Random-phase-approximation-based correlation energy functionals: benchmark results for atoms

The random phase approximation for the correlation energy functional of the density functional theory has recently attracted renewed interest. Formulated in terms of the Kohn-Sham orbitals and eigenvalues, it promises to resolve some of the fundamental limitations of the local density and generalized gradient approximations, as, for instance, their inability to account for dispersion forces. First results for atoms, however, indicate that the random phase approximation overestimates correlation effects as much as the orbital-dependent functional obtained by a second order perturbation expansion on the basis of the Kohn-Sham Hamiltonian. In this contribution, three simple extensions of the random phase approximation are examined; (a) its augmentation by a local density approximation for short-range correlation, (b) its combination with the second order exchange term, and (c) its combination with a partial resummation of the perturbation series including the second order exchange. It is found that the ground state and correlation energies as well as the ionization potentials resulting from the extensions (a) and (c) for closed subshell atoms are clearly superior to those obtained with the unmodified random phase approximation. Quite some effort is made to ensure highly converged data, so that the results may serve as benchmark data. The numerical techniques developed in this context, in particular, for the inherent frequency integration, should also be useful for applications of random phase approximation-type functionals to more complex systems.     

Die Molrefraktion von Aquo-Ionen metallischer Elemente und die Auswertung von Lichtbrechungsmessungen in der anorganischen Chemie

It is shown that molar polarisabilities α of aqueous solutions of electrolytes previously measured by HEYDWEILLER and other authors, and here of lanthanide (III) and bismuth (III) perchlorates, can be brought in much better agreement with α values for crystalline substances than usually thought, and that additivity of α for each constituent is a remarkably good approximation, except in the case of complexes having very intense electron transfer bands. In an isoelectronic series, α normally decreases from M(I) to M(II) but frequently increases in direction of M(III) and M(IV). The oscillator strength and contributions from inner shells are discussed, and an effect of half-filled shells on excitation energies pointed out.     

Sum Rules for the spin surface response of metal clusters within the time dependent local spin density approximation

We study surface spin collective modes of simple metallic clusters using a sum rule approach. We derive analytical expressions for the energy and cubic energy-weighted moments of the time-dependent local-spin-density approximation (TDLSDA) strength function. With these two moments we obtain a mean excitation energy of multipole spin modes and study its dispersion with cluster size up to very large sizes. The crucial roles played by the surface diffuseness and by correlation and kinetic energy effects on the resonance energies are stressed.     

The behaviour of allyl thiourea at a mercury-solution interface as an example of adsorption in several states with partial electron transfer

The superficial excesses determined from electrode charge measurements have been studied at constant potential or charge. The usual tests suggest a change in the orientation of the adsorbed molecule. It is shown theoretically that the Frumkin isotherm still offers an useful approximation when two adsorbed states are considered. In this case, two at least of the three adjustable parameters, the apparent adsorption energy, and the apparent molecular area, change with the electrical variable, being function of the adsorption energies for both states and also of the corresponding molecular areas. Consistent results are obtained from the consideration of isotherms using this approximation and from examination of the apparent adsorption valency.     

SAMPL6 host–guest challenge: binding free energies via a multistep approach

In this effort in the SAMPL6 host–guest binding challenge, a combination of molecular dynamics and quantum mechanical methods were used to blindly predict the host–guest binding free energies of a series of cucurbit[8]uril (CB8), octa-acid (OA), and tetramethyl octa-acid (TEMOA) hosts bound to various guest molecules in aqueous solution. Poses for host–guest systems were generated via molecular dynamics (MD) simulations and clustering analyses. The binding free energies for the structures obtained via cluster analyses of MD trajectories were calculated using the MMPBSA method and density functional theory (DFT) with the inclusion of Grimme’s dispersion correction, an implicit solvation model to model the aqueous solution, and the resolution-of-the-identity (RI) approximation (MMPBSA, RI-B3PW91-D3, and RI-B3PW91, respectively). Among these three methods tested, the results for OA and TEMOA systems showed MMPBSA and RI-B3PW91-D3 methods can be used to qualitatively rank binding energies of small molecules with an overbinding by 7 and 37 kcal/mol respectively, and RI-B3PW91 gave the poorest quality results, indicating the importance of dispersion correction for the binding free energy calculations. Due to the complexity of the CB8 systems, all of the methods tested show poor correlation with the experimental results. Other quantum mechanical approaches used for the calculation of binding free energies included DFT without the RI approximation, utilizing truncated basis sets to reduce the computational cost (memory, disk space, CPU time), and a corrected dielectric constant to account for ionic strength within the implicit solvation model.     

Protein-ligand interaction energies with dispersion corrected density functional theory and high-level wave function based methods

With dispersion-corrected density functional theory (DFT-D3) intermolecular interaction energies for a diverse set of noncovalently bound protein-ligand complexes from the Protein Data Bank are calculated. The focus is on major contacts occurring between the drug molecule and the binding site. Generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are used. DFT-D3 interaction energies are benchmarked against the best available wave function based results that are provided by the estimated complete basis set (CBS) limit of the local pair natural orbital coupled-electron pair approximation (LPNO-CEPA/1) and compared to MP2 and semiempirical data. The size of the complexes and their interaction energies (ΔE(PL)) varies between 50 and 300 atoms and from -1 to -65 kcal/mol, respectively. Basis set effects are considered by applying extended sets of triple- to quadruple-ζ quality. Computed total ΔE(PL) values show a good correlation with the dispersion contribution despite the fact that the protein-ligand complexes contain many hydrogen bonds. It is concluded that an adequate, for example, asymptotically correct, treatment of dispersion interactions is necessary for the realistic modeling of protein-ligand binding. Inclusion of the dispersion correction drastically reduces the dependence of the computed interaction energies on the density functional compared to uncorrected DFT results. DFT-D3 methods provide results that are consistent with LPNO-CEPA/1 and MP2, the differences of about 1-2 kcal/mol on average (<5% of ΔE(PL)) being on the order of their accuracy, while dispersion-corrected semiempirical AM1 and PM3 approaches show a deviating behavior. The DFT-D3 results are found to depend insignificantly on the choice of the short-range damping model. We propose to use DFT-D3 as an essential ingredient in a QM/MM approach for advanced virtual screening approaches of protein-ligand interactions to be combined with similarly "first-principle" accounts for the estimation of solvation and entropic effects.     

Basis set convergence of molecular correlation energy differences within the random phase approximation

The basis set convergence of energy differences obtained from the random phase approximation (RPA) to the correlation energy is investigated for a wide range of molecular interactions. For dispersion bound systems the basis set incompleteness error is most pronounced, as shown for the S22 benchmark [P. Jurecka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The use of very large basis sets (> quintuple-zeta) or extrapolation to the complete basis set (CBS) limit is necessary to obtain a reliable estimate of the binding energy for these systems. Counterpoise corrected results converge to the same CBS limit, but counterpoise correction without extrapolation is insufficient. Core-valence correlations do not play a significant role. For medium- and short-range correlation, quadruple-zeta results are essentially converged, as demonstrated for relative alkane conformer energies, reaction energies dominated by intramolecular dispersion, isomerization energies, and reaction energies of small organic molecules. Except for weakly bound systems, diffuse augmentation almost universally slows down basis set convergence. For most RPA applications, quadruple-zeta valence basis sets offer a good balance between accuracy and efficiency.     

Increasing the applicability of density functional theory. II. Correlation potentials from the random phase approximation and beyond

Density functional theory (DFT) results are mistrusted at times due to the presence of an unknown exchange correlation functional, with no practical way to guarantee convergence to the right answer. The use of a known exchange correlation functional based on wave-function theory helps to alleviate such mistrust. The exchange correlation functionals can be written exactly in terms of the density-density response function using the adiabatic-connection and fluctuation-dissipation framework. The random phase approximation (RPA) is the simplest approximation for the density-density response function. Since the correlation functional obtained from RPA is equivalent to the direct ring coupled cluster doubles (ring-CCD) correlation functional, meaning only Coulomb interactions are included, one can bracket RPA between many body perturbation theory (MBPT)-2 and CCD with the latter having all ring, ladder, and exchange contributions. Using an optimized effective potential strategy, we obtain correlation potentials corresponding to MBPT-2, RPA (ring-CCD), linear-CCD, and CCD. Using the suitable choice of the unperturbed Hamiltonian, Kohn-Sham self-consistent calculations are performed. The spatial behavior of the resulting potentials, total energies, and the HOMO eigenvalues are compared with the exact values for spherical atoms. Further, we demonstrate that the self-consistent eigenvalues obtained from these consistent potentials used in ab initio dft approximate all principal ionization potentials as demanded by ionization potential theorem.     

高能体系分子间相互作用研究: 含NNO~2和NH~2混合物

以abinitioHF/6-31G^*计算求得NH~3+NH~2NO~2的两种优化构型,经MP4电子相关能校正和Boys-Bernardi方案校正基组叠加误差求得精确的分子间相互作用能。还用PM3方法计算研究TATB(均三氨基三硝基苯)分别与HMX(奥克托金)和RDX(黑索金)的混合体系,经色散能校正电子相关近似地求得分子间相互作用能。结果表明,NH~3与NH~2NO~2之间的最大结合能为-38.32kJ/mol;分子间相互作用增强了N-NO~2键强度;TATB与HMX,RDX的结合能远大于石墨与HMX或RDX的结合能,表明TATB对HMX和RDX的润湿和钝感作用较石墨更强。     

The divide-expand-consolidate family of coupled cluster methods: numerical illustrations using second order Møller-Plesset perturbation theory

Previously, we have introduced the linear scaling coupled cluster (CC) divide-expand-consolidate (DEC) method, using an occupied space partitioning of the standard correlation energy. In this article, we show that the correlation energy may alternatively be expressed using a virtual space partitioning, and that the Lagrangian correlation energy may be partitioned using elements from both the occupied and virtual partitioning schemes. The partitionings of the correlation energy leads to atomic site and pair interaction energies which are term-wise invariant with respect to an orthogonal transformation among the occupied or the virtual orbitals. Evaluating the atomic site and pair interaction energies using local orbitals leads to a linear scaling algorithm and a distinction between Coulomb hole and dispersion energy contributions to the correlation energy. Further, a detailed error analysis is performed illustrating the error control imposed on all components of the energy by the chosen energy threshold. This error control is ultimately used to show how to reduce the computational cost for evaluating dispersion energy contributions in DEC.     

On the Stability of Cyclophane Derivates Using a Molecular Fragmentation Method

A molecular fragmentation method is used to study the stability of cyclophane derivates by decomposing the molecular energy into the molecular strain and intramolecular interaction energies. The molecular strain energies obtained by utilising the fragmentation method are in good agreement with existing experimental data. The intramolecular interaction energies calculated as the difference between the supermolecular energy and the bonded fragment energies are repulsive in the cyclophanes studied. The nature of this interaction is studied for groups of systematically extended doubled layered paracyclophane systems using the random‐phase approximation (RPA), two recently developed extensions to the RPA and standard density functional theory (DFT) methods including dispersion corrections. Upon a systematic increase in conjugation the strongly repulsive intramolecular interaction energy reduces and thus leads to an increase in the stability. Finally, existing experimental and theoretical estimates of the molecular strain are compared with the results of this work.     

Noncovalent interactions between cisplatin and graphene prototypes

Cisplatin (CP) has been widely used as an anticancer drug for more than 30 years despite severe side effects due to its low bioavailability and poor specificity. For this reason, it is paramount to study and design novel nanomaterials to be used as vectors capable to effectively deliver the drug to the biological target. The CP square‐planar geometry, together with its low water solubility, suggests that it could be possibly easily adsorbed on 2D graphene nanostructures through the interaction with the related highly conjugated π‐electron system. In this work, pyrene has been first selected as the minimum approximation to the graphene plane, which allows to properly study the noncovalent interactions determining the CP adsorption. In particular, electronic structure calculations at the MP2C and DFT‐SAPT levels of theory have allowed to obtain benchmark interaction energies for some limiting configurations of the CP–pyrene complex, as well as to assess the role of the different contributions to the total interaction: it has been found that the parallel configurations of the aggregate are mainly stabilized around the minimum region by dispersion, in a similar way as for complexes bonded through π‐π interactions. Then, the benchmark interaction energies have been used to test corresponding estimations obtained within the less expensive DFT to validate an optimal exchange‐correlation functional which includes corrections to take properly into account for the dispersion contribution. Reliable DFT interaction energies have been therefore obtained for CP adsorbed on graphene prototypes of increasing size, ranging from coronene, ovalene, and up to C₁₅₀H₃₀. Finally, DFT geometry optimizations and frequency calculations have also allowed a reliable estimation of the adsorption enthalpy of CP on graphene, which is found particularly favorable (about −20 kcal/mol at 298 K and 1 bar) being twice that estimated for the corresponding benzene adsorption. © 2017 Wiley Periodicals, Inc.     

Density-functional theory with effective potential expressed as a direct mapping of the external potential: applications to atomization energies and ionization potentials

In this paper the authors further develop and apply the direct-mapping density functional theory to calculations of the atomization energies and ionization potentials. Single-particle orbitals are determined by solving the Kohn-Sham [Phys. Rev. A. 140, 1133 (1965)] equations with a local effective potential expressed in terms of the external potential. A two-parametric form of the effective potential for molecules is proposed and equations for optimization of the parameters are derived using the exchange-only approximation. Orbital-dependent correlation functional is derived from the second-order perturbation theory in its Moller-Plesset-type zeroth-order approximation based on the Kohn-Sham orbitals and orbital energies. The total atomization energies and ionization potentials computed with the second-order perturbation theory were found to be in agreement with experimental values and benchmark results obtained with ab initio wave mechanics methods.     

Approximation function for the direct calculation of rate constants and Gibbs activation energies of enantiomerization of racemic mixtures from chromatographic parameters in dynamic chromatography

An approximation function for enantioselective dynamic chromatography of racemic mixtures of interconverting enantiomers has been derived that allows the direct calculation of enantiomerization rate constants (k1 and k(-1)) and Gibbs activation energies of enantiomerization, deltaG++ , from chromatographic parameters, i.e., retention times of the enantiomers A and B ((t(A)R and t(B)R), peak widths at half height (WA and wB) and the relative plateau height (hplateau), without computer simulation. The reaction rate constants of enantiomerization, k(-1), obtained with this approximation function, have been validated by comparison with a simulated dataset of 15,625 chromatograms. The mean, standard deviation and confidence interval show a high correlation between the approximated and simulated rate constants. The average deviation from the Gibbs activation enthalpy of enantiomerization, deltaG++, has been estimated to be as small as about +/- 0.11 RT.     

Dispersion interaction between helium pair from hydrodynamic analogy to quantum mechanics

Frequency-dependent multipole polarizabilities of the He sequence have been calculated from a hydrodynamic model of quantum mechanics and using an independent-particle model Hamiltonian. Our present scheme is parallel to the uncoupled Hartree–Fock approximation so our values of polarizabilities, multipole transition energies and dispersion force coefficients between the He? He pair are comparable with earlier works using the uncoupled Hartree–Fock approximation.     

New ab initio potential energy surface and the vibration-rotation-tunneling levels of (H2O)2 and (D2O)2

We report a new full-dimensional potential energy surface (PES) for the water dimer, based on fitting energies at roughly 30,000 configurations obtained with the coupled-cluster single and double, and perturbative treatment of triple excitations method using an augmented, correlation consistent, polarized triple zeta basis set. A global dipole moment surface based on Moller-Plesset perturbation theory results at these configurations is also reported. The PES is used in rigorous quantum calculations of intermolecular vibrational frequencies, tunneling splittings, and rotational constants for (H2O)2 and (D2O)2, using the rigid monomer approximation. Agreement with experiment is excellent and is at the highest level reported to date. The validity of this approximation is examined by comparing tunneling barriers within that model with those from fully relaxed calculations.     

Fluctuation-dissipation theorem density-functional theory

Using the fluctuation-dissipation theorem (FDT) in the context of density-functional theory (DFT), one can derive an exact expression for the ground-state correlation energy in terms of the frequency-dependent density response function. When combined with time-dependent density-functional theory, a new class of density functionals results that use approximations to the exchange-correlation kernel fxc as input. This FDT-DFT scheme holds promise to solve two of the most distressing problems of conventional Kohn-Sham DFT: (i) It leads to correlation energy functionals compatible with exact exchange, and (ii) it naturally includes dispersion. The price is a moderately expensive O(N6) scaling of computational cost and a slower basis set convergence. These general features of FDT-DFT have all been recognized previously. In this paper, we present the first benchmark results for a set of molecules using FDT-DFT beyond the random-phase approximation (RPA)-that is, the first such results with fxc not equal to 0. We show that kernels derived from the adiabatic local-density approximation and other semilocal functionals suffer from an "ultraviolet catastrophe," producing a pair density that diverges at small interparticle distance. Nevertheless, dispersion interactions can be treated accurately if hybrid functionals are employed, as is demonstrated for He2 and HeNe. We outline constraints that future approximations to fxc should satisfy and discuss the prospects of FDT-DFT.     

Ab initio Calculation of Intermolecular Dispersion Energy and Induction Energy of Nitramide Dimer

The dispersion energies, induction energies and their exchange counterparts (exchange-dispersion and exchange-induction energies) between two interacting nitramide molecules at several separations are derived based upon symmetry-adapted perturbation theory (SAPT). The results show that (1) the effect of intramonomer electron correlation on dispersion energies and induction energies for nitramide dimer system is remarkable especially in the region near the van der Waals minimum distance (0.42 nm). (2) At smaller separations the dispersion energies and the induction energies are largely quenched by their exchange counterparts, and this case in induction interaction is much more remarkable than in dispersion interaction. (3) Since at shorter distances there exists the strong short-range interaction due to electron transfer which quickly decays and even disappears at larger separations, the two different R-dependency formulae of induction energies were found: one is ca. R^-12.7 at short distances, and the other ca. R^-7.0 at large separations. The latter R-dependency is similar to that (ca.R^-7.2) of dispersion. (4) In the case of strong polar interaction existing in nitramide dimer, the “true“ induction correlation terms of higher order than ^1Eind^(22) may be important.     

Nonlocal van der Waals density functional: the simpler the better

We devise a nonlocal correlation energy functional that describes the entire range of dispersion interactions in a seamless fashion using only the electron density as input. The new functional is considerably simpler than its predecessors of a similar type. The functional has a tractable and robust analytic form that lends itself to efficient self-consistent implementation. When paired with an appropriate exchange functional, our nonlocal correlation model yields accurate interaction energies of weakly-bound complexes, not only near the energy minima but also far from equilibrium. Our model exhibits an outstanding precision at predicting equilibrium intermonomer separations in van der Waals complexes. It also gives accurate covalent bond lengths and atomization energies. Hence the functional proposed in this work is a computationally inexpensive electronic structure tool of broad applicability.