Reliable radical stabilization energies from diffusion Monte Carlo calculations.

We assess the performance of variational (VMC) and diffusion (DMC) quantum Monte Carlo methods for calculating the radical stabilization energies of a set of 43 carbon-centered radical species. Even using simple single-determinant trial wavefunctions, both methods perform exceptionally well, with mean absolute deviations from reference values well under the chemical accuracy standard of 1 kcal/mol. In addition, the use of DMC results in a highly concentrated spread of errors, with all 43 results within chemical accuracy at the 95% confidence level. These results indicate that DMC is an extremely reliable method for calculating radical stabilization energies and could be used as a benchmark method for larger systems in future.

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.

Density functional orbitals in quantum Monte Carlo: The importance of accurate densities.

There has been significant recent attention surrounding the accuracy of electronic densities produced by modern parameterized density functional approximations (DFAs). Here, we investigate the impact of using orbitals from density functional calculations in fixed-node Diffusion Monte Carlo (DMC) methods, which is common practice in the calculation of large systems. We find that the accuracy of the density is a strong indicator of the quality of the many-body nodal surface produced by a determinant of the corresponding Kohn-Sham orbitals. Functionals which produce the most accurate electronic densities also produce the lowest variational DMC energies, while functionals that produce poor densities lead to significantly higher energies. This result simplifies the process of choosing orbitals for DMC calculations of large systems and suggests that prioritizing accurate densities in the future development of DFAs would also contribute to the continued improvement of DMC.

Energy-based truncation of multi-determinant wavefunctions in quantum Monte Carlo.

We present a method for truncating large multi-determinant expansions for use in diffusion Monte Carlo calculations. Current approaches use wavefunction-based criteria to perform the truncation. Our method is more intuitively based on the contribution each determinant makes to the total energy. We show that this approach gives consistent behaviour across systems with varying correlation character, which leads to effective error cancellation in energy differences. This is demonstrated through accurate calculations of the electron affinity of oxygen and the atomisation energy of the carbon dimer. The approach is simple and easy to implement, requiring only quantities already accessible in standard configuration interaction calculations.

Performance of quantum Monte Carlo for calculating molecular bond lengths.

This work investigates the accuracy of real-space quantum Monte Carlo (QMC) methods for calculating molecular geometries. We present the equilibrium bond lengths of a test set of 30 diatomic molecules calculated using variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods. The effect of different trial wavefunctions is investigated using single determinants constructed from Hartree-Fock (HF) and Density Functional Theory (DFT) orbitals with LDA, PBE, and B3LYP functionals, as well as small multi-configurational self-consistent field (MCSCF) multi-determinant expansions. When compared to experimental geometries, all DMC methods exhibit smaller mean-absolute deviations (MADs) than those given by HF, DFT, and MCSCF. The most accurate MAD of 3 ± 2 × 10(-3) Å is achieved using DMC with a small multi-determinant expansion. However, the more computationally efficient multi-determinant VMC method has a similar MAD of only 4.0 ± 0.9 × 10(-3) Å, suggesting that QMC forces calculated from the relatively simple VMC algorithm may often be sufficient for accurate molecular geometries.

Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo.

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems.

An explicitly correlated approach to basis set incompleteness in full configuration interaction quantum Monte Carlo.

By performing a stochastic dynamic in a space of Slater determinants, the full configuration interaction quantum Monte Carlo (FCIQMC) method has been able to obtain energies which are essentially free from systematic error to the basis set correlation energy, within small and systematically improvable error bars. However, the weakly exponential scaling with basis size makes converging the energy with respect to basis set costly and in larger systems, impossible. To ameliorate these basis set issues, here we use perturbation theory to couple the FCIQMC wavefunction to an explicitly correlated strongly orthogonal basis of geminals, following the [2](R12) approach of Valeev et al. The required one- and two-particle density matrices are computed on-the-fly during the FCIQMC dynamic, using a sampling procedure which incurs relatively little additional computation expense. The F12 energy corrections are shown to converge rapidly as a function of sampling, both in imaginary time and number of walkers. Our pilot calculations on the binding curve for the carbon dimer, which exhibits strong correlation effects as well as substantial basis set dependence, demonstrate that the accuracy of the FCIQMC-F12 method surpasses that of all previous FCIQMC calculations, and that the F12 correction improves results equivalent to increasing the quality of the one-electron basis by two cardinal numbers.

Taming the First-Row Diatomics: A Full Configuration Interaction Quantum Monte Carlo Study.

The initiator full configuration interaction quantum Monte Carlo (i-FCIQMC) method has recently been developed as a highly accurate stochastic electronic structure technique. It has been shown to calculate the exact basis-set ground state energy of small molecules, to within modest stochastic error bars, using tractable computational cost. Here, we use this technique to elucidate an often troublesome series of first-row diatomics consisting of Be2, C2, CN, CO, N2, NO, O2, and F2. Using i-FCIQMC, the dissociation energies of these molecules are obtained almost entirely to within chemical accuracy of experimental results. Furthermore, the i-FCIQMC calculations are performed in a relatively black-box manner, without any a priori knowledge or specification of the wave function. The size consistency of i-FCIQMC is also demonstrated with regards to these diatomics at their more multiconfigurational stretched geometries. The clear and simple i-FCIQMC wave functions obtained for these systems are then compared and investigated to demonstrate the dynamic identification of the dominant determinants contributing to significant static correlation. The appearance and nature of such determinants is shown to provide insight into both the i-FCIQMC algorithm and the diatomics themselves.

Breaking the carbon dimer: the challenges of multiple bond dissociation with full configuration interaction quantum Monte Carlo methods.

The full configuration interaction quantum Monte Carlo (FCIQMC) method, as well as its "initiator" extension (i-FCIQMC), is used to tackle the complex electronic structure of the carbon dimer across the entire dissociation reaction coordinate, as a prototypical example of a strongly correlated molecular system. Various basis sets of increasing size up to the large cc-pVQZ are used, spanning a fully accessible N-electron basis of over 10(12) Slater determinants, and the accuracy of the method is demonstrated in each basis set. Convergence to the FCI limit is achieved in the largest basis with only O[10(7)] walkers within random errorbars of a few tenths of a millihartree across the binding curve, and extensive comparisons to FCI, CCSD(T), MRCI, and CEEIS results are made where possible. A detailed exposition of the convergence properties of the FCIQMC methods is provided, considering convergence with elapsed imaginary time, number of walkers and size of the basis. Various symmetries which can be incorporated into the stochastic dynamic, beyond the standard abelian point group symmetry and spin polarisation are also described. These can have significant benefit to the computational effort of the calculations, as well as the ability to converge to various excited states. The results presented demonstrate a new benchmark accuracy in basis-set energies for systems of this size, significantly improving on previous state of the art estimates.

Strongly absorbing pi-pi* states in heteroleptic dipyrrin/2,2'-bipyridine ruthenium complexes: excited-state dynamics from resonance raman spectroscopy.

A recently reported new class of ruthenium complexes containing 2,2'-bipyridine and a dipyrrin ligand in the coordination sphere exhibit both strong metal-to-ligand charge-transfer (MLCT) and pi-pi* transitions. Quantitative analysis of the resonance Raman scattering intensities and absorption spectra reveals only weak electronic interactions between these states despite direct coordination of the bipyridyl and dipyrrin ligands to the central ruthenium atom. On the basis of DFT calculations and time-dependent DFT (TD-DFT), we propose that the electronic excited states closely resemble "pure" MLCT and pi-pi* states. Resonance Raman intensity analysis demonstrates that a large amplitude transannular torsional motion provides a mechanism for relaxation on the pi-pi* excited-state surface. We assert that this result is generally applicable to a range of dipyrrin complexes such as boron-dipyrrin and metallodipyrrin systems. Despite the large torsional distortion between the phenyl ring and the dipyrromethene plane, pi-pi* excitation extends out onto the phenyl ring which may have important consequences in solar-energy-conversion applications of ruthenium-dipyrrin complexes.

Communications: Survival of the fittest: accelerating convergence in full configuration-interaction quantum Monte Carlo.

We provide a very simple adaptation of our recently published quantum Monte Carlo algorithm in full configuration-interaction (Slater determinant) spaces which dramatically reduces the number of walkers required to achieve convergence. A survival criterion is imposed for newly spawned walkers. We define a set of initiator determinants such that progeny of walkers spawned from such determinants onto unoccupied determinants are able to survive, while the progeny of walkers not in this set can survive only if they are spawned onto determinants which are already occupied. The set of initiators is originally defined to be all determinants constructable from a subset of orbitals, in analogy with complete-active spaces. This set is dynamically updated so that if a noninitiator determinant reaches an occupation larger than a preset limit, it becomes an initiator. The new algorithm allows sign-coherent sampling of the FCI space to be achieved with relatively few walkers. Using the N(2) molecule as an illustration, we show that rather small initiator spaces and numbers of walkers can converge with submilliHartree accuracy to the known full configuration-interaction (FCI) energy (in the cc-pVDZ basis), in both the equilibrium geometry and the multiconfigurational stretched case. We use the same method to compute the energy with cc-pVTZ and cc-pVQZ basis sets, the latter having an FCI space of over 10(15) with very modest computational resources.

Tuning the optical properties of ZnTPP using carbonyl ring fusion.

Zinc meso-tetraphenylporphyrin (ZnTPP) was modified in such a way to allow the effect of an asymmetric structural distortion on its optical properties to be investigated. This involved the fusion of a phenyl group to an adjacent pyrrole ring via a carbonyl bridge. With the aid of Density Functional Theory (DFT) and time-dependent DFT (TD-DFT) calculations it was found that the asymmetric distortion away from planarity induced by the carbonyl fusion resulted in a loss of degeneracy in the two lowest unoccupied molecular orbitals (LUMOs). The effect was a red shift of the electronic absorbance bands, an increased Q:B ratio from 0.046 in ZnTPP to 0.096 in the fused derivative, and the appearance of additional UV-vis peaks. This study therefore suggests that structural distortions, as well as electronic substituents may be used to alter absorbance spectra, a technique which is of interest in the design of light-harvesting dyes.

Linker conjugation effects in rhenium(I) bifunctional hole-transport/emitter molecules.

Spectroscopic, electrochemical and density functional theory (DFT) methods have been employed to investigate a group of [Re(CO)(3)(HT)(phen)](+) complexes (phen = 1,10-phenanthroline), and in particular the level of electronic communication between various hole-transporting (HT) ligands and the rhenium centre. Here, the HT ligand consists of a coordinating pyridine connected to dimethylaniline group through a single-, double- or triple-bond-connecting system. Electronic absorption, resonance Raman, and steady-state emission spectroscopy combined with lifetime studies and DFT calculations suggest that multiple dpi(Re)-->pi*(phen) metal-to-ligand charge transfers (MLCTs) exist for each complex, two of which significantly absorb at about 340 and 385 nm, and one that emits at approximately 540 nm. In the complexes containing more-conjugated HT ligands, non-emissive intraligand transitions (IL(HT)) exist with energies between the ground and MLCT excited states. The overlap of these IL(HT) transitions and the absorbing MLCT of lowest energy deactivates emission resulting from about 385 nm excitation, and lowers the quantum yield and excited-state lifetimes of these complexes. Cyclic voltammetry experiments indicate that throughout the series investigated, the highest occupied molecular orbital (HOMO) of each complex is centred on the HT ligand, while the occupied molecular orbitals localised on the rhenium are lower in energy.