Cluster-in-Cluster Approach for Computing MP2-Level Vibrational Infrared Spectra of Large Molecular Clusters.

Constructing the Hessian matrix (HM) for large molecules demands huge computational resources. Here, we report a cluster-in-cluster (CIC) procedure for efficiently evaluating HM and dipole derivatives for large molecular clusters by employing the second-order Møller-Plesset perturbation (MP2) theory. The highlight of the proposal is the separation of the estimations of Hartree-Fock (HF) and post-HF components. The parent cluster with n molecules is divided (virtually) into n subclusters centering each monomer and accommodating its near neighbors decided by a distance cutoff. The HF-level HM is obtained by doing full calculation (FC), while the correlation part is approximated by the respective subclusters. A software automating the procedure [followed by calculating infrared (IR) frequencies and intensities] is applied to deduce the IR spectrum for a variety of molecular clusters, particularly water clusters of various sizes, containing up to ∼2000 basis functions. The accuracy of the IR spectrum constructed using CIC is remarkable, with a substantial time advantage (with respect to its FC counterpart). The reduced computational resources and the tractability of the computations are other major benefits of the procedure.

Hydrogen bond energy estimation (H-BEE) in large molecular clusters: A Python program for quantum chemical investigations.

A procedure, derived from the fragmentation-based molecular tailoring approach (MTA), has been proposed and extensively applied by Deshmukh and Gadre for directly estimating the individual hydrogen bond (HB) energies and cooperativity contributions in molecular clusters. However, the manual fragmentation and high computational cost of correlated quantum chemical methods make the application of this method to large molecular clusters quite formidable. In this article, we report an in-house developed software for automated hydrogen bond energy estimation (H-BEE) in large molecular clusters. This user-friendly software is essentially written in Python and executed on a Linux platform with the Gaussian package at the backend. Two approximations to the MTA-based procedure, viz. the first spherical shell (SS1) and the Fragments-in-Fragments (Frags-in-Frags), enabling cost-effective, automated evaluation of HB energies and cooperativity contributions, are also implemented in this software. The software has been extensively tested on a variety of molecular clusters and is expected to be of immense use, especially in conjunction with correlated methods such as MP2, CCSD(T), and so forth.

REAlgo: Rapid and efficient algorithm for estimating MP2/CCSD energy gradients for large molecular clusters.

This work reports the development of an algorithm for rapid and efficient evaluation of energy gradients for large molecular clusters employing correlated methods viz. second-order Møller-Plesset perturbation theory (MP2) theory and couple cluster singles and doubles (CCSD). The procedure segregates the estimation of Hartree-Fock (HF) and correlation components. The HF energy and gradients are obtained by performing a full calculation. The correlation energy is approximated as the corresponding two-body interaction energy. Correlation gradients for each monomer are approximated from the respective monomer-centric fragments comprising its immediate neighbours. The programmed algorithm is explored for the geometry optimization of large molecular clusters using the BERNY optimizer as implemented in the Gaussian suite of software. The accuracy and efficacy of the method are critically probed for a variety of large molecular clusters containing up to 3000 basis functions, in particular large water clusters. The CCSD level geometry optimization of molecular clusters containing ∼800 basis functions employing a modest hardware is also reported.

Topology of electrostatic potential and electron density reveals a covalent to non-covalent carbon-carbon bond continuum.

The covalent and non-covalent nature of carbon-carbon (CC) interactions in a wide range of molecular systems can be characterized using various methods, including the analysis of molecular electrostatic potential (MESP), represented as V(r), and the molecular electron density (MED), represented as ρ(r). These techniques provide valuable insights into the bonding between carbon atoms in different molecular environments. By uncovering a fundamental exponential relationship between the distance of the CC bond and the highest eigenvalue (λv1) of V(r) at the bond critical point (BCP), this study establishes the continuum model for all types of CC interactions, including transition states. The continuum model is further delineated into three distinct regions, namely covalent, borderline cases, and non-covalent, based on the gradient, , with the bond distance of the CC interaction. For covalent interactions, this parameter exhibits a more negative value than -5.0 a.u. Å-1, while for non-covalent interactions, it is less negative than -1.0 a.u. Å-1. Borderline cases, which encompass transition state structures, fall within the range of -1.0 to -5.0 a.u. Å-1. Furthermore, this study expands upon Popelier's analysis of the Laplacian of the MED, denoted as ∇2ρ, to encompass the entire spectrum of covalent, non-covalent, and borderline cases of CC interactions. Therefore, the present study presents compelling evidence supporting the concept of a continuum model for CC bonds in chemistry. Additionally, this continuum model is further explored within the context of C-N, C-O, C-S, N-N, O-O, and S-S interactions, albeit with a limited dataset.

Combining fragmentation method and high-performance computing: Geometry optimization and vibrational spectra of proteins.

Exploring the structures and spectral features of proteins with advanced quantum chemical methods is an uphill task. In this work, a fragment-based molecular tailoring approach (MTA) is appraised for the CAM-B3LYP/aug-cc-pVDZ-level geometry optimization and vibrational infrared (IR) spectra calculation of ten real proteins containing up to 407 atoms and 6617 basis functions. The use of MTA and the inherently parallel nature of the fragment calculations enables a rapid and accurate calculation of the IR spectrum. The applicability of MTA to optimize the protein geometry and evaluate its IR spectrum employing a polarizable continuum model with water as a solvent is also showcased. The typical errors in the total energy and IR frequencies computed by MTA vis-à-vis their full calculation (FC) counterparts for the studied protein are 5-10 millihartrees and 5 cm-1, respectively. Moreover, due to the independent execution of the fragments, large-scale parallelization can also be achieved. With increasing size and level of theory, MTA shows an appreciable advantage in computer time as well as memory and disk space requirement over the corresponding FCs. The present study suggests that the geometry optimization and IR computations on the biomolecules containing ∼1000 atoms and/or ∼15 000 basis functions using MTA and HPC facility can be clearly envisioned in the near future.

On the Short-Range Nature of Cooperativity in Hydrogen-Bonded Large Molecular Clusters.

The variation in the hydrogen bond (HB) strength has considerable consequences on the physicochemical properties of molecular clusters. Such a variation mainly arises due to the cooperative/anti-cooperative networking effect of neighboring molecules connected by HBs. In the present work, we systematically study the effect of neighboring molecules on the strength of an individual HB and the respective cooperativity contribution toward each of them in a variety of molecular clusters. For this purpose, we propose a use of a small model of a large molecular cluster called the spherical shell-1 (SS1) model. This SS1 model is constructed by placingg the spheres of an appropriate radius centered on X and Y atoms of the X-H···Y HB under consideration. The molecules falling within these spheres constitute the SS1 model. Utilizing this SS1 model, the individual HB energies are calculated within the molecular tailoring approach-based framework and the results are compared with their actual counterparts. It is found that the SS1 is a reasonably good model of large molecular clusters, providing 81-99% of the total HB energy estimated using the actual molecular clusters. This in turn suggests that the maximum cooperativity contribution toward a particular HB is due to the fewer number of molecules (in the SS1 model) directly interacting with two molecules involved in its formation. We further demonstrate that the remaining part of the energy or cooperativity (∼1 to 19%) is captured by the molecules falling in the second spherical shell (SS2) centered on the hetero-atom of the molecules in the SS1 model. The effect of increasing size of a cluster on the strength of a particular HB, calculated by the SS1 model, is also investigated. The calculated value of the HB energy remains unchanged with the increase in the size of a cluster, emphasizing the short-ranged nature of the HB cooperativity in neutral molecular clusters.

A Healthy Diet is Associated with a Lower Risk of Hepatic Fibrosis.

BACKGROUND: Higher diet quality is associated with a lower risk of NAFLD. OBJECTIVES: We examined the relationship between diet quality and hepatic fibrosis. METHODS: We analyzed cross-sectional associations between 3 a priori diet quality scores-the Dietary Approaches to Stop Hypertension (DASH) score, the Alternative Healthy Eating Index (AHEI), and a modified Mediterranean-style Diet Score (MDS)-and hepatic fat [controlled attenuation parameter (CAP)] and fibrosis [liver stiffness measurement (LSM)] measured by vibration-controlled transient elastography (VCTE) in 2532 Framingham Heart Study (FHS) participants and 3295 participants of the National Health and Nutrition Examination Survey (NHANES). RESULTS: Higher diet quality scores were associated with lower LSM in both FHS and NHANES after adjustment for demographic and lifestyle factors. Additional adjustment for CAP or BMI attenuated the observed associations. Association strength was similar across all 3 diet quality scores. Fixed-effect meta-analysis demonstrated that, under CAP-adjusted models, the LSM decreases associated with 1-SD increase of the DASH, AHEI, and MDS scores were 2% (95% CI: 0.7%, 3.3%; P = 0.002), 2% (95% CI: 0.7%, 3.3%; P = 0.003), and 1.7% (95% CI: 0.7%, 2.6%; P = 0.001), respectively, whereas in the meta-analysis of BMI-adjusted models, LSM reductions associated with 1-SD increase of the DASH, AHEI, and MDS scores were 2.2% (95% CI: -0.1%, 2.2%; P = 0.07), 1.5% (95% CI: 0.3%, 2.7%; P = 0.02), and 0.9 (95% CI: -0.1%, 1.9%; P = 0.07), respectively. CONCLUSIONS: We demonstrated associations of higher diet quality with favorable hepatic fat and fibrosis measures. Our data suggest that a healthy diet may reduce the likelihood of obesity and hepatic steatosis as well as the progression of steatosis to fibrosis.

Ring-Polymer Instanton Tunneling Splittings of Tropolone and Isotopomers using a Δ-Machine Learned CCSD(T) Potential: Theory and Experiment Shake Hands.

Tropolone, a 15-atom cyclic molecule, has received much interest both experimentally and theoretically due to its H-transfer tunneling dynamics. An accurate theoretical description is challenging owing to the need to develop a high-level potential energy surface (PES) and then to simulate quantum-mechanical tunneling on this PES in full dimensionality. Here, we tackle both aspects of this challenge and make detailed comparisons with experiments for numerous isotopomers. The PES, of near CCSD(T)-quality, is obtained using a Δ-machine learning approach starting from a pre-existing low-level DFT PES and corrected by a small number of approximate CCSD(T) energies obtained using the fragmentation-based molecular tailoring approach. The resulting PES is benchmarked against DF-FNO-CCSD(T) and CCSD(T)-F12 calculations. Ring-polymer instanton calculations of the splittings, obtained with the Δ-corrected PES are in good agreement with previously reported experiments and a significant improvement over those obtained using the low-level DFT PES. The instanton path includes heavy-atom tunneling effects and cuts the corner, thereby avoiding passing through the conventional saddle-point transition state. This is in contradistinction with typical approaches based on the minimum-energy reaction path. Finally, the subtle changes in the splittings for some of the heavy-atom isotopomers seen experimentally are reproduced and explained.

Electrostatic Potential for Exploring Electron Delocalization in Infinitenes, Circulenes, and Nanobelts.

The π-conjugation, aromaticity, and stability of the newly synthesized 12-infinitene and of other infinitenes comprising 8-, 10-, 14-, and 16-arene rings are investigated using density functional theory. The π-electron delocalization and aromatic character rooted in infinitenes are quantified in terms of molecular electrostatic potential (MESP) topology. Structurally, the infinitene bears a close resemblance of its helically twisted structure to the infinity symbol. The MESP topology shows that infinitene possesses an infinity-shaped delocalization of the electron density that streams over the fused benzenoid rings. The parameter ∑i=13Δλi, derived from the eigenvalues (λi) corresponding to the MESP minima, is used for quantifying the aromatic character of arene rings of infinitene. The structure, stability, and MESP topology features of 8-, 10-, 12-, 14-, and 16-infinitenes are also compared with the corresponding isomeric circulenes and carbon nanobelts. Further, the strain in all such systems is evaluated by considering the respective isomeric planar benzenoid hydrocarbons as reference systems. The 12-infinitene turns out to be the most aromatic and the least strained among all the systems examined.

Constructing Potential Energy Surface with Correlated Theory for Dipeptides Using Molecular Tailoring Approach.

We demonstrate a cost-effective alternative employing the fragment-based molecular tailoring approach (MTA) for building the potential energy surface (PES) for two dipeptides viz. alanine-alanine and alanine-proline employing correlated theory, with augmented Dunning basis sets. About 1369 geometries are generated for each test dipeptide by systematically varying the dihedral angles Φ ${{\rm{\Phi }}}$ and Ψ ${{{\Psi }}}$ . These conformational geometries are partially optimized by relaxing all the other Z-matrix parameters, fixing the values of Φ ${{\rm{\Phi }}}$ and Ψ ${{{\Psi }}}$ . The MP2 level PES is constructed from the MTA-energies of chemically intact geometries using minimal hardware. The fidelity of MP2/aug-cc-pVDZ level PES is brought out by comparing it with its full calculation counterpart. Further, we bring out the power of the method by reporting the MTA-based CCSD/aug-cc-pVDZ level PES for these two dipeptides containing 498 and 562 basis functions respectively.

Development and testing of an algorithm for efficient MP2/CCSD(T) energy estimation of molecular clusters with the 2-body approach.

This work reports the development and testing of an automated algorithm for estimating the energies of weakly bound molecular clusters employing correlated theory. Firstly, the monomers and dimers of (homo/hetero) clusters are identified, and the sum of one-body and two-body contributions to correlation energy is calculated. The addition of this contribution to the Hartree-Fock full calculation (FC) energies provides a good estimate of the total energies at Møller-Plesset second-order perturbation theory (MP2)/coupled-cluster method with singles and doubles (CCSD) (T)-level theory using augmented Dunning basis sets. The estimated energies for several test clusters show an excellent agreement with their FC counterparts, with a substantial wall-clock time saving employing off-the-shelf hardware. Furthermore, the complete basis set (CBS) limit for MP2 energy computed using the two-body approach also agrees with its CBS energy with its FC counterpart.

Hydration shell model for expeditious and reliable individual hydrogen bond energies in large water clusters.

Recently, we have developed and tested a method, based on the molecular tailoring approach (MTA-based) to directly estimate the individual hydrogen bond (HB) energies in molecular clusters. Application of this MTA-based method to large molecular clusters is prohibitively difficult due to the evaluation of the energy of large-sized fragments. We propose here a smaller model system called the shell model, to overcome this difficulty. The shell model represents the first hydration shell of water molecules involved in the formation of HB under consideration. Utilizing the shell model as a parent system, fragmentation is carried out, in a fashion similar to the actual MTA-based method, to estimate individual HB energies in large water clusters (Wn, n = 10-16, 18 and 20). The estimated individual HB energies in these Wn clusters, employing the shell model, fall between 0.2 and 12.5 kcal mol-1 at the MP2/aug-cc-pVTZ level, with no net loss in the cooperativity contribution. We have also applied this shell model-based approach to estimate individual HB energies in the two lowest energy conformers of ammonia octamers (NH3)8 and mixed hydrogen fluoride-water clusters. The estimated individual HB energies employing the shell model, in all these molecular clusters studied in this work, are in good agreement with their actual MTA-based counterparts. The typical difference is less than 1 kcal mol-1. Importantly, the shell model has a huge computational time advantage over the actual MTA-based method and it requires only modest hardware.

Enabling Rapid and Accurate Construction of CCSD(T)-Level Potential Energy Surface of Large Molecules Using Molecular Tailoring Approach.

The construction of a potential energy surface (PES) of even a medium-sized molecule employing correlated theory, such as CCSD(T), is arduous due to the high computational cost involved. The present study reports the possibility of efficiently constructing such a PES of molecules containing up to 15 atoms and 550 basis functions by employing the fragment-based molecular tailoring approach (MTA) on off-the-shelf hardware. The MTA energies at the CCSD(T)/aug-cc-pVTZ level for several geometries of three test molecules, viz., acetylacetone, N-methylacetamide, and tropolone, are reported. These energies are in excellent agreement with their full calculation counterparts with a time advantage factor of 3-5. The energy barrier from the ground to transition state is also accurately captured. Further, we demonstrate the accuracy and efficiency of MTA for estimating the energy gradients at the CCSD(T) level. As a further application of our MTA methodology, the energies of acetylacetone at ∼430 geometries are computed at the CCSD(T)/aug-cc-pVTZ level and used for generating a Δ-machine learning (Δ-ML) PES. This leads to the H-transfer barrier of 3.02 kcal/mol, well in agreement with the benchmarked barrier of 3.19 kcal/mol. The fidelity of this Δ-ML PES is examined by geometry optimization and normal mode frequency calculations of global minima and saddle point geometries. We trust that the present work is a major development for the rapid and accurate construction of PES at the CCSD(T) level for molecules containing up to 20 atoms and 600 basis functions using off-the-shelf hardware.

Temporal dynamics of the neural representation of hue and luminance polarity.

Hue and luminance contrast are basic visual features. Here we use multivariate analyses of magnetoencephalography data to investigate the timing of the neural computations that extract them, and whether they depend on common neural circuits. We show that hue and luminance-contrast polarity can be decoded from MEG data and, with lower accuracy, both features can be decoded across changes in the other feature. These results are consistent with the existence of both common and separable neural mechanisms. The decoding time course is earlier and more temporally precise for luminance polarity than hue, a result that does not depend on task, suggesting that luminance contrast is an updating signal that separates visual events. Meanwhile, cross-temporal generalization is slightly greater for representations of hue compared to luminance polarity, providing a neural correlate of the preeminence of hue in perceptual grouping and memory. Finally, decoding of luminance polarity varies depending on the hues used to obtain training and testing data. The pattern of results is consistent with observations that luminance contrast is mediated by both L-M and S cone sub-cortical mechanisms.

Unusually Large Hydrogen-Bond Cooperativity in Hydrogen Fluoride Clusters, (HF)n, n = 3 to 8, Revealed by the Molecular Tailoring Approach.

In this work, our recently proposed molecular tailoring approach (MTA)-based method is employed for the evaluation of individual hydrogen-bond (HB) energies in linear (L) and cyclic (C) hydrogen fluoride clusters, (HF)n (n = 3 to 8). The estimated individual HB energies calculated at the MP2(full)/aug-cc-pVTZ level for the L-(HF)n are between 6.2 to 9.5 kcal/mol and those in the C-(HF)n lie between 7.9 to 11.4 kcal/mol. The zero-point energy corrections and basis set superposition corrections are found to be very small (less than 0.6 and 1.2 kcal/mol, respectively). The cooperativity contribution toward individual HBs is seen to fall between 1.0 to 4.8 kcal/mol and 3.2 to 6.9 kcal/mol for linear and cyclic clusters, respectively. Interestingly, the HB energies in dimers, cleaved from these clusters, lie in a narrow range (4.4 to 5.2 kcal/mol) suggesting that the large HB strength in (HF)n clusters is mainly due to the large cooperativity contribution, especially for n ≥ 5 (50 to 62% of the HBs energy). Furthermore, the HB energies in these clusters show a good qualitative correlation with geometrical parameters (H···F distance and F-H···F angles), stretching frequencies of F-H bonds, and electron density values at the (3, -1) bond critical points.

Antiaromaticity-Aromaticity Interplay in Fused Benzenoid Systems Using Molecular Electrostatic Potential Topology.

The phenomenon of antiaromaticity-aromaticity interplay in aromatic-antiaromatic (A-aA)-fused systems is studied using molecular electrostatic potential (MESP) analysis, which clearly brings out the electron-rich π-regions of molecular systems. Benzene, naphthalene, phenanthrene, and pyrene are the aromatic units and cyclobutadiene and pentalene are the antiaromatic units considered to construct the A-aA-fused systems. The fused system is seen to reduce the antiaromaticity by adopting a configuration containing the least number of localized bonds over antiaromatic moieties. This is clearly observed in 25 isomers of a fused system composed of three naphthalene and two cyclobutadiene units. Denoting the number of π-bonds in the cyclobutadiene rings by the notation (n, n'), the systems belonging to the class (0, 0) and (2, 2) turn out to be the most and least stable configurations, respectively. The stability of the fused system depends on the empty π-character of the antiaromatic ring, hence naphthalene and benzene prefer to fuse with cyclobutadiene in a linear and angular fashion, respectively. Generally, a configuration with the maximum number of 'empty' rings (0, 0, 0, ...) is considered to be the most stable for the given A-aA system. The stability and aromatic/antiaromatic character of A-aA-fused systems with pentalene is also interpreted in a similar way. MESP topology, clearly bringing out the distribution of double bonds in the fused systems, leads to a simple interpretation of the aromatic/antiaromatic character of them. Also, it leads to powerful predictions on stable macrocyclic A-aA systems.

Molecular Tailoring Approach for Estimating Individual Intermolecular Interaction Energies in Benzene Clusters.

There is no general method available for the estimation of individual intermolecular interaction energies in weakly bound molecular clusters, and such studies are limited only to the dimer. Recently, we proposed a molecular tailoring approach-based method for the estimation of individual O-H···O hydrogen bond energies in water clusters. In the present work, we extend the applicability of this method for estimating the individual intermolecular interaction energies in benzene clusters, which are expected to be small. The basis set superposition error (BSSE)-corrected individual intermolecular interaction energies in linear (LN) benzene clusters, LN-(Bz)n n = 3-7, were calculated to be in the range from -1.75 to -2.33 kcal/mol with the cooperativity contribution falling between 0.05 and 0.20 kcal/mol, calculated at the MP2.5/aug-cc-pVDZ level of theory. In the case of non-linear (NLN) benzene clusters, NLN-(Bz)n n = 3-5, the BSSE-corrected individual intermolecular interaction energies exhibit a wider range from -1.16 to -2.55 kcal/mol with cooperativity contribution in the range from 0.02 to -0.61 kcal/mol. The accuracy of these estimated values was validated by adding the sum of interaction energies to the sum of monomer energies. These estimated molecular energies of clusters were compared with their actual calculated values. The small difference (<0.3 kcal/mol) in these two values suggests that our estimated individual intermolecular interaction energies in benzene clusters are quite reliable.

Electrostatic Potential Topology for Probing Molecular Structure, Bonding and Reactivity.

Following the pioneering investigations of Bader on the topology of molecular electron density, the topology analysis of its sister field viz. molecular electrostatic potential (MESP) was taken up by the authors' groups. Through these studies, MESP topology emerged as a powerful tool for exploring molecular bonding and reactivity patterns. The MESP topology features are mapped in terms of its critical points (CPs), such as bond critical points (BCPs), while the minima identify electron-rich locations, such as lone pairs and π-bonds. The gradient paths of MESP vividly bring out the atoms-in-molecule picture of neutral molecules and anions. The MESP-based characterization of a molecule in terms of electron-rich and -deficient regions provides a robust prediction about its interaction with other molecules. This leads to a clear picture of molecular aggregation, hydrogen bonding, lone pair-π interactions, π-conjugation, aromaticity and reaction mechanisms. This review summarizes the contributions of the authors' groups over the last three decades and those of the other active groups towards understanding chemical bonding, molecular recognition, and reactivity through topology analysis of MESP.

Molecular Tailoring Approach for the Estimation of Intramolecular Hydrogen Bond Energy.

Hydrogen bonds (HBs) play a crucial role in many physicochemical and biological processes. Theoretical methods can reliably estimate the intermolecular HB energies. However, the methods for the quantification of intramolecular HB (IHB) energy available in the literature are mostly empirical or indirect and limited only to evaluating the energy of a single HB. During the past decade, the authors have developed a direct procedure for the IHB energy estimation based on the molecular tailoring approach (MTA), a fragmentation method. This MTA-based method can yield a reliable estimate of individual IHB energy in a system containing multiple H-bonds. After explaining and illustrating the methodology of MTA, we present its use for the IHB energy estimation in molecules and clusters. We also discuss the use of this method by other researchers as a standard, state-of-the-art method for estimating IHB energy as well as those of other noncovalent interactions.