High-level Theory Research Articles

Efficient and Accurate Approach To Estimate Hybrid Functional and Large Basis-Set Contributions to Condensed-Phase Systems and Molecule-Surface Interactions.

We present a graph theoretic approach to adaptively compute contributions from many-body approximations in an efficient manner and perform accurate hybrid density functional theory (DFT) electronic structure calculations for condensed-phase systems. The salient features of the approach are ONIOM-like. (a) The full-system calculation is performed at a lower level of theory (pure DFT) by enforcing periodic boundary conditions. (b) This treatment is then improved through a correction term that captures many-body interactions up to any given order within a higher (in this case, hybrid DFT) level of theory. (c) In the spirit of ONIOM, contributions from the many-body approximations that arise from the higher level of theory [i.e., from (b) above] are included through extrapolation from the lower level calculation. The approach is implemented in a general, system-independent, fashion using the graph-theoretic functionalities available within Python. For example, the individual one-body components within the unit cell are designated as "nodes" within a graph. The interactions between these nodes are captured through edges, faces, tetrahedrons, and so forth, thus building a many-body interaction hierarchy. Electronic energy extrapolation contributions from all of these geometric entities are included within the above-mentioned ONIOM paradigm. The implementation of the method simultaneously uses multiple electronic structure packages. Here, for example, we present results which use both the Gaussian suite of electronic structure programs and the Quantum ESPRESSO program within a single calculation. Thus, the method integrates both plane-wave basis functions and atom-centered basis functions within a single structure calculation. The method is demonstrated for a range of condensed-phase problems for computing (i) hybrid DFT energies for condensed-phase systems at pure DFT cost and (ii) large, triple-zeta, multiply polarized, and diffuse atom-centered basis-set energies at computational costs commensurate with much smaller sets of basis functions. The methods are demonstrated through calculations performed on (a) homogeneous water surfaces as well as heterogeneous surfaces that contain organic solutes studied using two-dimensional periodic boundary conditions and (b) bulk simulations of water enforced through three-dimensional periodic boundary conditions. A range of structures are considered, and in all cases, the results are in good agreement with those obtained using large atom-centered basis and hybrid DFT calculations on the full periodic systems at significantly lower cost.

Conclusive determination of ethynyl radical hydrogen abstraction energetics and kinetics*

The ethynyl radical (C 2 H) is ubiquitous, appearing in a variety of environments from interstellar space to oxy-acetylene flames. Under these diverse conditions, ethynyl has a high affinity to abstract hydrogen atoms from nearby molecules. In this study, C 2 H + HX → C 2 H 2 + X , X = CH 3 , NH 2 , OH, F, PH 2 , SH, Cl, C 2 H, CN, and NC reactions have been examined at a rigorously high level of theory. Various additive corrections have been appended to the coupled-cluster framework to converge the relative enthalpy of stationary points on the C 2 H + HX surfaces to subchemical accuracy (≤0.5 kcal mol − 1 ). The barriers for the abstraction of a hydrogen from NH 3 , PH 3 , and H 2 S are submerged below the relative enthalpy of their reactant asymptotes by 2.75, 2.48, and 1.39 kcal mol − 1 , respectively. ions from H 2 , CH 4 , H 2 O, and HCl are predicted to have moderate barriers to the abstraction of 2.64, 0.77, 3.82, and 2.19 kcal mol − 1 , respectively, suggesting these reactions will be significant to various systems at moderate to high temperatures. Accurate kinetics were obtained for the C 2 H + H 2 , CH 4 , NH 3 , and H 2 O reactions over a wide range of temperatures with excellent agreement to present experimental rate constants.

The Role of Structural Representation in the Performance of a Deep Neural Network for X-Ray Spectroscopy.

An important consideration when developing a deep neural network (DNN) for the prediction of molecular properties is the representation of the chemical space. Herein we explore the effect of the representation on the performance of our DNN engineered to predict Fe K-edge X-ray absorption near-edge structure (XANES) spectra, and address the question: How important is the choice of representation for the local environment around an arbitrary Fe absorption site? Using two popular representations of chemical space—the Coulomb matrix (CM) and pair-distribution/radial distribution curve (RDC)—we investigate the effect that the choice of representation has on the performance of our DNN. While CM and RDC featurisation are demonstrably robust descriptors, it is possible to obtain a smaller mean squared error (MSE) between the target and estimated XANES spectra when using RDC featurisation, and converge to this state a) faster and b) using fewer data samples. This is advantageous for future extension of our DNN to other X-ray absorption edges, and for reoptimisation of our DNN to reproduce results from higher levels of theory. In the latter case, dataset sizes will be limited more strongly by the resource-intensive nature of the underlying theoretical calculations.

Coupled-cluster techniques for computational chemistry: The CFOUR program package.

An up-to-date overview of the CFOUR program system is given. After providing a brief outline of the evolution of the program since its inception in 1989, a comprehensive presentation is given of its well-known capabilities for high-level coupled-cluster theory and its application to molecular properties. Subsequent to this generally well-known background information, much of the remaining content focuses on lesser-known capabilities of CFOUR, most of which have become available to the public only recently or will become available in the near future. Each of these new features is illustrated by a representative example, with additional discussion targeted to educating users as to classes of applications that are now enabled by these capabilities. Finally, some speculation about future directions is given, and the mode of distribution and support for CFOUR are outlined.

Multistate QM/QM Extrapolation of UV/Vis Absorption Spectra with Point Charge Embedding.

The simulation of UV/vis absorption spectra of large chromophores is prohibitively expensive with accurate quantum mechanical (QM) methods. Thus, hybrid methods, which treat the core chromophoric region at a high level of theory while the substituent effects are treated with a more computationally efficient method, may provide the best compromise between cost and accuracy. The ONIOM (Our own N-layered Integrated molecular Orbital molecular Mechanics) method has proved successful at describing ground-state processes. However, for excited states, it suffers from difficulties in matching the correct excited states among the different levels of theory. We devised an approach, based on the ONIOM extrapolation formula, to combine two QM levels of theory to extrapolate entire excitation bands rather than individual states. In this contribution, we extend the same QM/QM hybrid scheme to include polarization effects on the core region through point charge embedding. The charges are computed to reproduce the electrostatic potential of the entire chromophore at the low level of theory, with proper constraints to avoid overpolarization issues at the boundary between layers. We test this approach on a variety of model compounds that show how the multistate QM/QM-embedding scheme is able to accurately reproduce the spectrum of the entire system at the high level of theory better than (i) the bare QM/QM hybrid scheme, (ii) the low-level calculation on the entire system, and (iii) the high-level calculation on the core region.

Embedded, graph‐theoretically defined many‐body approximations for wavefunction‐in‐DFT and DFT‐in‐DFT: Applications to gas‐ and condensed‐phase ab initio molecular dynamics, and potential surfaces for quantum nuclear effects

AbstractWe present a graph‐theoretic approach to adaptively compute many‐body approximations in an efficient manner to perform (a) accurate post‐Hartree–Fock (HF) ab initio molecular dynamics (AIMD) at density functional theory (DFT) cost for medium‐ to large‐sized molecular clusters, (b) hybrid DFT electronic structure calculations for condensed‐phase simulations at the cost of pure density functionals, (c) reduced‐cost on‐the‐fly basis extrapolation for gas‐phase AIMD and condensed phase studies, and (d) accurate post‐HF‐level potential energy surfaces at DFT cost for quantum nuclear effects. The salient features of our approach are ONIOM‐like in that (a) the full system (cluster or condensed phase) calculation is performed at a lower level of theory (pure DFT for condensed phase or hybrid DFT for molecular systems), and (b) this approximation is improved through a correction term that captures all many‐body interactions up to any given order within a higher level of theory (hybrid DFT for condensed phase; CCSD or MP2 for cluster), combined through graph‐theoretic methods. Specifically, a region of chemical interest is coarse‐grained into a set of nodes and these nodes are then connected to form edges based on a given definition of local envelope (or threshold) of interactions. The nodes and edges together define a graph, which forms the basis for developing the many‐body expansion. The methods are demonstrated through (a) ab initio dynamics studies on protonated water clusters and polypeptide fragments, (b) potential energy surface calculations on one‐dimensional water chains such as those found in ion channels, and (c) conformational stabilization and lattice energy studies on homogeneous and heterogeneous surfaces of water with organic adsorbates using two‐dimensional periodic boundary conditions.

Probing the ionization potentials of the formaldehyde dimer.

In this work, we present a computational investigation on the ionization potentials (IPs) of the formaldehyde dimer, (H2CO)2. Twelve lowest lying IPs (corresponding to the entire valence orbitals) for both C2h and Cs symmetry conformers have been computed at the coupled cluster level of theory using large correlation consistent basis sets with extrapolation to the complete basis set limit and consideration of core electron correlation effects. Specifically, the equation-of-motion ionization potential coupled-cluster with single and double (EOMIP-CCSD) excitations method with the aug-cc-pVXZ and aug-cc-pCVXZ (X = T, Q, and 5) basis sets combined with the Feller-Peterson-Dixon approach was employed, as well as CCSD with perturbative triples [CCSD(T)] with the aug-cc-pVTZ basis sets. In general, excellent agreement was observed from the comparison between the results obtained through the use of these approaches. In addition, the IPs for the formaldehyde monomer were also obtained using such methodologies and the results compared with existing experimental data; excellent agreement was also observed in this case. To the best of our knowledge, this work represents the first of its kind to determine the IPs for all these systems using a high level theory approach and is presented to motivate experimental investigations, e.g., studies involving photoionization, particularly for the formaldehyde dimer. The equilibrium binding energy of the C2h dimer is calculated in this work at the CCSD(T)/aug-cc-pVTZ level of theory to be -4.71 kcal/mol. At this same level of theory, the equilibrium isomerization energy between C2h and Cs conformers is 0.76 kcal/mol (Cs conformer being more stable).

Neural network interpolation of exchange-correlation functional

Density functional theory (DFT) is one of the most widely used tools to solve the many-body Schrodinger equation. The core uncertainty inside DFT theory is the exchange-correlation (XC) functional, the exact form of which is still unknown. Therefore, the essential part of DFT success is based on the progress in the development of XC approximations. Traditionally, they are built upon analytic solutions in low- and high-density limits and result from quantum Monte Carlo numerical calculations. However, there is no consistent and general scheme of XC interpolation and functional representation. Many different developed parametrizations mainly utilize a number of phenomenological rules to construct a specific XC functional. In contrast, the neural network (NN) approach can provide a general way to parametrize an XC functional without any a priori knowledge of its functional form. In this work, we develop NN XC functionals and prove their applicability to 3-dimensional physical systems. We show that both the local density approximation (LDA) and generalized gradient approximation (GGA) are well reproduced by the NN approach. It is demonstrated that the local environment can be easily considered by changing only the number of neurons in the first layer of the NN. The developed NN XC functionals show good results when applied to systems that are not presented in the training/test data. The generalizability of the formulated NN XC framework leads us to believe that it could give superior results in comparison with traditional XC schemes provided training data from high-level theories such as the quantum Monte Carlo and post-Hartree-Fock methods.

Ab Initio Prediction of the Phase Transition for Solid Ammonia at High Pressures

Ammonia is one of the most basic components on the planet and its high-pressure characteristics play an important role in planetary science. Solid ammonia crystals frequently adopt multiple distinct polymorphs exhibiting different properties. Predicting the crystal structure of these polymorphs and under what thermodynamic conditions these polymorphs are stable would be of great value to environmental industry and other fields. Theoretical calculations based on the classical force fields and density-functional theory (DFT) are versatile methods but lack of accurate description of weak intermolecular interactions for molecular crystals. In this study, we employ an ab initio computational study on the solid ammonia at high pressures, using the second-order Møller-Plesset perturbation (MP2) theory and the coupled cluster singles, doubles, and perturbative triples (CCSD(T)) theory along with the embedded fragmentation method. The proposed algorithm is capable of performing large-scale calculations using high-level wavefunction theories, and accurately describing covalent, ionic, hydrogen bonding, and dispersion interactions within molecular crystals, and therefore can predict the crystal structures, Raman spectra and phase transition of solid ammonia phases I and IV accurately. We confirm the crystal structures of solid ammonia phases I and IV that have been controversial for a long time and predict their phase transition that occurs at 1.17 GPa and 210 K with small temperature dependence, which is in line with experiment.

Computational spectroscopy of diatomic tungsten carbide, WC

The bond length, electronic term symbols, bond dissociation energies (BDEs), and spectroscopic parameters of numerous low-lying electronic states of diatomic tungsten carbide (WC) have been calculated at a high level of theory. The calculations were done by using the Internally-Contracted multi-reference wave function IC-MRCI/aug-cc-pV5Z(-PP) approach. Davidson corrections were also included using the MRCI + Q method. Zero-point vibrational energy (ZPE) corrections, spin–orbit interactions, and relativistic effects are also included. The bond dissociation energy, equilibrium internuclear distance and the harmonic vibrational frequency of the ground electronic state WC(X3Δ) are computed to be D0 = 5.26 eV, Re = 1.714 Å and ωe = 979 cm−1, respectively. The energies of the lowest vibrational levels (v = 0, 1, 2 and 3) of WC(X3 Δ) are computed to be (0.00, 979.7, 1948.9, 2903.6 cm−1); their rotational constants, Bv, are also computed as (0.50717, 0.50966, 0.49990 and 0.49626 cm−1), respectively. Spectroscopic parameters (ωe, ωexe, Be and αe) and equilibrium bond lengths (Re) for several Λ-S and Ω bound states of WC are also provided in this work. These results are in excellent agreement with the available experimental data.

Predicting pKa Using a Combination of Semi-Empirical Quantum Mechanics and Radial Basis Function Methods.

The acid dissociation constant (pKa) has an important influence on molecular properties crucial to compound development in synthesis, formulation, and optimization of absorption, distribution, metabolism, and excretion properties. We will present a method that combines quantum mechanical calculations, at a semi-empirical level of theory, with machine learning to accurately predict pKa for a diverse range of mono- and polyprotic compounds. The resulting model has been tested on two external data sets, one specifically used to test pKa prediction methods (SAMPL6) and the second covering known drugs containing basic functionalities. Both sets were predicted with excellent accuracy (root-mean-square errors of 0.7-1.0 log units), comparable to other methodologies using a much higher level of theory and computational cost.

Dark Energy: is it ‘just’ Einstein's Cosmological Constant Λ?

The Cosmological Constant Λ, a concept introduced by Einstein in 1917, has been with us ever since in different variants and incarnations, including the broader concept of ‘Dark Energy’. Current observations are consistent with a value of Λ corresponding to about present-epoch 70% of the critical density of the Universe. This is causing the speeding up (acceleration) of the expansion of the Universe. Coupled with the flatness of the Universe and the amount of 30% matter (5% baryonic and 25% ‘Cold Dark Matter’), this forms the so-called ‘ΛCDM standard model’. However, there are currently indications of inconsistencies (‘tensions’ ) within ΛCDM on different values of the Hubble Constant and the clumpiness factor. Also, time variation of Dark Energy and slight deviations from General Relativity are not ruled out yet. Several grand projects are underway to test ΛCDM further. If ΛCDM will remain the standard model, then the ball is back in the theoreticians' court, to explain the physical meaning of Λ. Is Λ an alteration to the geometry of the Universe, or the energy of the vacuum? Or maybe it is something different, that manifests a yet unknown higher-level theory?

A theoretical study of X‐H∙∙∙π and X∙∙∙π interactions in the complexes of furan, thiophene, pyrrole and hydrogen halides

AbstractBy using ab initio geometry optimization calculations we obtained thirteen stable complexes containing H∙∙∙π and X∙∙∙π interactions between Furan, Thiophene, Pyrrole and HX (X = F, Cl, Br) at the MP2/6‐311++G(3df,2pd) high level of theory. The interaction energies corrected for only ZPE and both ZPE and BSSE range from ‐7.92 to ‐28.47 kJ.mol‐1 and ‐3.28 to ‐22.33 kJ.mol‐1, respectively. The results show that for the same HX, the stability of complexes decreases in going from Pyrrole to Thiophene and finally to Furan moiety, and increases in the order of HF < HCl < HBr monomer with the same π‐system. The obtained results from AIM and MEP analyses indicate that the H∙∙∙π interaction is more stable than X∙∙∙π one in all the investigated complexes. It is found that the electrostatic, dispersion and induction energy terms significantly contribute to strength of the studied complexes, in which two formers are for H∙∙∙π hydrogen bonded complexes and two latters are for X∙∙∙π halogen bonded complexes.

Identification of Water Hexamer on Cu(111) Surfaces.

While being considered as the building block of ice on a hydrophobic metal surface, the global minimum of the water hexamer is still elusive, which has impeded our understanding of water/metal interfaces. Herein, we comprehensively investigate water hexamer on Cu(111) theoretically and propose the boat configuration as the new in situ adsorption configuration from the scanning tunneling microscope experiments. All existing experimental measurements can therefore be well reproduced. Calculations in high-level theories reveal that the boat configuration is indeed the global minimum under experimental conditions, solving a long-standing discrepancy.

Thermodynamic stability and spectroscopic properties of alkaline earth monobromides: The cases of MgBr2+ and BaBr2+

The low-lying electronic states of the dications MgBr2+ and BaBr2+ are investigated at a high level of theory. Potential energy curves are constructed, and the associated spectroscopic parameters determined. BaBr2+ is thermodynamic stable and MgBr2+ metastable. The state X 2Π of BaBr2+ is bound (De) by 22.60 kcal mol−1, with (Re, ωe) equal to (6.146 a0, 123.9 cm−1). The state A 2Σ+ lies higher by 5049 cm−1 with De = 8.43 kcal mol−1, ωe = 86.9 cm−1. For the dication MgBr2+, the state X 2Π has a deep well with an effective De (barrier height) of 51.18 kcal mol−1, Re = 4.500 a0, and ωe = 308.3 cm−1. The first excited state (A 2Σ+) lies higher by 12,091 cm−1 with De = 26.48 kcal mol−1, ωe = 236.6 cm−1. Einstein spontaneous emission coefficients (Av́v́́) are reported, and lifetimes estimated. New experimental results for the mass spectra of MgBr2+ are also provided.

On the nature of the interaction of copper hydride and halide with substituted ethylene and acetylene.

The association of Cu-X (X = -H, -Cl, and -F) with H2CCHCHmYn and HCCCHmYn (Y = -Cl, -F, -OH, -CH3) has been studied at a high level of theory. The density functional theory (DFT) at B3LYP/6-311G(d,p)//B3LYP/6-311 + G(3df,2p) level has been chosen to calculate the structure and the relative stability of 24 different complexes. The interaction of Cu-F with the derivatives of ethylene and acetylene was found very strong, with interaction energies close to those of conventional covalent bonds. In all complexes, the most stable structure was found when Cu-X is positioned on the unsaturated CC bond, forming a three-membered ring that leads to longer CC bond distances. Both ethylene and acetylene complexes show similar trends of interaction energies with respect to the same moiety. All electronic indexes analyzed by means of the QTAIM, ELF, and NBO formalisms indicate that the strength of the interaction should increase with the number of withdrawing substituents in both series of compounds. Graphical abstractThe p-Interaction of ethylene and acetylene derivative with fluoride copper. The ELF graphs and its 2D projection show the disynaptic basins of the electrostatic binding.

Quantum embedding for material chemistry based on domain separation and open subsystems

AbstractThis perspective considers two theories we recently proposed to perform quantum embedding calculations for chemical systems: domain‐separated density functional theory (DS‐DFT) and locally coupled open subsystems (LCOS). The development includes both the fundamentals of each theory as well as potential applications, some technical aspects, and related challenges. DS‐DFT is suited to study intramolecular effects, where one can apply a high level of theory (based on DFT or wave function theory) to a region of interest inside a molecule or solid and lower level theory elsewhere, with smooth switching between the regions. LCOS, in contrast, is a fragment‐based embedding, which offers computational advantages to study intermolecular behavior such as electron hopping, spin‐environment interaction, and charge‐transfer excitations. However, both theories can exchange roles when appropriate. In addition, these theories allow for control of computational scaling of their algorithms. We explore paths to determine the charge‐transfer operator used in LCOS, and suggest an auxiliary energy minimization that can provide a practical estimate to this operator. We also briefly discuss how to implement density fitting techniques in domain separation, and how domain separation can be used for pure wave function‐based embedding.

Full-dimensional quantum dynamics of SO(X[formula omitted]) in collision with H2

A six-dimensional (6D) potential energy surface (PES) for the SO(X -HSO(X3Σ-)-H2 system is computed using high-level electronic structure theory and fit using a hybrid invariant polynomial method. Full-dimensional quantum close-coupling scattering calculations have been carried out using this potential for rotational and, for the first time, vibrational quenching transitions of SO induced by H2. State-to-state cross sections and rate coefficients of SO are reported for rotational transitions from rotational levels j1 = 0–10 in the ground vibrational state neglecting fine-structure. Some selected state-to-state rotational rate coefficients are compared with previous theoretical results obtained using a rigid-rotor approximation. For vibrational quenching, state-to-state and total cross sections and rate coefficients were calculated for the transitions in SO(v1=1,j1) + H2(v2=0,j2) → SO(v1′=0,j1′) + H2(v2′=0,j2′) collisions with j1 = 0–5. Cross sections for collision energies in the range 1 to 3000 cm−1 and rate coefficients in the temperature range of 5–600 K are obtained for both para-H2 (j2 = 0) and ortho-H2 (j2 = 1) collision partners. The application of the results to astrophysics is discussed.

Alchemical Hydration Free-Energy Calculations Using Molecular Dynamics with Explicit Polarization and Induced Polarity Decoupling: An On-the-Fly Polarization Approach.

We present a methodology using fixed charge force fields for alchemical solvation free energy calculations which accounts for the change in polarity that the solute experiences as it transfers from the gas-phase to the condensed phase. We update partial charges using QM/MM snapshots, decoupling the electric field appropriately when updating the partial charges. We also show how to account for the cost of self-polarization. We test our methodology on 30 molecules ranging from small polar to large druglike molecules. We use Minimum Basis Iterative Stockholder (MBIS), Restrained Electrostatic Potential (RESP), and AM1-BCC partial charge methodologies. Using our method with MP2/cc-pVTZ and MBIS partial charges yields an average absolute deviation (AAD) of 6.3 kJ·mol-1 in comparison with the AM1-BCC result of 8.6 kJ·mol-1. AM1-BCC is within experimental uncertainty on 10% of the data compared to 30% with our method. We conjecture that results can be further improved by using Lennard-Jones and torsional parameters refitted to MBIS and RESP partial charge methods that use high levels of theory.

An Investigation of the Relationship Between Corporation Social Responsibility and Senior Managers Influence & Poverty Experience

The high-level echelon theory states that business executives are not“fully rational people”with economic assumptions in actual work. The management decision-making process of business executives is often affected by cognitive abilities, values and moral emotion. Taking the A-share listed companies in China from 2012 to 2015 as the research object, this paper analyzes the impact of the interaction between senior managers’ influence and their poverty experience on the corporate social responsibility. This study indicates that the senior managers’ poverty experience enhances the sense of corporate social responsibility. When the sub-index of senior managers’ influence and poverty experience are tested by analysis of regression, it is found that compared with the poverty environment of managers’ early experience, their three-year difficult period experience and special poverty experience have played a more significant role in strengthening the positive correlation between the senior managers’ influence and the corporate social responsibility. This investigation is helpful and beneficial for further studies on the altruism factors of corporate social responsibility and it could enrich the theoretical system of corporate social responsibility.