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.

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.

Quantification of surface reaction rate constants of the reaction H + H2O2 → H2O + OH at low temperatures with the use of instanton theory.

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.