The MRCC program system: Accurate quantum chemistry from water to proteins.

MRCC is a package of ab initio and density functional quantum chemistry programs for accurate electronic structure calculations. The suite has efficient implementations of both low- and high-level correlation methods, such as second-order Møller-Plesset (MP2), random-phase approximation (RPA), second-order algebraic-diagrammatic construction [ADC(2)], coupled-cluster (CC), configuration interaction (CI), and related techniques. It has a state-of-the-art CC singles and doubles with perturbative triples [CCSD(T)] code, and its specialties, the arbitrary-order iterative and perturbative CC methods developed by automated programming tools, enable achieving convergence with regard to the level of correlation. The package also offers a collection of multi-reference CC and CI approaches. Efficient implementations of density functional theory (DFT) and more advanced combined DFT-wave function approaches are also available. Its other special features, the highly competitive linear-scaling local correlation schemes, allow for MP2, RPA, ADC(2), CCSD(T), and higher-order CC calculations for extended systems. Local correlation calculations can be considerably accelerated by multi-level approximations and DFT-embedding techniques, and an interface to molecular dynamics software is provided for quantum mechanics/molecular mechanics calculations. All components of MRCC support shared-memory parallelism, and multi-node parallelization is also available for various methods. For academic purposes, the package is available free of charge.

Thermochemistry of Uracil, Thymine, Cytosine, and Adenine.

The goal of this study is to give reliable and accurate thermochemical data for uracil, thymine, cytosine, and adenine. The gas-phase heats of formation of these compounds were determined with the diet-HEAT-F12 protocol, which uses explicitly correlated coupled-cluster calculations along with anharmonic vibrational, scalar relativistic, and diagonal Born-Oppenheimer corrections. The thermochemically relevant tautomers of cytosine were also investigated. To derive heats of formation in the gas and solid phases as well as sublimation enthalpies, the thermochemical network approach was utilized, i.e., the available literature data were collected, reviewed, and combined with our theoretical calculations. Solvation free energies were also determined with various methods and compared to experimental data.

High Accuracy Quantum Chemical and Thermochemical Network Data for the Heats of Formation of Fluorinated and Chlorinated Methanes and Ethanes.

Reliable heats of formation are reported for numerous fluorinated and chlorinated methane and ethane derivatives by means of an accurate thermochemical protocol, which involves explicitly correlated coupled-cluster calculations augmented with anharmonic, scalar relativistic, and diagonal Born-Oppenheimer corrections. The theoretical results, along with additional experimental data, are further enhanced with the help of the thermochemical network approach. For 28 species, out of 50, this study presents the best estimates, and discrepancies with previous reports are also highlighted. Furthermore, the effects of the less accurate theoretical data on the results yielded by thermochemical networks are discussed.

Accurate Theoretical Thermochemistry for Fluoroethyl Radicals.

An accurate coupled-cluster (CC) based model chemistry was applied to calculate reliable thermochemical quantities for hydrofluorocarbon derivatives including radicals 1-fluoroethyl (CH3-CHF), 1,1-difluoroethyl (CH3-CF2), 2-fluoroethyl (CH2F-CH2), 1,2-difluoroethyl (CH2F-CHF), 2,2-difluoroethyl (CHF2-CH2), 2,2,2-trifluoroethyl (CF3-CH2), 1,2,2,2-tetrafluoroethyl (CF3-CHF), and pentafluoroethyl (CF3-CF2). The model chemistry used contains iterative triple and perturbative quadruple excitations in CC theory, as well as scalar relativistic and diagonal Born-Oppenheimer corrections. To obtain heat of formation values with better than chemical accuracy perturbative quadruple excitations and scalar relativistic corrections were inevitable. Their contributions to the heats of formation steadily increase with the number of fluorine atoms in the radical reaching 10 kJ/mol for CF3-CF2. When discrepancies were found between the experimental and our values it was always possible to resolve the issue by recalculating the experimental result with currently recommended auxiliary data. For each radical studied here this study delivers the best heat of formation as well as entropy data.

High-accuracy theoretical thermochemistry of fluoroethanes.

A highly accurate coupled-cluster-based ab initio model chemistry has been applied to calculate the thermodynamic functions including enthalpies of formation and standard entropies for fluorinated ethane derivatives, C2HxF6-x (x = 0-5), as well as ethane, C2H6. The invoked composite protocol includes contributions up to quadruple excitations in coupled-cluster (CC) theory as well as corrections beyond the nonrelativistic and Born-Oppenheimer approximations. For species CH2F-CH2F, CH2F-CHF2, and CHF2-CHF2, where anti/gauche isomerism occurs due to the hindered rotation around the C-C bond, conformationally averaged enthalpies and entropies at 298.15 K are also calculated. The results obtained here are in reasonable agreement with previous experimental and theoretical findings, and for all fluorinated ethanes except CH2FCH3 and C2F6 this study delivers the best available theoretical enthalpy and entropy estimates.

Dissociation of the fluorine molecule.

The primary purpose of the present study is to resolve the discrepancy that exists between the two most recently published dissociation energies for the fluorine molecule [D0(F2)] and, consequently, for the associated heats of formation of the fluorine atom [ΔfH0°(F)]. We hope to provide a reliable, well-established theoretical estimate for these thermochemical quantities. To this end, a high-accuracy coupled-cluster-based composite ab initio model chemistry has been utilized. The protocol involves contributions of up to pentuple excitations in coupled-cluster theory augmented with basis set extrapolation techniques and additional corrections beyond the nonrelativistic and Born­Oppenheimer approximations. The augmented core­valence correlation consistent basis set families, aug-cc-pCVXZ, have been successively used, in some cases, up to octuple-ζ quality. Our best theoretical results for D0(F2) and ΔfH0°(F) obtained in this study are 154.95 ± 0.48 and 77.48 ± 0.24 kJ/mol, respectively. Because conflicting theoretical results are also reported about the existence of a barrier along the dissociation curve of F2, extensive multireference configuration interaction and coupled-cluster calculations have been performed using reference orbitals taken from all-electron complete active space self-consistent field computations. Extrapolations from the results obtained with the aug-cc-pCVXZ (X = T, Q, 5) basis sets clearly indicate that the barrier indeed exists. It is located at 3.80 ± 0.20 Å along the dissociation curve with a height of 42 ± 10 µEh (∼0.11 ± 0.03 kJ/mol). Because of the neglect of this effect during the evaluation of the raw experimental data used to obtain D0(F2) = 154.52 ± 0.12 kJ/mol and ΔfH0°(F) = 77.26 ± 0.06 kJ/mol [Stevens; et al. J. Phys. Chem. A 2010, 114, 13134], an additional error should be attached to these latter values. Obviously, the barrier does not affect either the experimental results, D0(F2) = 154.92 ± 0.10 kJ/mol and ΔfH0°(F) = 77.46 ± 0.05 kJ/mol [Yang; et al. J. Chem. Phys. 2005, 122, 134308; 2007, 127, 209901], which are based on the ion-pair dissociation of the molecule, or the data calculated theoretically. It is also noteworthy that our best estimates are in excellent agreement with those obtained from the ion-pair dissociation experiment.

Benchmark theoretical study on the dissociation energy of chlorine.

The currently accepted D(0)((35)Cl(2)) is 239.221 ± 0.001 kJ/mol, whereas popular theoretical model chemistries provide values in the range of 233-247 kJ/mol, and even the so-called high-accuracy protocols can yield values as low as 237.9 kJ/mol and as high as 240.1 kJ/mol for D(0)((35)Cl(2)). The aim of this study was to uncover the sources of error inherent in the theoretical approaches. Therefore, a coupled-cluster-based composite model chemistry was utilized that included contributions of up to pentuple excitations, as well as corrections beyond the nonrelativistic and Born-Oppenheimer approximations. In our calculations, correlation consistent basis set families were used up to octuple-ζ basis sets. It was found that the following factors, in order of significance, can be identified as the most important error sources: (i) the considerably large relativistic contributions carrying large uncertainties, (ii) the very slow convergence of the Møller-Plesset (MP2) correlation energy (with the octuple-ζ basis set, it still contains an error of a few tenth of a kJ/mol), (iii) the slow convergence of the coupled-cluster singles and doubles (CCSD) contribution (it needs a octuple-ζ basis set to converge within 0.1 kJ/mol), and (iv) the relatively large basis set (quadruple-ζ) needed in the calculation of an accurate perturbative quadruples contribution. It is also notable that, for chlorine, the use of a quintuple-ζ basis set for the Hartree-Fock energy, the MP2 correlation energy, and for the CCSD and perturbative triples contributions, which is the usual treatment in almost every high-accuracy model chemistry, resulted in the overestimation of all of these contributions (altogether about by 1.8 kJ/mol). However, this overestimation is accidentally compensated by (i) using an inappropriate, small basis set for the valence electron contribution due to quadruple excitations (∼1.2 kJ/mol), (ii) neglecting the effects of core electron contributions due to quadruple excitations (∼0.2 kJ/mol), and (iii) neglecting relativistic effects beyond the scalar relativistic treatment (∼0.3 kJ/mol). The most reliable theoretical estimate for D(0)((35)Cl(2)) obtained in this study, 239.27 ± 1.30 kJ/mol, differs by only 0.05 kJ/mol from the most accurate experimental result. This study also underpins the effect of relativistic contributions, which precludes current model chemistries to enter the range of sub-kJ/mol accuracy for second-row systems.

High-accuracy theoretical thermochemistry of atmospherically important nitrogen oxide derivatives.

High-accuracy quantum chemical calculations were performed for several atmospherically important nitrogen oxide derivatives, such as HOONO, HOONO(2), NH(2)NO(2), FNO, FNO(2), FONO, FONO(2), ClNO, ClONO, ClONO(2), and ClOONO. The stable conformers of the molecules were identified, and the corresponding heats of formation (Δ(f)H(0)° and Δ(f)H(298)°) and entropy values (S(298)°) were computed. On the basis of the thermodynamic functions, equilibrium constants were also calculated for a couple of reactions with importance in the chemistry of the atmosphere. In a number of cases this study provides more reliable estimates for the investigated thermodynamic properties than those can be collected from previous reports.

High-accuracy theoretical thermochemistry of atmospherically important sulfur-containing molecules.

In this study, several sulfur-containing molecules with atmospherical importance were investigated by means of high-accuracy quantum chemical calculations including: HSO, HOS, HOSO2, HSNO, SH, CH2SO, CH2SH, S2COH, and SCSOH. After identifying the stable conformers of the molecules, a coupled-cluster-based composite model chemistry, which includes contributions up to quadruple excitations as well as corrections beyond the nonrelativistic and Born­Oppenheimer approximations, was applied to calculate the corresponding heat of formation (Δ(f)H(0)° and Δ(f)H(298)°) and entropy (S(298)°) values. In most of the cases, this study delivers more reliable estimates for the investigated thermodynamic properties than those reported in previous investigations. Our data also suggest that the experimental heats of formation associated with the HSO molecule are very likely to belong to its structural isomer, HOS. It is also confirmed by the calculated thermodynamic properties including standard reaction entropies, enthalpies, and equilibrium constants that, in the reaction CS2 + OH CS2OH, the SCSOH structural isomer is produced. It is also noted that the currently accepted Δ(f)H(0)°(S(gas)) = 274.73 ± 0.3 kJ/mol value is in need of revision, and based on a recent measurement, which is also confirmed by our computations, it is advised to update it to Δ(f)H(0)°(S(gas)) = 277.25 ± 0.3 kJ/mol.

High-accuracy theoretical study on the thermochemistry of several formaldehyde derivatives.

In the case of several formaldehyde derivatives, with importance in atmospheric and combustion chemistry, the currently available thermochemical values suffer from considerably large uncertainties. In this study a high-accuracy theoretical model chemistry has been used to provide accurate thermochemical data including heats of formation at 0 and 298 K and standard molar entropies at 298 K for CF(2)O, FCO, HFCO, HClCO, FClCO, HOCO, and NH(2)CO. For most of the thermochemical quantities studied here, this investigation delivers the best available estimate.

High-accuracy thermochemistry of atmospherically important fluorinated and chlorinated methane derivatives.

High-precision quantum chemical calculations have been performed for atmospherically important halomethane derivatives including CF, CF(3), CHF(2), CH(2)F, CF(2), CF(4), CHF, CHF(3), CH(3)F, CH(2)F(2), CCl, CCl(3), CHCl(2), CH(2)Cl, CCl(2), CCl(4), CHCl, CHCl(3), CH(3)Cl, CH(2)Cl(2), CHFCl, CF(2)Cl, CFCl(2), CFCl, CFCl(3), CF(2)Cl(2), CF(3)Cl, CHFCl(2), CHF(2)Cl, and CH(2)FCl. Theoretical estimates for the standard enthalpy of formation at 0 and 298.15 K as well as for the entropy at 298.15 K are presented. The determined values are mostly within the experimental uncertainty where accurate experimental results are available, while for the majority of the considered heat of formation and entropy values the present results represent the best available estimates.

Calculation of weakly polar interaction energies in polypeptides using density functional and local Møller-Plesset perturbation theory.

The interaction energies of ubiquitous weakly polar interactions in proteins are comparable with those of hydrogen bonds, consequently, they stabilize local, secondary, and tertiary structures. However, the most widely-used density functionals fail to describe the weakly polar interactions. Thus, it is important to find and test functionals which adequately describe and quantify the energetics of such interactions. For this purpose, interaction energies in the hydrophobic core of rubredoxin (PDB id: 1rb9) and in the S22 subset of the JSCH-2005 benchmark database were computed with the BHandHLYP and PWPW91 functionals and with the pseudospectral implementation of the local MP2 (PS-LMP2) method. The cc-pVDZ, cc-pVTZ(-f), cc-pVTZ, cc-pVQZ(-g), aug-cc-pVDZ, aug-cc-VTZ(-f), and aug-cc-pVTZ basis sets were used for the calculations. In the S22 subset the PS-LMP2 results were extrapolated to the complete basis set limit. Furthermore, the a posteriori counterpoise method of Boys and Bernardi was used to correct the basis set superposition errors in the calculation of interaction energies. Calculations using the BHandHLYP functional, both for the various weakly polar interactions in rubredoxin and for the dispersion interactions in the S22 subset, were in good agreement with those using the coupled cluster (CCSD(T)) and the resolution of identity MP2 (RIMP2) methods and clearly outperformed both the PWPW91 functional and the PS-LMP2 method. The results for the S22 hydrogen bonded subset, obtained with PWPW91 calculations, were closest to those of the reference high level calculations. For the "mixed" (hydrogen bonded and dispersive) interactions in the S22 subset, results obtained with the BHandHLYP and PS-LMP2 calculations agreed well with the reference calculations.

The effect of electron correlation on the conformational space of melatonin.

The pineal gland hormone melatonin regulates several physiological processes including circadian rhythm and also alleviates oxidative stress-induced degenerative diseases. In spite of its important biological roles, no high level ab initio conformational study has been conducted to reveal its structural features. In this work, the conformational flexibility of melatonin was investigated using correlated ab initio calculations. Conformers, obtained previously at the Hartree-Fock level (HF/6-31G*), were fully optimized using second order Møller-Plesset perturbation theory applying the frozen core approximation (MP2(FC)/6-31G*). Furthermore, single-point MP4(SDQ,FC)/6-31G*//MP2(FC)/6-31G* computations were performed to investigate the effect of higher order perturbation terms. The HF and MP2 conformational spaces are considerably different: the initial 128 structures converged into 102 different local minima as confirmed by frequency calculations; 28 new minima appeared and 26 previous HF local minima disappeared; no "all-trans" C3 side chain conformations are seen at the MP2(FC) level. The MP2 global minimum conformation is stabilized by an aromatic-side chain interaction.

Quantum chemical quantification of weakly polar interaction energies in the TC5b miniprotein.

The tertiary structure of the TC5b miniprotein is stabilized by inter-residue interactions of the Trp-cage, which is composed of a Tyr and several Pro residues surrounding a central Trp residue. The interactions include Ar-Ar (aromatic side-chain-aromatic side-chain), Ar-NH (aromatic side-chain-backbone amide), and CH-pi (aromatic side-chain-aliphatic hydrogen) interactions. In the present work, the strength of the weakly polar interactions found in the TC5b miniprotein was quantified using all of the available 38 NMR structures (1L2Y) from the Protein Data Bank with DFT quantum chemical calculations at the BHandHLYP/cc-pVTZ level of theory and molecular fragmentation with capping of the partial structures. The energies of interaction between the individual residues of the Trp-cage range between -5.85+/-1.41 and -21.30+/-0.88 kcal mol(-1), leading to a significant total structural stabilization energy of -52.13+/-2.56 kcal mol(-1) of which about 50% is from the weakly polar interactions. Furthermore, the strengths of the individual weakly polar interactions are between -2.32+/-0.17 and -2.93+/-0.12 kcal mol(-1) for the CH-pi interactions, between -2.48+/-0.97 and -3.09+/-1.02 kcal mol(-1) for the Ar-NH interaction and -2.74+/-1.06 kcal mol(-1) for the Ar-Ar interaction.

Comment on "Causation or only correlation? Application of causal inference graphs for evaluating causality in nano-QSAR models" by N. Sizochenko, A. Gajewicz, J. Leszczynski and T. Puzyn, Nanoscale, 2016, 8, 7203.

In this comment we show that the accuracy of a recent nano-QSAR model for toxicity predictions of metal oxide nanoparticles towards bacteria E. coli can be greatly improved. On one hand, the experimental ionization energies of metal atoms could be substituted for the erroneous semi-empirically derived heat of formation values of metal ions as descriptors to construct a more reliable nano-QSAR model based on weighted linear least-squares fittings. On the other hand, if no experimental data is available, a model relying on ionization energy descriptors from quantum chemical calculations could also be used producing exactly the same toxicity values as the experimental model.

Moderate-Cost Ab Initio Thermochemistry with Chemical Accuracy.

A moderate-cost ab initio composite model chemistry including the explicitly correlated CCSD(T*)(F12) and conventional coupled-cluster methods up to perturbative quadruple excitations along with correlation consistent basis sets is developed. The model, named diet-HEAT-F12, is also augmented with diagonal Born-Oppenheimer and scalar relativistic corrections. The methods and basis sets used for the calculation of the individual components are selected to reproduce, as close as possible, without using any fitted parameters, the benchmark HEAT contributions. A well-defined recipe for calculating size-dependent 95% confidence intervals was also worked out for the model. The reliability of the protocol was checked using the W4-11 data set as well as a disjoint set of 23 accurate atomization energies collected from the literature and obtained by the procedure of Feller, Peterson, and Dixon. The best error statistics for the test set was yielded by the diet-HEAT-F12 protocol among the models W3X, W3X-L, and W3-F12 considered.

Enthalpy Differences of the n-Pentane Conformers.

The energy and enthalpy differences of alkane conformers in various temperature ranges have been the subject for both experimental and theoretical studies over the last few decades. It was shown previously for the conformers of butane [G. Tasi et al., J. Chem. Theory Comput. 2012, 8, 479-486] that quantum chemical results can compete with spectroscopic techniques and results obtained even from the most carefully performed experiments could be biased due to the improper statistical model utilized to evaluate the raw experimental data. In the current study, on one hand, the experimental values and their uncertainties for the enthalpy differences for pentane conformers are re-evaluated using the appropriate statistical model. On the other hand, a coupled-cluster-based focal-point analysis has been performed to calculate energy and enthalpy differences for the conformers of pentane. The model chemistry defined in this study includes contributions up to the perturbative quadruple excitations augmented with further small correction terms beyond the Born-Oppenheimer and nonrelativistic approximations. Benchmark quality energy and enthalpy differences for the pentane conformers are given at temperatures 0 and 298.15 K as well as for the various temperature ranges used in the gas-phase experimental measurements. Furthermore, a slight positive shift for the experimental enthalpy differences is also predicted due to an additional Raman active band belonging to the gauche-gauche conformer.