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We use full configuration interaction and density matrix quantum Monte Carlo methods to calculate the electronic free energy surface of the nitrogen dimer within the free-energy Born-Oppenheimer approximation. As the temperature is raised from T = 0, we find a temperature regime in which the internal energy causes bond strengthening. At these temperatures, adding in the entropy contributions is required to cause the bond to gradually weaken with increasing temperature. We predict a thermally driven dissociation for the nitrogen dimer between 22,000 to 63,200 K depending on symmetries and basis set. Inclusion of more spatial and spin symmetries reduces the temperature required. The origin of these observations is explored using the structure of the density matrix at various temperatures and bond lengths.

Finite size error is commonly removed from coupled cluster theory calculations by N -1 extrapolations over correlation energy calculations of different system sizes ( N ), where the N -1 scaling comes from the total energy rather than the correlation energy. However, previous studies in the quantum Monte Carlo community suggest an exchange-energy-like power law of N -2/3 should also be present in the correlation energy when using the conventional Coulomb interaction. The rationale for this is that the total energy goes as N -1 and the exchange energy goes as N -2/3 ; thus, the correlation energy should be a combination of these two power laws. Further, in coupled cluster theory, these power laws are related to the low G scaling of the transition structure factor, S ( G ), which is a property of the coupled cluster wave function calculated from the amplitudes. We show here that data from coupled cluster doubles calculations on the uniform electron gas fit a function with a low G behavior of S ( G ) ∼ G . The prefactor for this linear term is derived from the exchange energy to be consistent with an N -2/3 power law at large N . Incorporating the exchange structure factor into the transition structure factor results in a combined structure factor of S ( G ) ∼ G 2 , consistent with an N -1 scaling of the exchange-correlation energy. We then look for the presence of an N -2/3 power law in the energy. To do so, we first develop a plane-wave cutoff scheme with less noise than the traditional basis set used for the uniform electron gas. Then, we collect data from a wide range of electron numbers and densities to systematically test five methods using N -1 scaling, N -2/3 scaling, or combinations of both scaling behaviors. We find that power laws that incorporate both N -1 and N -2/3 scaling perform better than either alone, especially when the prefactor for N -2/3 scaling can be found from exchange energy calculations.

Density matrix quantum Monte Carlo (DMQMC) is a recently developed method for stochastically sampling the N -particle thermal density matrix to obtain exact-on-average energies for model and ab initio systems. We report a systematic numerical study of the sign problem in DMQMC based on simulations of atomic and molecular systems. In DMQMC, the density matrix is written in an outer product basis of Slater determinants. In principle, this means that DMQMC needs to sample a space that scales in the system size, N , as O[(exp(N)) 2 ]. In practice, removing the sign problem requires a total walker population that exceeds a system-dependent critical walker population ( N c ), imposing limitations on both storage and compute time. We establish that N c for DMQMC is the square of N c for FCIQMC. By contrast, the minimum N c in the interaction picture modification of DMQMC (IP-DMQMC) is only linearly related to the N c for FCIQMC. We find that this difference originates from the difference in propagation of IP-DMQMC versus canonical DMQMC: the former is asymmetric, whereas the latter is symmetric. When an asymmetric mode of propagation is used in DMQMC, there is a much greater stochastic error and is thus prohibitively expensive for DMQMC without the interaction picture adaptation. Finally, we find that the equivalence between IP-DMQMC and FCIQMC seems to extend to the initiator approximation, which is often required to study larger systems with large basis sets. This suggests that IP-DMQMC offers a way to ameliorate the cost of moving between a Slater determinant space and an outer product basis.

Recent calculations using coupled cluster on solids have raised the discussion of using a N -1/3 power law to fit the correlation energy when extrapolating to the thermodynamic limit, an approach which differs from the more commonly used N -1 power law, which is, for example, often used by quantum Monte Carlo methods. In this paper, we present one way to reconcile these viewpoints. Coupled cluster doubles calculations were performed on uniform electron gases reaching system sizes of 922 electrons for an extremely wide range of densities (0.1 < r s < 100.0) to study how the correlation energy approaches the thermodynamic limit. The data were corrected for the basis set incompleteness error and use a selected twist angle approach to mitigate the finite size error from shell filling effects. Analyzing these data, we initially find that a power law of N -1/3 appears to fit the data better than a N -1 power law in the large system size limit. However, we provide an analysis of the transition structure factor showing that N -1 still applies to large system sizes and that the apparent N -1/3 power law occurs only at low N .

We here apply the recently developed initiator density matrix quantum Monte Carlo (i-DMQMC) to a variety of atoms and molecules in vacuum. i-DMQMC samples the exact density matrix of a Hamiltonian at finite temperature and combines the accuracy of full configuration interaction quantum Monte Carlo (FCIQMC)-full configuration interaction (FCI) or exact energies in a finite basis set-with finite temperature. In order to explore the applicability of i-DMQMC for molecular systems, we choose to study a recently developed test set by Rubenstein and co-workers: Be, H 2 O, and H 10 at near-equilibrium and stretched geometries. We find that, for Be and H 2 O, i-DMQMC delivers energies with submillihartree accuracy when compared with finite temperature FCI. For H 2 O and both geometries of H 10 , we examine the difference between FT-AFQMC and i-DMQMC, which, in turn, estimates the difference in canonical versus grand canonical energies. We close with two discussions: one of simulation settings (initiator error, the interaction picture, and different basis sets), and another of energy difference calculations in the form of specific heat capacity and ionization potential calculations.

We here develop a fully quantum embedded version of initiator full configuration interaction quantum Monte Carlo ( i -FCIQMC) and apply it to study an ionic bond (lithium hydride, LiH) and a covalent bond (hydrogen flouride, HF) physisorbed to a benzene molecule. The embedding is performed using a recently developed Huzinaga projection operator approach, which affords good synergy with i -FCIQMC by minimizing the number of orbitals in the calculation. When considering the dissociation energy of these bonds into closed-shell ionic fragments, we find that i -FCIQMC embedded in density functional theory ( i -FCIQMC-in-DFT) delivers comparable accuracy with coupled cluster singles and doubles with perturbative triples embedded in density functional theory (CCSD(T)-in-DFT). In treating the bond dissociation energy curve of HF, i -FCIQMC-in-DFT has improved accuracy over CCSD(T)-in-DFT due to the presence of strong correlation. We discuss the implications of the new i -FCIQMC-in-DFT method as applied to bond breaking in catalysis.

The continued development of redox-active ligands requires an understanding as to how ligand modifications and related factors affect the locus of redox activity and spin density in metal complexes. Here we describe the synthesis, characterization, and electronic structure of nickel complexes containing triaryl NNNN ( 1 ) and SNNS ( 2 ) ligands derived from o -phenylenediamine. The tetradentate ligands in 1 and 2 were investigated and compared to those in metal complexes with compositionally similar ligands to determine how ligand-centered redox properties change when redox-active flanking groups are replaced with redox-innocent NMe 2 or SMe. A derivative of 2 in which the phenylene backbone was replaced with ethylene ( 3 ) was also prepared to interrogate the importance of o -phenylenediamine for ligand-centered redox activity. Cyclic voltammograms collected for 1 and 2 revealed two fully reversible ligand-centered redox events. Remarkably, several quasi-reversible ligand-centered redox waves were also observed for 3 despite the absence of the o -phenylenediamine subunit. Oxidizing 1 and 2 with silver salts containing different counteranions (BF 4 - , OTf - , NTf 2 - ) allowed the electrochemically generated complexes to be analyzed as a function of different oxidation states using single-crystal X-ray diffraction (XRD), EPR spectroscopy, and S K-edge X-ray absorption spectroscopy. The experimental data are corroborated by DFT calculations, and together, they reveal how the location of unpaired spin density and electronic structure in singly and doubly oxidized salts of 1 and 2 varies depending on the coordinating ability of the counteranions and exogenous ligands such as pyridine.

Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the past decade. The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact solution of such problems, for cases where very high accuracy is desired. The introduction of FCIQMC has subsequently led to the development of coupled cluster Monte Carlo (CCMC) and density matrix quantum Monte Carlo (DMQMC), allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively. In this Article, we describe the HANDE-QMC code, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semistochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included.

Hybrid interfaces combining inorganic and organic materials underpin the operation of many optoelectronic and photocatalytic systems and allow for innovative approaches to photon up- and down-conversion. However, the mechanism of exchange-mediated energy transfer of spin-triplet excitons across these interfaces remains obscure, particularly when both the macroscopic donor and acceptor are composed of many separately interacting nanoscopic moieties. Here, we study the transfer of excitons from colloidal lead sulfide (PbS) nanocrystals to the spin-triplet state of rubrene molecules. By reducing the length of the carboxylic acid ligands on the nanocrystal surface from 18 to 4 carbon atoms, thinning the effective ligand shell from 13 to 6 Å, we are able to increase the characteristic transfer rate by an order of magnitude. However, we observe that the energy transfer rate asymptotes for shorter separation distances (≤10 Å) which we attribute to the reduced Dexter coupling brought on by the increased effective dielectric constant of these solid-state devices when the aliphatic ligands are short. This implies that the shortest ligands, which hinder long-term colloidal stability, offer little advantage for energy transfer. Indeed, we find that hexanoic acid ligands are already sufficient for near-unity transfer efficiency. Using nanocrystals with these optimal-length ligands in an improved solid-state device structure, we obtain an upconversion efficiency of (7 ± 1)% with excitation at λ = 808 nm.