NECI: N-Electron Configuration Interaction with an emphasis on state-of-the-art stochastic methods.

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.

First-order properties from internally contracted multireference coupled-cluster theory with particular focus on hyperfine coupling tensors.

Internally contracted multireference coupled-cluster (icMRCC) theory is extended to the computation of first-order properties (expectation values). We use the previously defined Lagrange formulation of the energy functional to derive the required equations for the Lagrange multipliers and arrive at an expression for first-order properties according to the generalized Hellmann-Feynman theorem, analogous to single-reference coupled-cluster theory. The present formulation does not include orbital relaxation, but in line with previous experience in coupled-cluster theory, the single-excitation cluster operator can recover a significant portion of orbital relaxation. Further aspects of the theory that arise from the internal contraction approach are discussed. Using automated derivation techniques, we have implemented a pilot code for icMRCCSD and icMRCCSDT for testing the method numerically. We find good agreement with full configuration interaction for several properties of boron monohydride and dipole moment curves of hydrogen fluoride and chromium hydride. A particular focus is given to spin-dependent properties: The hyperfine coupling tensors of Σ and Π radicals have been computed and compared to experiment and previous computations. We discuss the problem of describing spin polarization with properly spin-adapted wavefunctions, which requires either including pseudo-triple excitations or employing sufficiently flexible reference functions.

Response Formalism within Full Configuration Interaction Quantum Monte Carlo: Static Properties and Electrical Response.

We formulate a general, arbitrary-order stochastic response formalism within the full configuration interaction quantum Monte Carlo framework. This modified stochastic dynamic allows for the exact response properties of correlated multireference electronic systems to be systematically converged upon for systems far out of reach of traditional exact treatments. This requires a simultaneous coupled evolution of a response state alongside the zero-order state, which is shown to be stable, nontransient, and unbiased. We demonstrate this with application to the static dipole polarizability of molecular systems and, in doing so, resolve a discrepancy between restricted and unrestricted high-level coupled-cluster linear response results which were the high-accuracy benchmark in the literature.

Quantum tunneling during interstellar surface-catalyzed formation of water: the reaction H + H2O2 → H2O + OH.

The final step of the water formation network on interstellar grain surfaces starting from the H + O2 route is the reaction between H and H2O2. This reaction is known to have a high activation energy and therefore at low temperatures it can only proceed via tunneling. To date, however, no rate constants are available at temperatures below 200 K. In this work, we use instanton theory to compute rate constants for the title reaction with and without isotopic substitutions down to temperatures of 50 K. The calculations are based on density functional theory, with additional benchmarks for the activation energy using unrestricted single-reference and multireference coupled-cluster single-point energies. Gas-phase bimolecular rate constants are calculated and compared with available experimental data not only for H + H2O2 → H2O + OH, but also for H + H2O2 → H2 + HO2. We find a branching ratio where the title reaction is favored by at least two orders of magnitude at 114 K. In the interstellar medium this reaction predominantly occurs on water surfaces, which increases the probability that the two reactants meet. To mimic this, one, two, or three spectator H2O molecules are added to the system. Eley-Rideal bimolecular and Langmuir-Hinshelwood unimolecular rate constants are presented here. The kinetic isotope effects for the various cases are compared to experimental data as well as to expressions commonly used in astrochemical models. Both the rectangular barrier and the Eckart approximations lead to errors of about an order of magnitude. Finally, fits of the rate constants are provided as input for astrochemical models.

Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications.

We present here a comprehensive account of the formulation and pilot applications of the second-order perturbative analogue of the recently proposed unitary group adapted state-specific multireference coupled cluster theory (UGA-SSMRCC), which we call as the UGA-SSMRPT2. We also discuss the essential similarities and differences between the UGA-SSMRPT2 and the allied SA-SSMRPT2. Our theory, like its parent UGA-SSMRCC formalism, is size-extensive. However, because of the noninvariance of the theory with respect to the transformation among the active orbitals, it requires the use of localized orbitals to ensure size-consistency. We have demonstrated the performance of the formalism with a set of pilot applications, exploring (a) the accuracy of the potential energy surface (PES) of a set of small prototypical difficult molecules in their various low-lying states, using natural, pseudocanonical and localized orbitals and compared the respective nonparallelity errors (NPE) and the mean average deviations (MAD) vis-a-vis the full CI results with the same basis; (b) the efficacy of localized active orbitals to ensure and demonstrate manifest size-consistency with respect to fragmentation. We found that natural orbitals lead to the best overall PES, as evidenced by the NPE and MAD values. The MRMP2 results for individual states and of the MCQDPT2 for multiple states displaying avoided curve crossings are uniformly poorer as compared with the UGA-SSMRPT2 results. The striking aspect of the size-consistency check is the complete insensitivity of the sum of fragment energies with given fragment spin-multiplicities, which are obtained as the asymptotic limit of super-molecules with different coupled spins.

Excited states with internally contracted multireference coupled-cluster linear response theory.

In this paper, the linear response (LR) theory for the variant of internally contracted multireference coupled cluster (ic-MRCC) theory described by Hanauer and Köhn [J. Chem. Phys. 134, 204211 (2011)] has been formulated and implemented for the computation of the excitation energies relative to a ground state of pronounced multireference character. We find that straightforward application of the linear-response formalism to the time-averaged ic-MRCC Lagrangian leads to unphysical second-order poles. However, the coupling matrix elements that cause this behavior are shown to be negligible whenever the internally contracted approximation as such is justified. Hence, for the numerical implementation of the method, we adopt a Tamm-Dancoff-type approximation and neglect these couplings. This approximation is also consistent with an equation-of-motion based derivation, which neglects these couplings right from the start. We have implemented the linear-response approach in the ic-MRCC singles-and-doubles framework and applied our method to calculate excitation energies for a number of molecules ranging from CH2 to p-benzyne and conjugated polyenes (up to octatetraene). The computed excitation energies are found to be very accurate, even for the notoriously difficult case of doubly excited states. The ic-MRCC-LR theory is also applicable to systems with open-shell ground-state wavefunctions and is by construction not biased towards a particular reference determinant. We have also compared the linear-response approach to the computation of energy differences by direct state-specific ic-MRCC calculations. We finally compare to Mk-MRCC-LR theory for which spurious roots have been reported [T.-C. Jagau and J. Gauss, J. Chem. Phys. 137, 044116 (2012)], being due to the use of sufficiency conditions to solve the Mk-MRCC equations. No such problem is present in ic-MRCC-LR theory.