Chemical language models (CLMs) have emerged as promising competitors to popular classical machine learning models for molecular property prediction (MPP) tasks. However, an increasing number of studies have reported inconsistent and contradictory results for the performance of CLMs across various MPP benchmark tasks. In this study, we conduct and analyze hundreds of meticulously controlled experiments to systematically investigate the effects of various factors, such as dataset size, model size, and standardization, on the pre-training and fine-tuning performance of CLMs for MPP. In the absence of well-established scaling laws for encoder-only masked language models, our aim is to provide comprehensive numerical evidence and a deeper understanding of the underlying mechanisms affecting the performance of CLMs for MPP tasks, some of which appear to be entirely overlooked in the literature.

The simulation environment for atomistic and molecular modeling (SEAMM) is an open-source software package written in Python that provides a graphical interface for setting up, executing, and analyzing molecular and materials simulations. The graphical interface reduces the entry barrier for the use of new simulation tools, facilitating the interoperability of a wide range of simulation tools available to solve complex scientific and engineering problems in computational molecular science. Workflows are represented graphically by user-friendly flowcharts, which are shareable and reproducible. When a flowchart is executed within the SEAMM environment, all results, as well as metadata describing the workflow and codes used, are saved in a datastore that can be viewed using a browser-based dashboard, which allows collaborators to view the results and use the flowcharts to extend the results. SEAMM is a powerful productivity and collaboration tool that enables interoperability between simulation codes and ensures reproducibility and transparency in scientific research. We illustrate the flexibility and productivity of SEAMM with three examples: a simple molecular dynamics calculation to provide an overview; exploring the rearrangement of methylisocyanide to acetonitrile using a wide range of quantum codes and force fields; and using SEAMM for industrial research on battery materials with simulations of the diffusivity and ionic conductivity of electrolytes and the density, thermal expansion, and thermal conductivity of cathode materials as a function of lithiation.

We present a unified representation of the most popular neural network activation functions. Adopting Mittag-Leffler functions of fractional calculus, we propose a flexible and compact functional form that is able to interpolate between various activation functions and mitigate common problems in training neural networks such as vanishing and exploding gradients. The presented gated representation extends the scope of fixed-shape activation functions to their adaptive counterparts whose shape can be learnt from the training data. The derivatives of the proposed functional form can also be expressed in terms of Mittag-Leffler functions making it a suitable candidate for gradient-based backpropagation algorithms. By training multiple neural networks of different complexities on various datasets with different sizes, we demonstrate that adopting a unified gated representation of activation functions offers a promising and affordable alternative to individual built-in implementations of activation functions in conventional machine learning frameworks.

We investigate the numerical accuracy of the extended Koopmans's theorem (EKT) in reproducing the full configuration interaction (FCI) and complete active-space configuration interaction (CAS-CI) ionization energies (IEs) of atomic and molecular systems calculated as the difference between the energies of N and (N - 1) electron states. In particular, we study the convergence of the EKT IEs to their exact values as the basis set and the active space sizes vary. We find that the first FCI EKT IEs approach their exact counterparts as the basis set size increases. However, increasing the basis set or the active space sizes does not always lead to more accurate CAS-CI EKT IEs. Our investigation supports the observation of Davidson et al. [J. Chem. Phys. 155, 051102 (2021)] that the FCI EKT IEs can be systematically improved with arbitrary numerical accuracy by supplementing the basis set with diffuse functions of appropriate symmetry, which allow the detached electron to travel far away from the reference system. By changing the exponent and the center of the diffuse functions, our results delineate a complex pattern for the CAS-CI EKT IE of LiH, which can be important for the spectroscopic studies of small molecules.

The An error in the conversion from LaTeX to XML has occurred here. MolSSI is a research and education center that supports software development in the An error in the conversion from LaTeX to XML has occurred here. CMS. One of An error in the conversion from LaTeX to XML has occurred here. MolSSI’s core objectives is to provide education and training for the next generation of computational researchers. An error in the conversion from LaTeX to XML has occurred here. MolSSI Education targets various career stages and skill levels through its live workshops, online resources, and software fellowship program. An error in the conversion from LaTeX to XML has occurred here. MolSSI Education focuses its efforts within four areas: programming and software development, An error in the conversion from LaTeX to XML has occurred here. HPC and An error in the conversion from LaTeX to XML has occurred here. AI, faculty and curriculum development, and the An error in the conversion from LaTeX to XML has occurred here. MolSSI software fellowship program. This article delineates educational efforts at the An error in the conversion from LaTeX to XML has occurred here. MolSSI, overall goals, and resources that can be useful to researchers in the computational molecular sciences.

The Molecular Sciences Software Institute (MolSSI) is a research and education center that supports software development in the computational molecular sciences (CMS). One of MolSSI's core objectives is to provide education and training for the next generation of computational researchers. MolSSI Education targets various career stages and skill levels through its live workshops, online resources, and software fellowship program. MolSSI Education focuses its efforts on four areas: programming and software development, high-performance computing, artificial intelligence, faculty and curriculum development, and the software fellowship program. This article delineates educational efforts at the MolSSI, overall goals, and resources that can be useful to researchers in the CMS.

The realization of fractional quantum chemistry is presented. Adopting the integro-differential operators of the calculus of arbitrary-order, we develop a general framework for the description of quantum nonlocal effects in the complex electronic environments. After a brief overview of the historical and fundamental aspects of the calculus of arbitrary-order, various classes of fractional Schrödinger equations are discussed and pertinent controversies and open problems around their applications to model systems are detailed. We provide a unified approach toward fractional generalization of the quantum chemical models such as Hartree-Fock and Kohn-Sham density functional theory and develop fractional variants of the fundamental molecular integrals and correlation energy. Furthermore, we offer various strategies for modeling static and dynamic quantum nonlocal effects through constant- and variable-order fractional operators, respectively. Possible directions for future developments of fractional quantum chemistry are also outlined.

The realization of fractional quantum chemistry is presented. Adopting the integro-differential operators of the calculus of arbitrary-order, we develop a general framework for the description of quantum nonlocal effects in the complex electronic environments. After a brief overview of the historical and fundamental aspects of the calculus of arbitrary-order, various classes of fractional Schrodinger equations are discussed and pertinent controversies and open problems around their applications to model systems are detailed. We provide a unified approach toward fractional generalization of the quantum chemical models such as Hartree-Fock and Kohn-Sham density functional theory and develop fractional variants of the fundamental molecular integrals and correlation energy. Furthermore, we offer various strategies for modeling static- and dynamic-order quantum nonlocal effects through constant- and variable-order fractional operators, respectively. Possible directions for future developments of fractional quantum chemistry are also outlined.

A global hybrid extension of multiconfiguration pair-density functional theory (MC-PDFT) is developed. Using a linear decomposition of the electron-electron repulsion term, a fraction λ of the nonlocal exchange interaction, obtained from variational two-electron reduced-density matrix (v2RDM)-driven complete active-space self-consistent field (CASSCF) theory, is combined with its local counterpart, obtained from an on-top pair-density functional. The resulting scheme (called λ-MC-PDFT) inherits the benefits of MC-PDFT (e.g., its simplicity and the resolution of the symmetry dilemma) and, when combined with the v2RDM approach to CASSCF, requires only polynomially scaling computational effort. As a result, λ-MC-PDFT can efficiently describe static and dynamical correlation effects in strongly correlated systems. The efficacy of the approach is assessed for several challenging multiconfigurational problems, including the dissociation of molecular nitrogen, the double dissociation of a water molecule, and the 1,3-dipolar cycloadditions of ozone to ethylene and ozone to acetylene in the O3ADD6 benchmark set.

We present a heterogeneous CPU+GPU algorithm for the direct variational optimization of the two-electron reduced-density matrix (2RDM) under two-particle N-representability conditions. This variational 2RDM (v2RDM) approach is the driver for a polynomially-scaling approximation to configuration-interaction-driven complete active space self-consistent field (CASSCF) theory. For v2RDM-based CASSCF com- putations involving an active space consisting of 50 electrons in 50 orbitals [denoted (50e,50o)], we observe a speedup of a factor of 3.7 when the code is executed on a combination of an NVIDIA TITAN V GPU and an Intel Core i7-6850k CPU, relative to the case when the code is executed on the CPU alone. We use this GPU-accelerated v2RDM-CASSCF algorithm to explore the electronic structure of the 3,k-circumacene and 3,k-periacene series (k=2–7) and compare indicators of polyradical character in the lowest-energy singlet states to those observed for oligoacene molecules. The singlet states in larger circumacene and periacene molecules display the same polyradical characteristics observed in oligoacenes, with the onset of this behavior occuring at smallest k for periacenes, followed by the circumacenes and then the oligoacenes. However, the unpaired electron density that accumulates along the zig-zag edge of the circumacenes is slightly less than that which accumulates in the oligoacenes, while periacenes clearly exhibit the greatest build-up of unpaired electron density in this region.

We present a basis-independent metric to assess the quality of the electron density obtained from Kohn-Sham (KS) density functional theory (DFT). Given an exact reference density, Levy's constrained search (CS) formalism yields the exact non-interacting kinetic energy. The difference between this value and the kinetic energy obtained from a KSDFT procedure employing an approximate density functional serves as a measure of the density-driven error in the KS solution, which complements other error analyses based solely on the density. The CS also has the nice feature that it provides an estimate of the exact kinetic correlation energy as a byproduct of the procedure.

Complete active space self-consistent field (CASSCF) computations can be realized at polynomial cost via the variational optimization of the active-space two-electron reduced-density matrix (2-RDM). Like conventional approaches to CASSCF, variational 2-RDM (v2RDM) driven CASSCF captures nondynamical electron correlation in the active space, but it lacks a description of the remaining dynamical correlation effects. Such effects can be modeled through a combination of v2RDM-CASSCF and on-top pair-density functional theory (PDFT). The resulting v2RDM-CASSCF-PDFT approach provides a computationally inexpensive framework for describing both static and dynamical correlation effects in multiconfigurational and strongly correlated systems. On-top pair-density functionals can be derived from familiar Kohn-Sham exchange-correlation (XC) density functionals through the translation of the v2RDM-CASSCF reference densities [ Li Manni et al. J. Chem. Theory Comput. 2014 , 10 , 3669 - 3680 ]. Translated and fully translated on-top PDFT versions of several common XC functionals are applied to the potential energy curves of N2, H2O, and CN-, as well as to the singlet/triplet energy splittings in the linear polyacene series. Using v2RDM-CASSCF-PDFT and the translated PBE functional, the singlet/triplet energy splitting of an infinitely long acene molecule is estimated to be 4.87 kcal mol-1.

We review the fundamental ideas of free complement (FC) method through its application on both ground and first excited states of helium atom. We have found that lower energies can be obtained with fewer number of terms in the FC expansion of the ground state wavefunction. In this case, the optimization of orbital exponents was not necessary for achieving spectroscopic accuracy, especially at higher orders where the structure of the FC wavefunction converges to that of the exact one. We have discovered that permanents naturally appear in the FC expansion of the first triplet excited state wavefunction. Including permanents in the FC expansion is shown to be energetically important for the first triplet excited state of helium atom whereas it is not computationally favorable at higher orders. Finally, considering the group theoretical properties of the symmetric group S-2 and using immanants, a compact and more elegant form for the FC expansion of the first triplet excited state of the helium atom is achieved.

Based on the relation between quantum mechanical concepts such as effective Hamiltonians (EHs), perturbation theory (PT), and unitary transformations, and phenomenological aspects of spin Hamiltonians (SHs), the present tutorial tries to address the basics of the SH formalism. Using simple physical models and historical important examples, we have reviewed the derivation methods and applications of the SHs for a brief and in‐depth description of various sources of anisotropies and interactions such as electronic (EZ), and nuclear Zeeman (NZ), terms, electron‐exchange interaction (EE), zero‐field splitting (ZFS), spin–spin (SS), spin‐orbit (SO), nuclear quadrupole (NQ), and hyperfine couplings (HFCs), in a step‐wise manner. In this way, this tutorial is tailored for the graduate students and young researchers who intend to begin their studies in the field of magnetism, electron magnetic resonance (EMR), spectroscopy, and related areas. © 2014 Wiley Periodicals, Inc.

Ab initio potential energy curves and transition dipole moments have been calculated for the X 2Σ+, A 2Π and B′ 2Σ+ states of MgH using the multi-reference configuration interaction method with large active space and basis sets. Accurate transition dipole moments are reported at Mg–H distances from 2.2 a0 to 20 a0, and they can be combined with the available experimental data on MgH (analytic and Rydberg-Klein-Rees potential energy curves for the X 2Σ+, A 2Π and B′ 2Σ+ states), to calculate the Einstein A coefficients for all rovibronic transitions of MgH appearing in solar and stellar spectra.