Accuracy of the effective fragment potential (EFP) method was explored for describing intermolecular interaction energies in three dimers with strong H-bonded interactions, formic acid, formamide, and formamidine dimers, which are a part of HBC6 database of noncovalent interactions. Monomer geometries in these dimers change significantly as a function of intermonomer separation. Several EFP schemes were considered, in which fragment parameters were prepared for a fragment in its gas-phase geometry or recomputed for each unique fragment geometry. Additionally, a scheme in which gas-phase fragment parameters are shifted according to relaxed fragment geometries is introduced and tested. EFP data are compared against the coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) method in a complete basis set (CBS) and the symmetry adapted perturbation theory (SAPT). All considered EFP schemes provide a good agreement with CCSD(T)/CBS for binding energies at equilibrium separations, with discrepancies not exceeding 2 kcal/mol. However, only the schemes that utilize relaxed fragment geometries remain qualitatively correct at shorter than equilibrium intermolecular distances. The EFP scheme with shifted parameters behaves quantitatively similar to the scheme in which parameters are recomputed for each monomer geometry and thus is recommended as a computationally efficient approach for large-scale EFP simulations of flexible systems.

The dispersion energy term between quantum-mechanical (QM) and classical (represented by effective fragment potentials, EFP) subsystems is developed and implemented. A new formulation is based on long-range perturbation theory and uses dynamic polarizability tensors of the effective fragments and electric field integrals and orbital energies of the quantum-mechanical subsystem. No parametrization is involved. The accuracy of the QM–EFP dispersion energy is tested on a number of model systems; the average mean unsigned error is 0.8 kcal/mol or 13% with respect to the symmetry adapted perturbation theory on the S22 data set of noncovalent interactions. The computational cost of the dispersion energy computation is low compared to the self-consistent field calculation of the QM subsystem. The dispersion energy is sensitive to the level of theory employed for the QM part and to the electrostatic interactions in the system. The latter means that the dispersion interactions in the QM/EFP method are not purely two-body but have more complex many-body behavior.

Most approximations to the exchange-correlation functional of Kohn–Sham density functional theory lead to delocalization errors that undermine the description of charge-transfer phenomena. We explore how various approximate functionals and charge-distribution schemes describe ground-state atomic-charge distributions in the lithium–benzene complex, a model system of relevance to carbon-based supercapacitors. To understand the trends, we compare Hartree–Fock (HF) and correlated post-HF calculations, confirming that the HOMO–LUMO gap is narrower in semilocal functionals but widened by hybrid functionals with large fractions of HF exchange. For semilocal functionals, natural bond orbital (NBO) and Mulliken schemes yield opposite pictures of how charge transfer occurs. In PBE, for example, when lithium and benzene are <1.5 Å apart, NBO yields a positive charge on the lithium atom, but the Mulliken scheme yields a negative charge. Furthermore, the partial charges in conjugated materials depend on the interplay between the charge-distribution scheme employed and the underlying exchange-correlation functional, being critically sensitive to the admixture of HF exchange. We analyze and explain why this happens, discuss implications, and conclude that hybrid functionals with an admixture of about one-fourth of HF exchange are particularly useful in describing charge transfer in the lithium–benzene model.

Oxidative stress plays a role in many biological phenomena, but involved mechanisms and individual reactions are not well understood. Correlated electronic structure calculations with the MP2, MP4, and CCSD(T) methods detail thermodynamic and kinetic information for the free radical oxygen protein oxidation pathway studied in a trialanine model system. The pathway includes aerobic, anaerobic and termination reactions. The course of the oxidation process depends on local conditions and availability of specific reactive oxygen species (ROS). A chemical mechanism is proposed for how oxidative stress promotes β-structure formation in the amyloid diseases. The work can be used to aid experimentalists as they explore individual reactions and mechanisms involving oxygen free radicals and oxidative stress in β-structured proteins.

The effective fragment potential (EFP) approach, which can be described as a nonempirical polarizable force field, affords an accurate first-principles treatment of noncovalent interactions in extended systems. EFP can also describe the effect of the environment on the electronic properties (e.g., electronic excitation energies and ionization and electron-attachment energies) of a subsystem via the QM/EFP (quantum mechanics/EFP) polarizable embedding scheme. The original formulation of the method assumes that the system can be separated, without breaking covalent bonds, into closed-shell fragments, such as solvent and solute molecules. Here, we present an extension of the EFP method to macromolecules (mEFP). Several schemes for breaking a large molecule into small fragments described by EFP are presented and benchmarked. We focus on the electronic properties of molecules embedded into a protein environment and consider ionization, electron-attachment, and excitation energies (single-point calculations only). The model systems include chromophores of green and red fluorescent proteins surrounded by several nearby amino acid residues and phenolate bound to the T4 lysozyme. All mEFP schemes show robust performance and accurately reproduce the reference full QM calculations. For further applications of mEFP, we recommend either the scheme in which the peptide is cut along the Cα–C bond, giving rise to one fragment per amino acid, or the scheme with two cuts per amino acid, along the Cα–C and Cα–N bonds. While using these fragmentation schemes, the errors in solvatochromic shifts in electronic energy differences (excitation, ionization, electron detachment, or electron-attachment) do not exceed 0.1 eV. The largest error of QM/mEFP against QM/EFP (no fragmentation of the EFP part) is 0.06 eV (in most cases, the errors are 0.01–0.02 eV). The errors in the QM/molecular mechanics calculations with standard point charges can be as large as 0.3 eV.

The mechanism by which carbon condenses to form PAHs or fullerenes is a problem that has garnered considerable theoretical and experimental attention. The ring-coalescence and annealing model for the formation of C60 involves a [2 + 2] cycloaddition reaction of a cyclopolyyne to form a tetraalkynyl cyclobuta-1,3-diene intermediate, followed by a Bergman cycloaromatization reaction of the enediyne moiety. Intramolecular trapping of the incipient p-benzyne diradical across a diyne moiety of the macrocyclic ring affords an aromatic ring that must undergo further intramolecular reactions via polyradical intermediates to produce a condensed graphitic structure or fullerene. Computational studies of a model system for the intriguing tetraalkynylcyclobuta-1,3-diene intermediate, however, reveal that the corresponding p-benzyne diradical lies in a shallow minimum with a very low barrier to ring opening to cyclooctadienediyne. This pathway has not been previously considered in the mechanism for carbon condensation.

Noncovalent interactions play an important role in the stabilization of biological molecules. The effective fragment potential (EFP) is a computationally inexpensive ab initio-based method for modeling intermolecular interactions in noncovalently bound systems. The accuracy of EFP is benchmarked against the S22 and S66 data sets for noncovalent interactions [Jurečka, P.; Šponer, J.; Černý, J.; Hobza, P. Phys. Chem. Chem. Phys.2006, 8, 1985; Řezáč, J.; Riley, K. E.; Hobza, P. J. Chem. Theory Comput.2011, 7, 2427]. The mean unsigned error (MUE) of EFP interaction energies with respect to coupled-cluster singles, doubles, and perturbative triples in the complete basis set limit [CCSD(T)/CBS] is 0.9 and 0.6 kcal/mol for S22 and S66, respectively, which is similar to the MUE of MP2 and SCS-MP2 for the same data sets, but with a greatly reduced computational expense. Moreover, EFP outperforms classical force fields and popular DFT functionals such as B3LYP and PBE, while newer dispersion-corrected functionals provide a more accurate description of noncovalent interactions. Comparison of EFP energy components with the symmetry-adapted perturbation theory (SAPT) energies for the S22 data set shows that the main source of errors in EFP comes from Coulomb and polarization terms and provides a valuable benchmark for further improvements in the accuracy of EFP and force fields in general.

The effects of ethynyl substitution on the electronic structure of cyclobutadiene are investigated in this work. Ethynyl substituted cyclobutadienes may be involved in Bergman cyclization reactions and are possible intermediates in the formation of fullerenes and graphitic sheets. Prediction of the electronic structure of cyclobutadiene is challenging for single-reference ab initio methods because of Jahn–Teller distortions and the diradical character of the singlet state. The equation-of-motion spin-flip coupled-cluster with single and double excitations (EOM-SF-CCSD) method accurately describes diradical states and is used to determine vertical and adiabatic singlet–triplet energy splittings in the substituted cyclobutadienes. The adiabatic singlet–triplet gaps decrease upon substituent addition, but the singlet states remain lower in energy. However, the results are affected by spin-contamination of the reference state and deteriorate when an unrestricted HF reference is employed. Additional insights in the electronic structure of cyclobutadienes are obtained by analyzing natural charges and spin densities. The substituents pull the charge out of the cyclobutadiene ring; however, the natural charges and spin densities are found to be nearly independent of the geometry and spin state.

Structure and bonding patterns in tert-butanol (TBA)–water mixtures are investigated by using molecular dynamics simulations with the effective fragment potential (EFP) method. EFP is a model potential in which all parameters are obtained from a set of ab initio calculations on isolated fragment molecules. Mixed-basis EFP potentials (called “EFPm”) for water and TBA molecules were prepared and tested in this work. The accuracy of these EFP potentials is justified by comparison of structures and binding energies in water, TBA, and water–TBA dimers with MP2/6-311++G(d,p) data. It has been found that the discrepancies between EFP and MP2 do not exceed 0.1 Å in intermolecular distances and 1 kcal/mol in binding energies. Structures of TBA–water solutions with 0.0, 0.06, 0.11, 0.16, and 0.50 TBA mole fractions were analyzed by using radial distribution functions (RDFs) and coordination numbers. These results suggest that, at low TBA concentrations, the structure of water is enhanced and water and TBA are not homogeneously mixed at the molecular level. In the equimolar TBA–water solution, the microscopic mixing is more complete. Analysis of the energy components in TBA–water solutions shows that, while the electrostatic and exchange-repulsion terms provide the largest contributions to the total potential energy, the relative importance of the polarization and dispersion terms depends on the concentration of TBA. With an increase of TBA concentration, the fraction of the dispersion energy increases, while the fraction of polarization energy diminishes. However, both polarization and dispersion terms are essential for accurate description of these systems.

Solvatochromic shifts of the electronic states of a chromophore can be used as a measure of solute−solvent interactions. The shifts of the electronic states of a model organic chromophore, p-nitroaniline (pNA), embedded in solvents with different polarities (water, 1,4-dioxane, and cyclohexane) are studied using a hybrid quantum mechanics/molecular-mechanics-type technique in which the chromophore is described by the configuration interaction singles with perturbative doubles (CIS(D)) method while the solvent is treated by the effective fragment potential (EFP) method. This newly developed CIS(D)/EFP scheme includes the quantum-mechanical coupling of the Coulomb and polarization terms; however, short-range dispersion and exchange-repulsion terms of EFP are not included in the quantum Hamiltonian. The CIS(D)/EFP model is benchmarked against the more accurate equation of motion coupled cluster with singles and doubles (EOM-CCSD)/EFP method on a set of small pNA-water clusters. CIS(D)/EFP accurately predicts the red solvatochromic shift of the charge-transfer π → π* state of pNA in polar water. The shift is underestimated in less polar dioxane and cyclohexane probably because of the omission of the explicit quantum-mechanical treatment of the short-range terms. Different solvation of singlet and triplet states of pNA results in different probabilities of intersystem crossing (ISC) and internal conversion (IC) pathways of energy relaxation in solvents of different polarity. Computed singlet−triplet splittings in water and dioxane qualitatively explain the active ISC channel in dioxane and predict almost no conversion to the triplet manifold in water, in agreement with experimental findings.

It has been suggested that fluorescence from amine-containing dendrimer compounds could be the result of a charge transfer between amine groups and molecular oxygen [Chu, C.-C.; Imae, T. Macromol. Rapid Commun.2009, 30, 89.]. In this paper we employ equation-of-motion coupled cluster computational methods to study the electronic structure of an ammonia–oxygen model complex to examine this possibility. The results reveal several bound electronic states with charge transfer character with emission energies generally consistent with previous observations. However, further work involving confinement, solvent, and amine structure effects will be necessary for more rigorous examination of the charge transfer fluorescence hypothesis.

A hybrid quantum mechanics/molecular mechanics (QM/MM) method for the electronic excited states has been developed. The equation-of-motion coupled cluster with single and double excitations method (EOM-CCSD) is used for the QM region, while the effective fragment potential (EFP) method describes a MM part. The EFP method overcomes the most significant limitation of QM/MM by replacing empirical MM interactions and QM/MM coupling by parameter-free first-principles-based ones, while retaining the computational efficiency of QM/MM. The developed QM/MM scheme involves quantum-mechanical coupling of the electrostatic and polarization terms in the QM/MM Hamiltonian and allows accurate calculation of the electronic excited states of chromophores in various environments. Applications to the water complexes of formaldehyde and p-nitroaniline show that the orbital relaxation of the solute in the electric field of the solvent provides the majority of the solvatochromic effect, and the response of the polarizable environment to the density of the specific electronic state is much smaller in magnitude.

The implementation of the effective fragment potential (EFP) method within the Q-CHEM electronic structure package is presented. The EFP method is used to study noncovalent π−π and hydrogen-bonding interactions in DNA strands. Since EFP is a computationally inexpensive alternative to high-level ab initio calculations, it is possible to go beyond the dimers of nucleic acid bases and to investigate the asymptotic behavior of different components of the total interaction energy. The calculations demonstrated that the dispersion energy is a leading component in π-stacked oligomers of all sizes. Exchange-repulsion energy also plays an important role. The contribution of polarization is small in these systems, whereas the magnitude of electrostatics varies. Pairwise fragment interactions (i.e., the sum of dimer binding energies) were found to be a good approximation for the oligomer energy.