Electron iso-density surfaces provide a thermodynamically consistent representation of atomic and molecular surfaces.

The surface area of atoms and molecules plays a crucial role in shaping many physiochemical properties of materials. Despite its fundamental importance, precisely defining atomic and molecular surfaces has long been a puzzle. Among the available definitions, a straightforward and elegant approach by Bader describes a molecular surface as an iso-density surface beyond which the electron density drops below a certain cut-off. However, so far neither this theory nor a decisive value for the density cut-off have been amenable to experimental verification due to the limitations of conventional experimental methods. In the present study, we employ a state-of-the-art experimental method based on the recently developed concept of thermodynamically effective (TE) surfaces to tackle this longstanding problem. By studying a set of 104 molecules, a close to perfect agreement between quantum chemical evaluations of iso-density surfaces contoured at a cut-off density of 0.0016 a.u. and experimental results obtained via thermodynamic phase change data is demonstrated, with a mean unsigned percentage deviation of 1.6% and a correlation coefficient of 0.995. Accordingly, we suggest the iso-density surface contoured at an electron density value of 0.0016 a.u. as a representation of the surface of atoms and molecules.

Comparison of Implicit and Explicit Solvent Approaches in Ab Initio Evaluation of Thermochemistry in Solution: Application in Studying Boron Isotope Fractionation in Water.

Evaluation of thermochemistry in solution plays a key role in numerous fields. For this task, the solvent effects are commonly included in theoretical computations based on either implicit or explicit solvent approaches. In the present study, we evaluate and compare the performance of some of the most widely applied methods based on these two approaches. For studying the solvent effect on thermochemistry with an explicit solvent, we demonstrate that partial normal mode analysis with frozen geometry of solvent molecules for multiple solute-solvent configurations can yield quite accurate and reliable results for a drastically reduced computational cost. As a case study, we consider the evaluation of the equilibrium constant for the boron isotope exchange between boric acid and borate (k3-4) in pure and saline water which is of high geochemical importance. Employing three different rigorous and high-precision theoretical approaches, we provide a reliable estimation of k3-4 which is a value within 1.028 to 1.030 for both pure and saline water which is in excellent agreement with experimental data.

Dependence of Vaporization Enthalpy on Molecular Surfaces and Temperature: Thermodynamically Effective Molecular Surfaces.

Approximation of molecular surfaces is of central importance in numerous scientific fields. In this study we theoretically derive a physical model to relate phase-change thermodynamics to molecular surfaces. The model allows accurately predicting vaporization enthalpy of compounds for a wide temperature range without requiring any empirical parameter. Through the new model, we conceptualize thermodynamically effective molecular surfaces and show that they, although only marginally different than van der Waals surfaces, substantially improve predictability of multiple thermodynamic quantities.

Hyperelastic Microcantilever AFM: Efficient Detection Mechanism Based on Principal Parametric Resonance.

The impetus of writing this paper is to propose an efficient detection mechanism to scan the surface profile of a micro-sample using cantilever-based atomic force microscopy (AFM), operating in non-contact mode. In order to implement this scheme, the principal parametric resonance characteristics of the resonator are employed, benefiting from the bifurcation-based sensing mechanism. It is assumed that the microcantilever is made from a hyperelastic material, providing large deformation under small excitation amplitude. A nonlinear strain energy function is proposed to capture the elastic energy stored in the flexible component of the device. The tip-sample interaction is modeled based on the van der Waals non-contact force. The nonlinear equation governing the AFM's dynamics is established using the extended Hamilton's principle, obeying the Euler-Bernoulli beam theory. As a result, the vibration behavior of the system is introduced by a nonlinear equation having a time-dependent boundary condition. To capture the steady-state numerical response of the system, a developed Galerkin method is utilized to discretize the partial differential equation to a set of nonlinear ordinary differential equations (ODE) that are solved by the combination of shooting and arc-length continuation method. The output reveals that while the resonator is set to be operating near twice the fundamental natural frequency, the response amplitude undergoes a significant drop to the trivial stable branch as the sample's profile experiences depression in the order of the picometer. According to the performed sensitivity analysis, the proposed working principle based on principal parametric resonance is recommended to design AFMs with ultra-high detection resolution for surface profile scanning.

Accurate evaluation of combustion enthalpy by ab-intio computations.

Accurate evaluation of combustion enthalpy is of high scientific and industrial importance. Although ab-initio computation of the heat of reactions is one of the promising and well-established approaches in computational chemistry, reliable and precise computation of heat of combustion reactions by ab-initio methods is surprisingly scarce in the literature. A handful of works carried out for this purpose report significant inconsistencies between the computed and experimentally determined combustion enthalpies and suggest empirical corrections to improve the accuracy of the ab-initio predicted data. The main aim of the present study is to investigate the reasons behind those reported inconsistencies and propose guidelines for a high-accuracy estimation of heat of reactions via ab-initio computations. We show comparably accurate prediction of combustion enthalpy of 40 organic molecules based on a DSD-PBEP86 double-hybrid density functional theory approach and CCSD(T)-F12 coupled-cluster computations, with mean unsigned errors with respect to experimental data being below 0.5% for both methods.

Implicitly perturbed Hamiltonian as a class of versatile and general-purpose molecular representations for machine learning.

Unraveling challenging problems by machine learning has recently become a hot topic in many scientific disciplines. For developing rigorous machine-learning models to study problems of interest in molecular sciences, translating molecular structures to quantitative representations as suitable machine-learning inputs play a central role. Many different molecular representations and the state-of-the-art ones, although efficient in studying numerous molecular features, still are suboptimal in many challenging cases, as discussed in the context of the present research. The main aim of the present study is to introduce the Implicitly Perturbed Hamiltonian (ImPerHam) as a class of versatile representations for more efficient machine learning of challenging problems in molecular sciences. ImPerHam representations are defined as energy attributes of the molecular Hamiltonian, implicitly perturbed by a number of hypothetic or real arbitrary solvents based on continuum solvation models. We demonstrate the outstanding performance of machine-learning models based on ImPerHam representations for three diverse and challenging cases of predicting inhibition of the CYP450 enzyme, high precision, and transferrable evaluation of non-covalent interaction energy of molecular systems, and accurately reproducing solvation free energies for large benchmark sets.

Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect.

In recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This paper attempts to explore the free and forced vibrations of a micro/nanobeam made of a hyperelastic material incorporating strain-stiffening, size effect, and moderate rotation. The beam is modelled based on the Euler-Bernoulli beam theory, and strains are obtained via an extended von Kármán theory. Boundary conditions and governing equations are derived by way of Hamilton's principle. The multiple scales method is applied to obtain the frequency response equation, and Hamilton's technique is utilized to obtain the free undamped nonlinear frequency. The influence of important system parameters such as the stiffening parameter, damping coefficient, length of the beam, length-scale parameter, and forcing amplitude on the frequency response, force response, and nonlinear frequency is analyzed. Results show that the hyperelastic microbeam shows a nonlinear hardening behavior, which this type of nonlinearity gets stronger by increasing the strain-stiffening effect. Conversely, as the strain-stiffening effect is decreased, the nonlinear frequency is decreased accordingly. The evidence from this study suggests that incorporating strain-stiffening in hyperelastic beams could improve their vibrational performance. The model proposed in this paper is mathematically simple and can be utilized for other kinds of micro/nanobeams with different boundary conditions.

Improved prediction of solvation free energies by machine-learning polarizable continuum solvation model.

Theoretical estimation of solvation free energy by continuum solvation models, as a standard approach in computational chemistry, is extensively applied by a broad range of scientific disciplines. Nevertheless, the current widely accepted solvation models are either inaccurate in reproducing experimentally determined solvation free energies or require a number of macroscopic observables which are not always readily available. In the present study, we develop and introduce the Machine-Learning Polarizable Continuum solvation Model (ML-PCM) for a substantial improvement of the predictability of solvation free energy. The performance and reliability of the developed models are validated through a rigorous and demanding validation procedure. The ML-PCM models developed in the present study improve the accuracy of widely accepted continuum solvation models by almost one order of magnitude with almost no additional computational costs. A freely available software is developed and provided for a straightforward implementation of the new approach.