A quantum computing view on unitary coupled cluster theory.

We present a review of the Unitary Coupled Cluster (UCC) ansatz and related ansätze which are used to variationally solve the electronic structure problem on quantum computers. A brief history of coupled cluster (CC) methods is provided, followed by a broad discussion of the formulation of CC theory. This includes touching on the merits and difficulties of the method and several variants, UCC among them, in the classical context, to motivate their applications on quantum computers. In the core of the text, the UCC ansatz and its implementation on a quantum computer are discussed at length, in addition to a discussion on several derived and related ansätze specific to quantum computing. The review concludes with a unified perspective on the discussed ansätze, attempting to bring them under a common framework, as well as with a reflection upon open problems within the field.

On the order problem in construction of unitary operators for the variational quantum eigensolver.

One of the main challenges in the variational quantum eigensolver (VQE) framework is construction of the unitary transformation. The dimensionality of the space for unitary rotations of N qubits is 4N- 1, which makes the choice of a polynomial subset of generators an exponentially difficult process. Moreover, due to non-commutativity of generators, the order in which they are used strongly affects results. Choosing the optimal order in a particular subset of generators requires testing the factorial number of combinations. We propose an approach based on the Lie algebra-Lie group connection and corresponding closure relations that systematically eliminates the order problem.

Excess electrons bound to H2S trimer and tetramer clusters.

We have prepared the hydrogen sulfide trimer and tetramer anions, (H2S)3- and (H2S)4-, measured their anion photoelectron spectra, and applied high-level quantum chemical calculations to interpret the results. The sharp peaks at low electron binding energies in their photoelectron spectra and their diffuse Dyson orbitals are evidence for them both being dipole-bound anions. While the dipole moments of the neutral (H2S)3 and (H2S)4 clusters are small, the excess electron induces structural distortions that enhance the charge-dipolar attraction and facilitate the binding of diffuse electrons.

Dyson Orbitals and Double Rydberg Anions: Methylated, Annulated, and Paramagnetic.

A double Rydberg anion (DRA) consists of a saturated, closed-shell, molecular cation and two electrons that occupy diffuse orbitals. Techniques of ab initio electron propagator theory (EPT) predict the existence and spectra of three new classes of DRAs. The first, with the formula NH4-n(CH3)n-, has vertical electron detachment energies (VEDEs) that vary between 0.24 and 0.39 eV and corresponding Dyson orbitals that accumulate near the periphery of N-H bonds. An internal hydrogen bond that forms a ring with five members occurs in the second class. In paramagnetic DRA isomers, electrons are assigned to two, diffuse, triplet-coupled spin-orbitals that localize outside the N-H bonds of a cationic, tetrahedral center or outside bonds on a nearby amide or methyl group. Effects of delocalization, dispersion, and radial correlation between diffuse electrons on VEDEs are described in terms of Dyson orbitals and their pole strengths. These concepts of EPT connect ground-state and spectral properties to each other and provide a rigorous, systematic, and insightful approach to predicting and characterizing novel patterns of chemical bonding and molecular electronic structure.

Electron Propagator Methods for Vertical Electron Detachment Energies of Anions: Benchmarks and Case Studies.

Ab initio electron propagator methods are efficient and accurate means of calculating vertical electron detachment energies of closed-shell, molecular anions with nuclei from the first three periods. Basis set extrapolations enable definitive comparisons between electron propagator results and benchmarks defined by total energy differences obtained with coupled-cluster, single, double, plus perturbative triple substitution theory. The best compromises of accuracy and efficiency are provided by the renormalized, partial third-order, diagonal (P3+) self-energy and by the nondiagonal, renormalized, second-order (NR2) approximation. The outer-valence Green function, the two-particle-one-hole Tamm-Dancoff approximation, the third-order algebraic diagrammatic construction, and the renormalized third-order methods also are examined. A detailed analysis of errors for small anions is performed. Case studies include F-(H2O) and Cl-(H2O) complexes, C5H5-, two P2N3- pentagonal rings, and a superhalide, Al(BO2)4-, whose electron detachment energy is more than double those of the halide anions. These applications illustrate the versatility of electron propagator methods, their utility for interpreting negative-ion photoelectron spectra, and their promise in the discovery of unusual properties and patterns of chemical bonding. Composite methods, which combine basis set effects calculated at the relatively efficient diagonal, second-order level and higher correlation effects calculated with small basis sets, provide excellent estimates of basis set-extrapolated P3+ or NR2 results and facilitate applications to large molecules. In the P3+ and NR2 methods, a judicious choice of low-order couplings between hole operators that correspond to the assumptions of Koopmans's theorem and operators that describe final-state relaxation and polarization and initial-state correlation leads to predictive accuracy, computational efficiency, and interpretive lucidity.

Comment on "Are polynuclear superhalogens without halogen atoms probable? A high-level ab initio case study on triple-bridged binuclear anions with cyanide ligands" [J. Chem. Phys. 140, 094301 (2014)].

For the vertical electron detachment energies of triply-bridged Mg2(CN)5- superhalides, the Outer Valence Green Function (OVGF) yields results similar to those of the coupled-cluster singles and doubles plus approximate triples, or CCSD(T), method. Invalid comparisons between states with different symmetry or localization properties underlie the assertion of Yin et al that OVGF produces large discrepancies with respect to CCSD(T) for several isomers of Mg2(CN)5-.

Composite electron propagator methods for calculating ionization energies.

Accurate ionization energies of molecules may be determined efficiently with composite electron-propagator (CEP) techniques. These methods estimate the results of a calculation with an advanced correlation method and a large basis set by performing a series of more tractable calculations in which large basis sets are used with simpler approximations and small basis sets are paired with more demanding correlation techniques. The performance of several CEP methods, in which diagonal, second-order electron propagator results with large basis sets are combined with higher-order results obtained with smaller basis sets, has been tested for the ionization energies of closed-shell molecules from the G2 set. Useful compromises of accuracy and computational efficiency employ complete-basis-set extrapolation for second-order results and small basis sets in third-order, partial third-order, renormalized partial-third order, or outer valence Green's function calculations. Analysis of results for vertical as well as adiabatic ionization energies leads to specific recommendations on the best use of regular and composite methods. Results for 22 organic molecules of interest in the design of photovoltaic devices, benzo[a]pyrene, Mg-octaethylporphyrin, and C60 illustrate the capabilities of CEP methods for calculations on large molecules.

Comment on "Is the regulation of the electronic properties of organic molecules by polynuclear superhalogens more effective than that by mononuclear superhalogens? A high-level ab initio case study" by M.-M. Li, J.-F. Li, H.-C. Bai, Y.-Y. Sun, J.-L. Li and B. Yin, Phys. Chem. Chem. Phys., 2015, 17, 20338.

The Outer Valence Green Function (OVGF) and coupled-cluster singles and doubles plus approximate triples, or CCSD(T), methods yield similar results for the vertical detachment energies of superhalides studied recently by Li et al. The success of the OVGF method contradicts claims by Li et al. in their recent article.

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules IV: Electron-Propagator Methods.

Comparison of ab initio electron-propagator predictions of vertical ionization potentials and electron affinities of organic, acceptor molecules with benchmark calculations based on the basis set-extrapolated, coupled cluster single, double, and perturbative triple substitution method has enabled identification of self-energy approximations with mean, unsigned errors between 0.1 and 0.2 eV. Among the self-energy approximations that neglect off-diagonal elements in the canonical, Hartree-Fock orbital basis, the P3 method for electron affinities, and the P3+ method for ionization potentials provide the best combination of accuracy and computational efficiency. For approximations that consider the full self-energy matrix, the NR2 methods offer the best performance. The P3+ and NR2 methods successfully identify the correct symmetry label of the lowest cationic state in two cases, naphthalenedione and benzoquinone, where some other methods fail.

A generalized any-particle propagator theory: prediction of proton affinities and acidity properties with the proton propagator.

We have recently extended the electron propagator theory to the treatment of any type of particle using an Any-Particle Molecular Orbital (APMO) wavefunction as reference state. This approach, called APMO/PT, has been implemented in the LOWDIN code to calculate correlated binding energies, for any type of particle in molecular systems. In this work, we present the application of the APMO/PT approach to study proton detachment processes. We employed this method to calculate proton binding energies and proton affinities for a set of inorganic and organic molecules. Our results reveal that the second-order proton propagator (APMO/PP2) quantitatively reproduces experimental trends with an average deviation of less than 0.41 eV. We also estimated proton affinities with an average deviation of 0.14 eV and the proton hydration free energy using APMO/PP2 with a resulting value of -270.2 kcal/mol, in agreement with other results reported in the literature. Results presented in this work suggest that the APMO/PP2 approach is a promising tool for studying proton acid/base properties.