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.
We recently developed a scheme to use low-cost calculations to find a single twist angle where the coupled cluster doubles energy of a single calculation matches the twist-averaged coupled cluster doubles energy in a finite unit cell. We used initiator full configuration interaction quantum Monte Carlo as an example of an exact method beyond coupled cluster doubles theory to show that this selected twist angle approach had comparable accuracy in methods beyond coupled cluster. Furthermore, at least for small system sizes, we show that the same twist angle can also be found by comparing the energy directly (at the level of second-order Moller–Plesset theory), suggesting a route toward twist angle selection, which requires minimal modification to existing codes that can perform twist averaging.
i),(ii) , 1, a) William Z. Van Benschoten (i),(ii) , 1, a) Sai Kumar Ramadugu (i),(ii) , 1 and James J. Shepherd (i),(ii) 1, b)
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.
A series of polymers that possessed a backbone solely composed of alternating nitrogen and sulfur single bonds were synthesized for the first time. The structures of these polymers were based on polythiazyl (SN)x, which only possesses nitrogen and sulfur and is electrically conducting at room temperature in the absence of doping and superconducting at low temperatures. The polymers reported in this manuscript were synthesized using the reaction between sulfur dichloride (SCl2) and either anilines or octylamine. The isolated yields ranged from 48% to 74%, and the molecular weights were found using light scattering and refractive index detectors to be 6,200–35,000 g mol–1. The UV–vis spectra of the polymers were obtained, and the polymers possessed peak maxima around 450 nm and appeared red. The poly[(N,N-amino)sulfide] (polyNAS) synthesized from octylamine also was red, which demonstrated that the color was due to conjugation along the NS backbone. These polymers are the first polymers containing a backbone of alternating N and S, and are easily processed due to the groups attached to the nitrogens.
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