Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data.

We present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules in which Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy.

Dermatoscopic and clinical features of congenital or congenital-type nail matrix nevi: A multicenter prospective cohort study by the International Dermoscopy Society.

BACKGROUND: Congenital nail matrix nevi (NMN) are difficult to diagnose because they feature clinical characteristics suggestive of adult subungual melanoma. Nail matrix biopsy is difficult to perform, especially in children. OBJECTIVE: To describe the initial clinical and dermatoscopic features of NMN appearing at birth (congenital) or after birth but before the age of 5 years (congenital-type). METHODS: We conducted a prospective, international, and consecutive data collection in 102 hospitals or private medical offices across 30 countries from 2009 to 2019. RESULTS: There were 69 congenital and 161 congenital-type NMNs. Congenital and congenital-type NMN predominantly displayed an irregular pattern of longitudinal microlines (n = 146, 64%), reminiscent of subungual melanoma in adults. The distal fibrillar ("brush-like") pattern, present in 63 patients (27.8%), was more frequently encountered in congenital NMN than in congenital-type NMN (P = .012). Moreover, congenital NMN more frequently displayed a periungual pigmentation (P = .029) and Hutchinson's sign (P = .027) than did congenital-type NMN. LIMITATIONS: Lack of systematic biopsy-proven diagnosis and heterogeneity of clinical and dermatoscopic photographs. CONCLUSION: Congenital and congenital-type NMN showed worrisome clinical and dermatoscopic features similar to those observed in adulthood subungual melanoma. The distal fibrillar ("brush-like") pattern is a suggestive feature of congenital and congenital-type NMN.

Machine learning for a finite size correction in periodic coupled cluster theory calculations.

We introduce a straightforward Gaussian process regression (GPR) model for the transition structure factor of metal periodic coupled cluster singles and doubles (CCSD) calculations. This is inspired by the method introduced by Liao and Grüneis for interpolating over the transition structure factor to obtain a finite size correction for CCSD [K. Liao and A. Grüneis, J. Chem. Phys. 145, 141102 (2016)] and by our own prior work using the transition structure factor to efficiently converge CCSD for metals to the thermodynamic limit [Mihm et al., Nat. Comput. Sci. 1, 801 (2021)]. In our CCSD-FS-GPR method to correct for finite size errors, we fit the structure factor to a 1D function in the momentum transfer, G. We then integrate over this function by projecting it onto a k-point mesh to obtain comparisons with extrapolated results. Results are shown for lithium, sodium, and the uniform electron gas.

How the Exchange Energy Can Affect the Power Laws Used to Extrapolate the Coupled Cluster Correlation Energy to the Thermodynamic Limit.

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) ∼ G2, 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.

A shortcut to the thermodynamic limit for quantum many-body calculations of metals.

Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schrödinger equation are crucial for computational materials science. Methods such as coupled cluster theory show potential for widespread adoption if computational cost bottlenecks can be removed. For example, extremely dense k-point grids are required to model long-range electronic correlation effects, particularly for metals. Although these grids can be made more effective by averaging calculations over an offset (or twist angle), the resultant cost in time for coupled cluster theory is prohibitive. We show here that a single special twist angle can be found using the transition structure factor, which provides the same benefit as twist averaging with one or two orders of magnitude reduction in computational time. We demonstrate that this not only works for metal systems but also is applicable to a broader range of materials, including insulators and semiconductors.