized Excitation for Excimer Complex and Diabatic Coupling

We describe a block-localized excitation (BLE) method to carry out constrained optimization of block-localized orbitals for constructing valence bond-like, diabatic excited configurations using multistate density functional theory (MSDFT). The method is an extension of the previous block-localized wave function method through a fragment-based ΔSCF approach to optimize excited determinants within a molecular complex. In BLE, both the number of electrons and the electronic spin of different fragments in a whole system can be constrained, whereas electrostatic, exchange, and polarization interactions among different blocks can be fully taken into account of. To avoid optimization collapse to unwanted states, a ΔSCF projection scheme and a maximum overlap of wave function approach have been presented. The method is illustrated by the excimer complex of two naphthalene molecules. With a minimum of eight spin-adapted configurational state functions, it was found that the inversion of L_a^- and L_b^- states near the optimal structure of the excimer complex is correctly produced, which is in quantitative agreement with DMRG-CASPT2 calculations and experiments. Trends in the computed transfer integrals associated with excited-state energy transfer both in the singlet and triplet states are discussed. The results suggest that MSDFT may be used as an efficient approach to treat intermolecular interactions in excited states with a minimal active space (MAS) for interpretation of the results and for dynamic simulations, although the selection of a small active space is often system dependent.

FCIQMC-Tailored Distinguishable Cluster Approach

The tailored approach is applied to the distinguishable cluster method together with a stochastic FCI solver (FCIQMC). It is demonstrated that the new method is more accurate than the corresponding tailored coupled cluster and the pure distinguishable cluster methods. An F12 correction for tailored methods and FCIQMC is introduced, which drastically improves the basis set convergence. A new black-box approach to define the active space using the natural orbitals from the distinguishable cluster is evaluated and found to be a convenient alternative to the usual CASSCF approach.

Polynomial-product states: A symmetry-projection-based factorization of the full coupled cluster wavefunction in terms of polynomials of double excitations

Our goal is to remedy the failure of symmetry-adapted coupled-cluster theory in the presence of strong correlation. Previous work along these lines has taken us from a diagram-level analysis of the coupled-cluster equations to an understanding of the collective modes which can occur in various channels of the coupled-cluster equations to the exploration of non-exponential wavefunctions in efforts to combine coupled-cluster theory with symmetry projection. In this manuscript, we extend these efforts by introducing a new, polynomial product wavefunction ansatz that incorporates information from symmetry projection into standard coupled-cluster theory in a way that attempts to mitigate the effects of the lack of size extensivity and size consistency characteristic of symmetry-projected methods. We describe the new approach in detail within the context of our previous efforts, explore some illustrative calculations, and consider one route for reducing the computational cost of the new method.

Geminal perturbation theory based on the unrestricted Hartree-Fock wavefunction

A perturbative correction exploiting natural orbitals and the pair function structure of the unrestricted Hartree-Fock (UHF) wavefunction is devised. The method offers a simple framework for describing multireference systems where static correlation is captured by UHF. The UHF wavefunction is built of two-electron fragments (geminals), involving both singlet and triplet (m_s = 0) parts. At order zero of the perturbative treatment, configuration interaction coefficients of UHF geminals are relaxed. The zero order Hamiltonian is of the Dyall-type, including explicit two-electron interaction within geminals and leading to a formal 6th power scaling. Adopting an effective one-electron zero order Hamiltonian term for the subset of virtual orbitals reduces scaling of the correction step to 4th power. Formal properties of the proposed schemes are discussed. Energetic data and natural occupation numbers of illustrative test systems are used to assess the new approach. The cases where the wavefunction becomes essentially spin pure at the level of reference show good performance. Spin contamination remaining at order zero is found to undermine the perturbative correction.

Distinguishing artificial and essential symmetry breaking in a single determinant: approach and application to the C60, C36, and C20 fullerenes

The existence of a generalized Hartree–Fock solution in C₆₀ has led to controversy on whether C₆₀ is polyradicaloid (or strongly correlated). We attempt to end the controversy with κ-OOMP2 which removes the illusion of this artificial symmetry breaking. We conclude that C₆₀ is not strongly correlated.

Generalized Unitary Coupled Cluster Wave functions for Quantum Computation

We introduce a unitary coupled-cluster (UCC) ansatz termed k-UpCCGSD that is based on a family of sparse generalized doubles operators, which provides an affordable and systematically improvable unitary coupled-cluster wave function suitable for implementation on a near-term quantum computer. k-UpCCGSD employs k products of the exponential of pair coupled-cluster double excitation operators (pCCD), together with generalized single excitation operators. We compare its performance in both efficiency of implementation and accuracy with that of the generalized UCC ansatz employing the full generalized single and double excitation operators (UCCGSD), as well as with the standard ansatz employing only single and double excitations (UCCSD). k-UpCCGSD is found to show the best scaling for quantum computing applications, requiring a circuit depth of [Formula: see text], compared with [Formula: see text] for UCCGSD, and [Formula: see text] for UCCSD, where N is the number of spin orbitals and η is the number of electrons. We analyzed the accuracy of these three ansätze by making classical benchmark calculations on the ground state and the first excited state of H₄ (STO-3G, 6-31G), H₂O (STO-3G), and N₂ (STO-3G), making additional comparisons to conventional coupled cluster methods. The results for ground states show that k-UpCCGSD offers a good trade-off between accuracy and cost, achieving chemical accuracy for lower cost of implementation on quantum computers than both UCCGSD and UCCSD. UCCGSD is also found to be more accurate than UCCSD but at a greater cost for implementation. Excited states are calculated with an orthogonally constrained variational quantum eigensolver approach. This is seen to generally yield less accurate energies than for the corresponding ground states. We demonstrate that using a specialized multideterminantal reference state constructed from classical linear response calculations allows these excited state energetics to be improved.

Automatic Construction of the Initial Orbitals for Efficient Generalized Valence Bond Calculations of Large Systems

We propose an efficient general strategy for generating initial orbitals for generalized valence bond (GVB) calculations which makes routine black-box GVB calculations on large systems feasible. Two schemes are proposed, depending on whether the restricted Hartree-Fock (RHF) wave function is stable (scheme I) or not (scheme II). In both schemes, the first step is the construction of active occupied orbitals and active virtual orbitals. In scheme I, active occupied orbitals are composed of the valence orbitals (the inner core orbitals are excluded), and the active virtual orbitals are obtained from the original virtual space by requiring its maximum overlap with the virtual orbital space of the same system at a minimal basis set. In scheme II, active occupied orbitals and active virtual orbitals are obtained from the set of unrestricted natural orbitals (UNOs), which are transformed from two sets of unrestricted HF spatial orbitals. In the next step, the active occupied orbitals and active virtual ones are separately transformed to localized orbitals. Localized occupied and virtual orbital pairs are formed using the Kuhn-Munkres (KM) algorithm and are used as the initial guess for the GVB orbitals. The optimized GVB wave function is obtained using the second-order self-consistent-field algorithm in the GAMESS program. With this procedure, GVB energies have been obtained for the lowest singlet and triplet states of polyacenes (up to decacene with 96 pairs) and the singlet ground state of two di-copper-oxygen-ammonia complexes. We have also calculated the singlet-triplet gaps for some polyacenes and the relative energy between two di-copper-oxygen-ammonia complexes with the block-correlated second-order perturbation theory based on the GVB reference.

A simplified ab initio treatment of diradicaloid structures produced from stretching and breaking chemical bonds

With a proper choice of active spaces, the single root perturbation theory employing improved virtual orbitals can flawlessly describe the ground, excited, ionized, and dissociated states having varying degrees of degeneracy at the expense of low computational cost.

A Deterministic Projector Configuration Interaction Approach for the Ground State of Quantum Many-Body Systems

In this work we propose a novel approach to solve the Schrödinger equation which combines projection onto the ground state with a path-filtering truncation scheme. The resulting projector configuration interaction (PCI) approach realizes a deterministic version of the full configuration interaction quantum Monte Carlo (FCIQMC) method [Booth, G. H.; Thom, A. J. W.; Alavi, A. J. Chem. Phys. 2009, 131, 054106]. To improve upon the linearized imaginary-time propagator, we develop an optimal projector scheme based on an exponential Chebyshev expansion in the limit of an infinite imaginary time step. After writing the exact projector as a path integral in determinant space, we introduce a path filtering procedure that truncates the size of the determinantal basis and approximates the Hamiltonian. The path filtering procedure is controlled by one real threshold that determines the accuracy of the PCI energy and is not biased toward any determinant. Therefore, the PCI approach can equally well describe static and dynamic electron correlation effects. This point is illustrated in benchmark computations on N2 at both equilibrium and stretched geometries. In both cases, the PCI achieves chemical accuracy with wave functions that contain less than 0.5% determinants of full CI space. We also report computations on the ground state of C2 with up to quaduple-ζ basis sets and wave functions as large as 200 million determinants, which allow a direct comparison of the PCI, FCIQMC, and density matrix renormalization group (DMRG) methods. The size of the PCI wave function grows modestly with the number of unoccupied orbitals, and its accuracy may be tuned to match that of FCIQMC and DMRG.

Electronic Properties of Zigzag Graphene Nanoribbons Studied by TAO-DFT

Accurate prediction of the electronic properties of zigzag graphene nanoribbons (ZGNRs) has been very challenging for conventional electronic structure methods due to the presence of strong static correlation effects. To meet the challenge, we study the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, and symmetrized von Neumann entropy (i.e., a measure of polyradical character) of hydrogen-terminated ZGNRs with different widths and lengths using our recently developed thermally-assistedoccupation density functional theory (TAO-DFT) [Chai, J.-D. J. Chem. Phys. 2012, 136, 154104], a very efficient method for the study of large strongly correlated systems. Our results are in good agreement with the available experimental and high-accuracy ab initio data. The ground states of ZGNRs are shown to be singlets for all the widths and lengths investigated. With the increase of ribbon length, the singlet-triplet energy gaps, vertical ionization potentials, and fundamental gaps decrease monotonically, while the vertical electron affinities and symmetrized von Neumann entropy increase monotonically. On the basis of the calculated orbitals and their occupation numbers, the longer ZGNRs are shown to possess increasing polyradical character in their ground states, where the active orbitals are mainly localized at the zigzag edges.