Absolute Energies Research Articles

Intrinsic exciton transitions of isotopically purified 13C studied by photoluminescence and transmission spectroscopy

The intrinsic exciton transitions of isotopically purified (13C) and natural-abundance (N.A.C) diamond are studied by photoluminescence and transmission spectroscopies at liquid helium temperatures. The comparative study shows that 13C has the same fine structure splitting with N.A.C, indicating that the isotopic effect of diamond does not influence the internal excitonic structure. This approach also deduces the absolute energies of excitons and phonons in 13C and N.A.C at the Δ [k = (0.76, 0, 0) × (2π/a)] point.

Calculation of absolute binding free energies between the hERG channel and structurally diverse drugs

The human ether-a-go-go-related gene (hERG) encodes a voltage-gated potassium channel that plays an essential role in the repolarization of action potentials in cardiac muscle. However, various drugs can block the ion current by binding to the hERG channel, resulting in potentially lethal cardiac arrhythmia. Accordingly, in silico studies are necessary to clarify the mechanisms of how these drugs bind to the hERG channel. Here, we used the experimental structure of the hERG channel, determined by cryo-electron microscopy, to perform docking simulations to predict the complex structures that occur between the hERG channel and structurally diverse drugs. The absolute binding free energies for the models were calculated using the MP-CAFEE method; calculated values were well correlated with experimental ones. By applying the regression equation obtained here, the affinity of a drug for the hERG channel can be accurately predicted from the calculated value of the absolute binding free energy.

Reproducing benchmark potential energy curves of molecular bond dissociation with small complete active space aided with density and density-matrix functional corrections.

Various effects of electron correlation accompany molecular bond dissociation, which makes the efficient calculation of potential energy curves a notoriously difficult problem. In an attempt to reliably reproduce both absolute energies and shapes of the benchmark dissociation curves, calculations with the combined CASΠDFT method are carried out for the prototype molecules H2, BH, F2, and N2. The complete active space (CAS) part of CASΠDFT accounts for long-range nondynamic correlation, while short-range dynamic correlation is accounted for with the corrected Lee-Yang-Parr correlation functional of density functional theory (DFT). The correction represents the suppression of dynamic correlation with nondynamic correlation, and it is a function of the ratio x(r) between the conditional and conventional densities obtained with the CAS on-top pair density Π(r). For the single-bonded molecules H2, BH, and F2, CASΠDFT succeeds in reproducing the shapes and absolute energies (for H2 and BH) of the benchmark curves, while for the triple-bonded N2 molecule, the addition to CASΠDFT of a multibond correction is required. It accounts for the middle-range dynamic correlation of the same-spin electrons in the (symmetrized) high-spin atomic electron configurations of the dissociating N2.

Accurate absolute core-electron binding energies of molecules, solids, and surfaces from first-principles calculations

Core-electron x-ray photoelectron spectroscopy is a powerful technique for studying the electronic structure and chemical composition of molecules, solids and surfaces. However, the interpretation of measured spectra and the assignment of peaks to atoms in specific chemical environments is often challenging. Here, we address this problem and introduce a parameter-free computational approach for calculating absolute core-electron binding energies. In particular, we demonstrate that accurate absolute binding energies can be obtained from the total energy difference of the ground state and a state with an explicit core hole when exchange and correlation effects are described by a recently developed meta-generalized gradient approximation and relativistic effects are included even for light elements. We carry out calculations for molecules, solids and surface species and find excellent agreement with available experimental measurements. For example, we find a mean absolute error of only 0.16 eV for a reference set of 103 molecular core-electron binding energies. The capability to calculate accurate absolute core-electron binding energies will enable new insights into a wide range of chemical surface processes that are studied by x-ray photoelectron spectroscopy.

PELE-MSM: A Monte Carlo Based Protocol for the Estimation of Absolute Binding Free Energies.

In this study, we present a fully automatic platform based on our Monte Carlo algorithm, the Protein Energy Landscape Exploration method (PELE), for the estimation of absolute protein-ligand binding free energies, one of the most significant challenges in computer aided drug design. Based on a ligand pathway approach, an initial short enhanced sampling simulation is performed to identify reasonable starting positions for more extended sampling. This stepwise approach allows for a significant faster convergence of the free energy estimation using the Markov State Model (MSM) technique. PELE-MSM was applied on four diverse protein and ligand systems, successfully ranking compounds for two systems. Based on the results, current limitations and challenges with physics-based methods in computational structural biology are discussed. Overall, PELE-MSM constitutes a promising step toward computing absolute binding free energies and in their application into drug discovery projects.

Large‐Sized Ammonia Clusters and Solvation Energies of the Proton in Ammonia

The absolute solvation energies (free energies and enthalpies) of the proton in ammonia are used to compute the pKa of species embedded in ammonia. They are also used to compute the solvation energies of other ions in ammonia. Despite their importance, it is not possible to determine experimentally the solvation energies of the proton in a given solvent. We propose in this work a direct approach to compute the solvation energies of the proton in ammonia from large-sized neutral and protonated ammonia clusters. To undertake this investigation, we performed a geometry optimization of neutral and protonated ammonia 30-mer, 40-mer, and 50 mer to locate stable structures. These structures have been fully optimized at both APFD/6-31++g(d,p) and M06-2X/6-31++g(d,p) levels of theory. An infrared spectroscopic study of these structures has been provided to assess the reliability of our investigation. Using these structures, we have computed the absolute solvation free energy and the absolute solvation enthalpy of the proton in ammonia. It comes out that the absolute solvation free energy of the proton in ammonia is calculated to be -1192 kJ mol-1 , whereas the absolute solvation enthalpy is evaluated to be -1214 kJ mol-1 . © 2019 Wiley Periodicals, Inc.

Perturbation potentials to overcome order/disorder transitions in alchemical binding free energy calculations.

We investigate the role of order/disorder transitions in alchemical simulations of protein-ligand absolute binding free energies. We show, in the context of a potential of mean force description, that for a benchmarking system (the complex of the L99A mutant of T4 lysozyme with 3-iodotoluene) and for a more challenging system relevant for medicinal applications (the complex of the farnesoid X receptor with inhibitor 26 from a recent D3R challenge) that order/disorder transitions can significantly hamper Hamiltonian replica exchange sampling efficiency and slow down the rate of equilibration of binding free energy estimates. We further show that our analytical model of alchemical binding combined with the formalism developed by Straub et al. for the treatment of order/disorder transitions of molecular systems can be successfully employed to analyze the transitions and help design alchemical schedules and soft-core functions that avoid or reduce the adverse effects of rare binding/unbinding transitions. The results of this work pave the way for the application of these techniques to the alchemical estimation with explicit solvation of hydration free energies and absolute binding free energies of systems undergoing order/disorder transitions.

Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theory.

We investigate the basis-set convergence of electronic correlation energies calculated using coupled cluster theory and a recently proposed finite basis-set correction technique. The correction is applied to atomic and molecular systems and is based on a diagrammatically decomposed coupled cluster singles and doubles (CCSD) correlation energy. Only the second-order energy and the particle-particle ladder term are corrected for their basis-set incompleteness error. We present absolute correlation energies and results for a large benchmark set. Our findings indicate that basis set reductions by two cardinal numbers are possible for atomization energies, ionization potentials, and electron affinities without compromising accuracy when compared to conventional CCSD calculations. In the case of reaction energies, we find that reductions by one cardinal number are possible compared to conventional CCSD calculations. The employed technique can readily be applied to other many-electron theories without the need for three- or four-electron integrals.

Proton Control of Transitions in an Amino Acid Transporter

Amino acid transport into the cell is often coupled to the proton electrochemical gradient, as found in the solute carrier 36 family of proton-coupled amino acid transporters. Although no structure of a human proton-coupled amino acid transporter exists, the crystal structure of a related homolog from bacteria, GkApcT, has recently been solved in an inward-occluded state and allows an opportunity to examine how protons are coupled to amino acid transport. Our working hypothesis is that release of the amino acid substrate is facilitated by the deprotonation of a key glutamate residue (E115) located at the bottom of the binding pocket, which forms part of the intracellular gate, allowing the protein to transition from an inward-occluded to an inward-open conformation. During unbiased molecular dynamics simulations, we observed a transition from the inward-occluded state captured in the crystal structure to a much more open state, which we consider likely to be representative of the inward-open state associated with substrate release. To explore this and the role of protons in these transitions, we have used umbrella sampling to demonstrate that the transition from inward occluded to inward open is more energetically favorable when E115 is deprotonated. That E115 is likely to be protonated in the inward-occluded state and deprotonated in the inward-open state is further confirmed via the use of absolute binding free energies. Finally, we also show, via the use of absolute binding free energy calculations, that the affinity of the protein for alanine is very similar regardless of either the conformational state or the protonation of E115, presumably reflecting the fact that all the key interactions are deep within the binding cavity. Together, our results give a detailed picture of the role of protons in driving one of the major transitions in this transporter.

Branching Ratios and Rate Constants for Decomposition and Isomerization of β-Hydroxyalkoxy Radicals Formed from OH Radical-Initiated Reactions of C6-C13 2-Methyl-1-Alkenes in the Presence of NOx.

A series of C6-C13 2-methyl-1-alkenes were reacted with OH radicals in the presence of NOx in a Teflon environmental chamber, and molar yields of the 2-ketone products were measured using gas chromatography. Yields were corrected for secondary reactions with OH radicals and for gas-wall partitioning of the 2-methyl-1-alkene and 2-ketone, with the latter correction being determined from measurements of gas-wall partitioning of 2-ketone standards. Molar yields of 2-ketones decreased with increasing 2-methyl-1-alkene carbon number from a maximum of 0.82 for C6 to a minimum of 0.34 ± 0.02 for C9-C13, which after normalization for the fraction of reaction that occurred by OH radical addition to the C═C double bond (with the rest occurring by H atom abstraction) were 0.86 and 0.39 ± 0.01. These yields were combined with branching ratios determined previously for site-specific OH radical addition to the C═C double bond and for formation of β-hydroxynitrates to determine branching ratios for decomposition and isomerization of β-hydroxyalkoxy radicals. Branching ratios for decomposition decreased with increasing 2-methyl-1-alkene carbon number from a maximum of 0.97 for C6 to a minimum of 0.49 ± 0.01 for C9-C13, while the corresponding values for isomerization increased from 0.03 to 0.51 ± 0.01. The results were used to estimate absolute rate constants and activation energies for decomposition and isomerization and were also combined with previously measured yields of β-hydroxynitrates, dihydroxynitrates, trihydroxynitrates, and H atom abstraction products to obtain yields of ∼75% for the C9-C13 reaction products, with the remainder likely being mostly dihydroxycarbonyls and trihydroxycarbonyls.

Extension of the Einstein molecule method for solid free energy calculation to non-periodic and semi-periodic systems

Free energy calculations on solid phases are important for understanding the phase behavior of various systems. For periodic crystalline solids, the Einstein molecule method can be used to determine the free energy difference between the solid of interest and an ideal crystal for which the free energy can be found analytically. In this work, we show how this method is extensible to systems which are nonperiodic or periodic in some dimensions but not in others. This allows for the calculation of exact absolute free energies of finite-sized crystals having specific shapes and surface geometries. We demonstrate this using the fcc Lennard-Jones solid and also illustrate how surface contributions to free energies can easily be extracted from simulations of this solid in semi-infinite slab geometries. We have developed a software package which interfaces with the LAMMPS molecular dynamics code to perform these calculations.

The impact of low-energy ionizing radiation on glutamine

New data on the fragmentation of the glutamine molecule (C5H10N2O3) under low-energy electron impact are presented. These data are related to the formation of the ionized products due to the low-energy electron impact. The resulting fragments were identified via an extensive DFT-theory approach. The results allow us to predict the principal pathways of the electron-impact glutamine molecule fragmentation. The absolute appearance energies for several fragments were both experimentally measured and theoretically calculated. Both types of data were then compared and analysed.

Robust Free Energy Perturbation Protocols for Creating Molecules in Solution.

Accurate methods to estimate free energies play an important role for studying diverse condensed-phase problems in chemistry and biochemistry. The most common methods used in conjunction with molecular dynamics (MD) and Monte Carlo statistical mechanics (MC) simulations are free energy perturbation (FEP) and thermodynamic integration (TI). For common applications featuring the conversion of one molecule to another, simulations are run in stages or multiple "λ-windows" to promote convergence of the results. For computation of absolute free energies of solvation or binding, calculations are needed in which the solute is typically annihilated in the solvent and in the complex. The present work addresses identification of optimal protocols for such calculations, specifically, the creation/annihilation of organic molecules in aqueous solution. As is common practice, decoupling of the perturbations for electrostatic and Lennard-Jones interactions was performed. Consistent with earlier reports, FEP calculations for molecular creations are much more efficient, while annihilations require many more windows and may converge to incorrect values. Strikingly, we find that as few as four windows may be adequate for creation calculations for solutes ranging from argon to ethylbenzene. For a larger druglike molecule, MIF180, which contains 22 non-hydrogen atoms and three rotatable bonds, 10 creation windows are found to be adequate to yield the correct free energy of hydration. Convergence is impeded with procedures that use any sampling in the annihilation direction, and there is no need for postprocessing methods such as the Bennett acceptance ratio (BAR).

Enantioselective [2+2] Cycloadditions of Cinnamate Esters: Generalizing Lewis Acid Catalysis of Triplet Energy Transfer.

We report the enantioselective [2+2] cycloaddition of simple cinnamate esters, the products of which are useful synthons for the controlled assembly of cyclobutane natural products. This method utilizes a cocatalytic system in which a chiral Lewis acid accelerates the transfer of triplet energy from an excited-state Ir(III) photocatalyst to the cinnamate ester. Computational evidence indicates that the principal role of the Lewis acid cocatalyst is to lower the absolute energies of the substrate frontier molecular orbitals, leading to greater electronic coupling between the sensitizer and substrate and increasing the rate of the energy transfer event. These results suggest Lewis acids can have multiple beneficial effects on triplet sensitization reactions, impacting both the thermodynamic driving force and kinetics of Dexter energy transfer.

Phase Equilibria of Solid and Fluid Phases from Molecular Dynamics Simulations with Equilibrium and Nonequilibrium Free Energy Methods.

In this work, we present a methodology to determine phase coexistence lines for atomic and rigid molecular systems with an emphasis on solid-fluid and on solid-solid equilibria. Phase coexistence points are found by computing the absolute free energy for each candidate phase separately. For solid phases, a combination of the extended Einstein crystal and the Einstein molecule method is presented which constitutes a convenient way to compute the absolute free energy with fixed center of mass. We compare results from equilibrium methods-thermodynamic integration and reweighting using the multistate Bennett acceptance ratio estimator (MBAR)-with simulations using a nonequilibrium method and discuss their advantages and disadvantages. Once absolute free energies of different phases are available, they are combined with simulations performed in the isothermal isobaric ensemble and MBAR, which enables efficient, iterative tracing of coexistence lines. The method is applicable to both liquid-solid as well as solid-solid transitions and is comparably simple and convenient to apply since the same method (MBAR) is used to compute free energies and to trace the coexistence line. Furthermore, statistical uncertainties can readily be computed in a transparent manner. We apply the method to an atomic solid (fcc argon) as well as small molecular systems (methanol and water) using the LAMMPS simulation package. Our study shows that all methods can be used to reliably compute the absolute free energy of solid phases, while MBAR is the most flexible method with high statistical efficiency. We find the nonequilibrium method is an attractive choice since it is simple to set up and to postprocess and is, hence, less prone to errors. The presented workflow provides a flexible, efficient, and robust way to compute phase diagrams using openly available software.

On the distinguishable cluster approximation for triple excitations.

The distinguishable cluster approximation applied to coupled cluster doubles equations greatly improves absolute and relative energies. We apply the same approximation to the triples equations and demonstrate that it can also improve the results of the coupled cluster method with singles, doubles, and triples. The resulting method has a nominal computational scaling of O(N7) in the real-space representation, and is orbital invariant, size extensive, and exact for three electrons.

Fully numerical Hartree‐Fock and density functional calculations. I. Atoms

AbstractAlthough many programs have been published for fully numerical Hartree‐Fock (HF) or density functional (DF) calculations on atoms, we are not aware of any programs that support hybrid DFs, which are popular within the quantum chemistry community due to their better accuracy for many applications, or that can be used to calculate electric properties. Here, we present a variational atomic finite element solver in the HelFEM program suite that overcomes these limitations. A basis set of the type is used, where B n(r) are finite element shape functions and are spherical harmonics, which allows for an arbitrary level of accuracy. HelFEM supports nonrelativistic HF and DF calculations even with hybrid functionals, which are not available in other commonly available program packages. Hundreds of functionals at the local spin‐density approximation (LDA), generalized‐gradient approximation (GGA), as well as the meta‐GGA levels of theory are included through an interface with the Libxc library. Electric response properties are achievable via finite field calculations. We introduce an alternative grid that yields faster convergence to the complete basis set limit than commonly used alternatives. We also show that high‐order Lagrange interpolating polynomials yield the best convergence, and that excellent agreement with literature HF limit values for electric properties, such as static dipole polarizabilities, can be achieved with the present approach. Dipole moments and dipole polarizabilities at finite field are also reported with the PBE, PBEh, TPSS, and TPSSh functionals. Finally, we show that a recently published Gaussian basis set is able to reproduce absolute HF and DF energies of neutral atoms, cations, as well as anions within a few dozen microhartrees.

New and Efficient Equation-of-Motion Coupled-Cluster Framework for Core-Excited and Core-Ionized States.

We present a fully analytical implementation of the core-valence separation (CVS) scheme for the equation-of-motion (EOM) coupled-cluster singles and doubles (CCSD) method for calculations of core-level states. Inspired by the CVS idea as originally formulated by Cederbaum, Domcke, and Schirmer, pure valence excitations are excluded from the EOM target space and the frozen-core approximation is imposed on the reference-state amplitudes and multipliers. This yields an efficient, robust, practical, and numerically balanced EOM-CCSD framework for calculations of excitation and ionization energies as well as state and transition properties (e.g., spectral intensities, natural transition, and Dyson orbitals) from both the ground and excited states. The errors in absolute excitation/ionization energies relative to the experimental reference data are on the order of 0.2-3.0 eV, depending on the K-edge considered and on the basis set used, and the shifts are systematic for each edge. Compared to a previously proposed CVS scheme where CVS was applied as a posteriori projection only during the solution of the EOM eigenvalue equations, the new scheme is computationally cheaper. It also achieves better cancellation of errors, yielding similar spectral profiles but with absolute core excitation and ionization energies that are systematically closer to the corresponding experimental data. Among the presented results are calculations of transient-state X-ray absorption spectra, relevant for interpretation of UV-pump/X-ray probe experiments.

Electrostatic Spectral Tuning Maps for Biological Chromophores.

The mechanism by which the absorption wavelength of a molecule is modified by a protein is known as spectral tuning. Spectral tuning is often achieved by electrostatic interactions that stabilize/destabilize or modify the shape of the excited and ground-state potential energy surfaces of the chromophore. We present a protocol for the construction of three-dimensional "electrostatic spectral tuning maps" that describe how vertical excitation energies in a chromophore are influenced by nearby charges. The maps are built by moving a charge on the van der Waals surface of the chromophore and calculating the change in its excitation energy. The maps are useful guides for protein engineering of color variants, for interpreting spectra of chromophores that act as probes of their environment, and as starting points for further quantum mechanical/molecular mechanical studies. The maps are semiquantitative and can approximate the magnitude of the spectral shift induced by a point charge at a given position with respect to the chromophore. We generate and discuss electrostatic spectral tuning maps for model chromophores of photoreceptor proteins, fluorescent proteins, and aromatic amino acids. Such maps may be extended to other properties such as oscillator strengths, absolute energies (stability), ionization energies, and electron affinities.

Dimerization energetics of curli fiber subunits CsgA and CsgB

Curli fibers are functional amyloids that exhibit strong adhesion and robust self-assembly as biofilm structural components; however, the binding energetics and mechanical properties of wild-type curli are not well understood. To address this, we present dimer structures made up of the major and minor curli subunits (CsgA and CsgB), perform free energy calculations to obtain absolute binding energies, and estimate the Young’s modulus and persistence length of curli fibers. Equilibrium molecular dynamics simulations are used to evaluate nonbonded interactions. Binding energies are most favorable for CsgB–CsgA, while CsgA–CsgA dimers have a higher binding energy than CsgB–CsgB despite possessing less favorable nonbonded interaction energies. Decomposing each potential of mean force of separation indicated that solvent effects positively impact CsgA–CsgA binding but not CsgB–CsgB and CsgB–CsgA. Charged residues and conserved polar residues were also notable contributors to attractive nonbonded interactions, underlining their importance in dimer assembly. Our findings elucidate sequence effects on binding energy contributions and establish theoretical limits for the elasticity, persistence length, and strength of curli fibers.