Michal Pitoňák

A Transferable H-Bonding Correction for Semiempirical Quantum-Chemical Methods

Semiempirical methods could offer a feasible compromise between ab initio and empirical approaches for the calculation of large molecules with biological relevance. A key problem for attempts in this direction is the rather bad performance of current semiempirical methods for noncovalent interactions, especially hydrogen-bonding. On the basis of the recently introduced PM6-DH method, which includes empirical corrections for dispersion (D) and hydrogen-bond (H) interactions, we have developed an improved and transferable H-bonding correction for semiempirical quantum chemical methods. The performance of the improved correction is evaluated for PM6, AM1, OM3, and SCC-DFTB (enhanced by standard empirical dispersion corrections) with several test sets for noncovalent interactions and is shown to reach the quality of current DFT-D approaches for these types of problems.

Benzene Dimer: High-Level Wave Function and Density Functional Theory Calculations.

High-level OVOS (optimized virtual orbital space) CCSD(T) interaction energy calculations (up to the aug-cc-pVQZ basis set) and various extrapolations toward the complete basis set (CBS) limit are presented for the most important structures on the benzene dimer potential energy surface. The geometries of these structures were obtained via an all-coordinate gradient geometry optimization using the DFT-D/BLYP method, covering the empirical dispersion correction fitted exclusively for this system. The fit was carried out against two estimated CCSD(T)/CBS potential energy curves corresponding to the distance variation between two benzene rings for the parallel-displaced (PD) and T-shaped (T) structures. The effect of the connected quadruple excitations on the interaction energy was estimated using the CCSD(TQf) method in a 6-31G*(0.25) basis set, destabilizing the T and T-shaped tilted (TT) structures by ≈0.02 kcal/mol and the PD structure by ≈0.04 kcal/mol. Our best CCSD(T)/CBS results show, within the error bars of the applied methodology, that the energetically lowest-lying structure is the TT structure, which is nearly 0.1 kcal/mol more stable than the almost isoenergetic PD and T structures. The specifically parametrized DFT-D/BLYP method leads to a correct energy ordering of the structures, with the errors being smaller by 0.2 kcal/mol with respect to the most accurate CCSD(T) values.

On the Structure and Geometry of Biomolecular Binding Motifs (Hydrogen-Bonding, Stacking, X-H···π): WFT and DFT Calculations.

The strengths of noncovalent interactions are generally very sensitive to a number of geometric parameters. Among the most important of these parameters is the separation between the interacting moieties (in the case of an intermolecular interaction, this would be the intermolecular separation). Most works seeking to characterize the properties of intermolecular interactions are mainly concerned with binding energies obtained at the potential energy minimum (as determined at some particular level of theory). In this work, in order to extend our understanding of these types of noncovalent interactions, we investigate the distance dependence of several types of intermolecular interactions, these are hydrogen bonds, stacking interactions, dispersion interactions, and X-H···π interactions. There are several methods that have traditionally been used to treat noncovalent interactions as well as many new methods that have emerged within the past three or four years. Here we obtain reference data using estimated CCSD(T) values at the complete basis set limit (using the CBS(T) method); potential energy curves are also produced using several other methods thought to be accurate for intermolecular interactions, these are MP2/cc-pVTZ, MP2/aug-cc-pVDZ, MP2/6-31G*(0.25), SCS(MI)-MP2/cc-pVTZ, estimated MP2.5/CBS, DFT-SAPT/aug-cc-pVTZ, DFT/M06-2X/6-311+G(2df,2p), and DFT-D/TPSS/6-311++G(3df,3pd). The basis set superposition error is systematically considered throughout the study. It is found that the MP2.5 and DFT-SAPT methods, which are both quite computationally intensive, produce potential energy curves that are in very good agreement to those of the reference method. Among the MP2 techniques, which can be said to be of medium computational expense, the best results are obtained with MP2/cc-pVTZ and SCS(MI)-MP2/cc-pVTZ. DFT-D/TPSS/6-311++G(3df,3pd) is the DFT-based method that can be said to give the most well-balanced description of intermolecular interactions.

Comparative Study of Selected Wave Function and Density Functional Methods for Noncovalent Interaction Energy Calculations Using the Extended S22 Data Set

In this paper, an extension of the S22 data set of Jurecka et al. ( Jurečka , P. ; Šponer , J. ; Černý , J. ; Hobza , P. Phys. Chem. Chem. Phys. 2006 , 8 , 1985. ), the data set of benchmark CCSD(T)/CBS interaction energies of twenty-two noncovalent complexes in equilibrium geometries, is presented. The S22 data set has been extended by including the stretched (one shortened and three elongated) complex geometries of the S22 data set along the main noncovalent interaction coordinate. The goal of this work is to assess the accuracy of the popular wave function methods (MP2-, MP3- and, CCSD-based) and density functional methods (with and without empirical correction for the dispersion energy) for noncovalent complexes based on a statistical evaluation not only in equilibrium, but also in nonequilibrium geometries. The results obtained in this work provide information on whether an accurate and balanced description of the different interaction types and complex geometry distortions can be expected from the tested methods. This information has an important implication in the calculation of large molecular complexes, where the number of distant interacting molecular fragments, often in far from equilibrium geometries, increases rapidly with the system size. The best performing WFT methods were found to be the SCS-CCSD (spin-component scaled CCSD, according to Takatani , T. ; Hohenstein , E. G. ; Sherrill , C. D. J. Chem. Phys. 2008 , 128 , 124111 ), MP2C (dispersion-corrected MP2, according to Hesselmann , A. J. Chem. Phys. 2008 , 128 , 144112 ), and MP2.5 (scaled MP3, according to Pitoňák , M. ; Neogrády , P. ; Černý , J. ; Grimme , S. ; Hobza , P. ChemPhysChem 2009 , 10 , 282. ). Since none of the DFT methods fulfilled the required statistical criteria proposed in this work, they cannot be generally recommended for large-scale calculations. The DFT methods still have the potential to deliver accurate results for large molecules, but most likely on the basis of an error cancellation.

Optimized virtual orbitals for correlated calculations: an alternative approach

We propose an alternative formulation for creating the optimized virtual orbital space (OVOS). Our technique exploits and extends the method developed by Adamowicz and co-workers [L. Adamowicz, R.J. Bartlett. J. chem. Phys., 86, 6314 (1987); L. Adamowicz, R.J. Bartlett, A.J. Sadlej. J. chem. Phys., 88, 5749 (1988).]. The aim of the OVOS technique is to reduce the original SCF basis of the virtual molecular orbitals and to reduce the computer time in the coupled cluster (CC) and related highly sophisticated correlated methods. OVOS is created by using an invariant unitary rotation of the virtual orbitals subspace. New optimization functionals are proposed and implemented. The first type are ‘energy’ functionals. Their optimization leads to the minimal difference between the CCSD, CCD, or the second-order perturbation energy, MP2, in the original orbital basis and the OVOS basis, respectively. Alternatively, linearized ‘overlap’ functionals optimize the overlap between the correlated wave function in the full and the OVOS space, respectively. The original exponential parametrization was replaced by the efficient algorithm for the virtual orbital subspace rotation based on the Lagrangian multipliers technique which ensures orthogonality within rotated virtual orbitals.  The method is illustrated by calculations of correlation energies and/or reaction energies, spectroscopic constants or dipole moments of HF, HCN, HNC, CO and F2 molecules and dissociation energies of pentane to propene and ethane. The ‘overlap’ functional is shown to be more efficient than the ‘energy’ one, particularly in representing triple excitations using OVOS. The basis set dependence of the efficiency of the OVOS technique was also studied.

Evaluation of the intramolecular basis set superposition error in the calculations of larger molecules: [n]helicenes and Phe-Gly-Phe tripeptide

Correlated ab initio calculations on large systems, such as the popular MP2 (or RI‐MP2) method, suffer from the intramolecular basis set superposition error (BSSE). This error is typically manifested in molecules with folded structures, characterized by intramolecular dispersion interactions. It can dramatically affect the energy differences between various conformers as well as intramolecular stabilities, and it can even impair the accuracy of the predictions of the equilibrium molecular structures. In this study, we will present two extreme cases of intramolecular BSSE, the internal stability of [n]helicene molecules and the relative energies of various conformers of phenylalanyl‐glycyl‐phenylalanine tripeptide (Phe‐Gly‐Phe), and compare the calculated data with benchmark values (experimental or high‐level theoretical data). As a practical and cheap solution to the accurate treatment of the systems with large anticipated value of intramolecular BSSE, the recently developed density functional method augmented with an empirical dispersion term (DFT‐D) is proposed and shown to provide very good results in both of the above described representative cases.

MP2.5 and MP2.X: approaching CCSD(T) quality description of noncovalent interaction at the cost of a single CCSD iteration.

The performance of the second-order Møller-Plesset perturbation theory MP2.5 and MP2.X methods, tested on the S22, S66, X40, and other benchmark datasets is briefly reviewed. It is found that both methods produce highly accurate binding energies for the complexes contained in these data sets. Both methods also provide reliable potential energy curves for the complexes in the S66 set. Among the routinely used wavefunction methods, the only other technique that consistently produces lower errors, both for stabilization energies and geometry scans, is the spin-component-scaled coupled-clusters method covering iterative single- and double-electron excitations, which is, however, substantially more computationally intensive. The structures originated from full geometrical gradient optimizations at the MP2.5 and MP2.X level of theory were confirmed to be the closest to the CCSD(T)/CBS (coupled clusters covering iterative single- and double-electron excitations and perturbative triple-electron excitations performed at the complete basis set limit) geometries among all the tested methods (e.g. MP3, SCS(MI)-MP2, MP2, M06-2X, and DFT-D method evaluated with the TPSS functional). The MP2.5 geometries for the tested complexes deviate from the references almost negligibly. Inclusion of the scaled third-order correlation energy results in a substantial improvement of the ability to accurately describe noncovalent interactions. The results shown here serve to support the notion that MP2.5 and MP2.X are reasonable alternative methods for benchmark calculations in cases where system size or (lack of) computational resources preclude the use of CCSD(T)/CBS computations. MP2.X allows for the use of smaller basis sets (i.e. 6-31G*) with results that are nearly identical to those of MP2.5 with larger basis sets, which dramatically decreases computation times and makes calculations on much larger systems possible.

Convergence of the CCSD(T) Correction Term for the Stacked Complex Methyl Adenine-Methyl Thymine: Comparison with Lower-Cost Alternatives.

We have performed large-scale calculations for the interaction energy of the stacked methyl adenine-methyl thymine complex at the CCSD(T)/aug-ccpVXZ (X = D,T) levels. The results can serve as benchmarks for the evaluation of two methods, MP2.5, introduced recently, and the widely used ΔCCSD(T) correction defined as the difference between the CCSD(T) and MP2 energies. Our results confirm that the ΔCCSD(T) correction converges much faster toward the complete basis set (CBS) limit than toward the MP2 or CCSD(T) energies. This justifies approximating the CBS energy by adding the ΔCCSD(T) correction calculated with a modest basis set to a large basis MP2 energy. The fast convergence of the ΔCCSD(T) correction is not obvious, as the individual CCSD and (T) contributions converge less rapidly than their sum. The MP2.5 method performs very well for this system, with results very close to CCSD(T). It is conjectured that using a ΔMP2.5 correction, defined analogously to ΔCCSD(T), with large basis sets may yield more reliable nonbonded interaction energies than using ΔCCSD(T) with a smaller basis set. This would result in important computational savings as the MP3 scales computationally much less steep than CCSD(T), although higher than SCS-MP2, a similar approximation.

Complete Basis Set Extrapolation and Hybrid Schemes for Geometry Gradients of Noncovalent Complexes.

In this paper, we focus on the performance of popular WFT (MP2, MP2.5, MP3, SCS(MI)-MP2, CCSD(T)) and DFT (M06-2X, TPSS-D) methods in optimizations of geometries of noncovalent complexes. Apart from the straightforward comparison of the accuracy of the resulting geometries with respect to the most accurate, computationally affordable, reference method, we have also attempted to determine the most efficient utilization of the information contained in the gradient of a particular method and basis set. Essentially, we have transferred the ideas successfully used for noncovalent interaction energy calculations to geometry optimizations. We have assessed the performance of the hybrid gradients (for instance, MP2 and CCSD(T) calculated in different basis sets), investigated the possibility of extrapolating gradients calculated with a particular method in a series of systematically built basis sets, and finally compared the extrapolated gradients with the counterpoise(CP)-corrected optimizations, in order to determine which of these approaches is more efficient, in terms of their convergence toward the CBS geometry for the respective calculation cost. Further, we compared the efficiency of the CP-corrected, extrapolated, and hybrid gradients in terms of the rate of convergence with respect to basis set size. We have found that CCSD(T) geometries are most faithfully reproduced by the MP2.5 and MP3 methods, followed by the comparably well performing SCS(MI)-MP2 and MP2 methods, and finally by the worst performing DFT-D and M06 methods. Basis set extrapolation of gradients was shown to improve the results and can be considered as a low-cost alternative to the use of CP-corrected gradients. A hybrid gradient scheme was shown to deliver geometries close to the regular gradient reference. Analogously to a similar hybrid scheme, which nowadays is routinely used for the calculation of interaction energies, such a hybrid gradient scheme can save a huge amount of computer time, when high accuracy is desired.

Adsorption of Organic Molecules to van der Waals Materials: Comparison of Fluorographene and Fluorographite with Graphene and Graphite

Understanding strength and nature of noncovalent binding to surfaces imposes significant challenge both for computations and experiments. We explored the adsorption of five small nonpolar organic molecules (acetone, acetonitrile, dichloromethane, ethanol, ethyl acetate) to fluorographene and fluorographite using inverse gas chromatography and theoretical calculations, providing new insights into the strength and nature of adsorption of small organic molecules on these surfaces. The measured adsorption enthalpies on fluorographite range from −7 to −13 kcal/mol and are by 1–2 kcal/mol lower than those measured on graphene/graphite, which indicates higher affinity of organic adsorbates to fluorographene than to graphene. The dispersion-corrected functionals performed well, and the nonlocal vdW DFT functionals (particularly optB86b-vdW) achieved the best agreement with the experimental data. Computations show that the adsorption enthalpies are controlled by the interaction energy, which is dominated by London dispersion forces (∼70%). The calculations also show that bonding to structural features, like edges and steps, as well as defects does not significantly increase the adsorption enthalpies, which explains a low sensitivity of measured adsorption enthalpies to coverage. The adopted Langmuir model for fitting experimental data enabled determination of adsorption entropies. The adsorption on the fluorographene/fluorographite surface resulted in an entropy loss equal to approximately 40% of the gas phase entropy.