Incorporation of charge transfer into the explicit polarization fragment method by grand canonical density functional theory

A double exponential coupled cluster theory in the fragment molecular orbital framework

Fragmentation-based methods enable electronic structure calculations for large chemical systems through partitioning them into smaller fragments. Here, we have developed and benchmarked a dual exponential operator-based coupled cluster theory to account for high-rank electronic correlation of large chemical systems within the fragment molecular orbital (FMO) framework. Upon partitioning the molecular system into several fragments, the zeroth order reference determinants for each fragment and fragment pair are constructed in a self-consistent manner with two-body FMO expansion. The dynamical correlation is induced through a dual exponential ansatz with a set of fragment-specific rank-one and rank-two operators that act on the individual reference determinants. While the single and double excitations for each fragment are included through the conventional rank-one and rank-two cluster operators, the triple excitation space is spanned via the contraction between the cluster operators and a set of rank-two scattering operators over a few optimized fragment-specific occupied and virtual orbitals. Thus, the high-rank dynamical correlation effects within the FMO framework are computed with rank-one and rank-two parametrization of the wave operator, leading to significant reduction in the number of variables and associated computational scaling over the conventional methods. Through a series of pilot numerical applications on various covalent and non-covalently bonded systems, we have shown the quantitative accuracy of the proposed methodology compared to canonical, as well as FMO-based coupled-cluster single double triple. The accuracy of the proposed method is shown to be systematically improvable upon increasing the number of contractible occupied and virtual molecular orbitals employed to simulate triple excitations.

Quantum mechanical force fields for condensed phase molecular simulations

Molecular simulations are powerful tools for providing atomic-level details into complex chemical and physical processes that occur in the condensed phase. For strongly interacting systems where quantum many-body effects are known to play an important role, density-functional methods are often used to provide the model with the potential energy used to drive dynamics. These methods, however, suffer from two major drawbacks. First, they are often too computationally intensive to practically apply to large systems over long time scales, limiting their scope of application. Second, there remain challenges for these models to obtain the necessary level of accuracy for weak non-bonded interactions to obtain quantitative accuracy for a wide range of condensed phase properties. Quantum mechanical force fields (QMFFs) provide a potential solution to both of these limitations. In this review, we address recent advances in the development of QMFFs for condensed phase simulations. In particular, we examine the development of QMFF models using both approximate and ab initio density-functional models, the treatment of short-ranged non-bonded and long-ranged electrostatic interactions, and stability issues in molecular dynamics calculations. Example calculations are provided for crystalline systems, liquid water, and ionic liquids. We conclude with a perspective for emerging challenges and future research directions.

Ionization Energies and Aqueous Redox Potentials of Organic Molecules: Comparison of DFT, Correlated ab Initio Theory and Pair Natural Orbital Approaches

The calculation of redox potentials involves large energetic terms arising from gas phase ionization energies, thermodynamic contributions, and solvation energies of the reduced and oxidized species. In this work we study the performance of a wide range of wave function and density functional theory methods for the prediction of ionization energies and aqueous one-electron oxidation potentials of a set of 19 organic molecules. Emphasis is placed on evaluating methods that employ the computationally efficient local pair natural orbital (LPNO) approach, as well as several implementations of coupled cluster theory and explicitly correlated F12 methods. The electronic energies are combined with implicit solvation models for the solvation energies. With the exception of MP2 and its variants, which suffer from enormous errors arising at least partially from the poor Hartree-Fock reference, ionization energies can be systematically predicted with average errors below 0.1 eV for most of the correlated wave function based methods studies here, provided basis set extrapolation is performed. LPNO methods are the most efficient way to achieve this type of accuracy. DFT methods show in general larger errors and suffer from inconsistent behavior. The only exception is the M06-2X functional which is found to be competitive with the best LPNO-based approaches for ionization energies. Importantly, the limiting factor for the calculation of accurate redox potentials is the solvation energy. The errors in the predicted solvation energies by all continuum solvation models tested in this work dominate the final computed reduction potential, resulting in average errors typically in excess of 0.3 V and hence obscuring the gains that arise from choosing a more accurate electronic structure method.

Optical and positron annihilation spectroscopic studies on PMMA polymer doped by rhodamine B/chloranilic acid charge transfer complex: Special relevance to the effect of γ-ray irradiation

Polymeric sheets of poly (methylmethaclyerate) (PMMA) containing charge transfer (CT) complex of rhodamine B/chloranilic acid (Rho B/CHA) were synthesized in methanol solvent at room temperature. The systematic analysis done on the Rho B and its CT complex in the form of powder or polymeric sheets confirmed their structure and thermal stability. The IR spectra interpreted the charge transfer mode of interaction between the CHA central positions and the terminal carboxylic group. The polymer sheets were irradiated with 70 kGy of γ radiation using (60)Co source to study the enhanced changes in the structure and optical parameters. The microstructure changes of the PMMA sheets caused by γ-ray irradiation were analyzed using positron annihilation lifetime (PAL) and positron annihilation Doppler broadening (PADB) techniques. The positron life time components (τ(i)) and their corresponding intensities (I(i)) as well as PADB line-shape parameters (S and W) were found to be highly sensitive to the enhanced disorder occurred in the organic chains of the polymeric sheets due to γ-irradiation.

Intermediate electrostatic field for the generalized elongation method

An intermediate electrostatic field is introduced to improve the accuracy of fragment-based quantum-chemical computational methods by including long-range polarizations of biomolecules. The point charge distribution of the intermediate field is generated by a charge sensitivity analysis that is parameterized for five different population analyses, namely, atoms-in-molecules, Hirshfeld, Mulliken, natural orbital, and Voronoi population analysis. Two model systems are chosen to demonstrate the performance of the generalized elongation method (ELG) combined with the intermediate electrostatic field. The calculations are performed for the STO-3G, 6-31G, and 6-31G(d) basis sets and compared with reference Hartree-Fock calculations. It is shown that the error in the total energy is reduced by one order of magnitude, independently of the population analyses used. This demonstrates the importance of long-range polarization in electronic-structure calculations by fragmentation techniques.

Structural and computational insights into the versatility of cadmium binding to proteins

Cadmium is a highly toxic group XII metal, similar to zinc and mercury. Unlike zinc, which is one of the most common metal cofactors in biology, cadmium is highly toxic. Many Zn(2+)-binding proteins can bind Cd(2+)-ions without significantly affecting their structures. Here, the protein data bank is analysed with regard to protein-cadmium interactions, which shows that cadmium can bind to a variety of ion binding sites in proteins. Statistical analysis of Cd(2+)-side chain interactions is compared with a similar analysis of other ions. This analysis reveals that with regard to amino acid side-chain preference, Cd(2+) is more similar to Mn(2+) than to Zn(2+) or Hg(2+). Finally, the interaction energies of three native metal binding proteins are calculated where Cd(2+) binds instead of Zn(2+), Ca(2+) or Cu(2+). The interaction energies are decomposed into individual components whose contributions are discussed.

Parametrization of an Orbital-Based Linear-Scaling Quantum Force Field for Noncovalent Interactions

We parametrize a linear-scaling quantum mechanical force field called mDC for the accurate reproduction of nonbonded interactions. We provide a new benchmark database of accurate ab initio interactions between sulfur-containing molecules. A variety of nonbond databases are used to compare the new mDC method with other semiempirical, molecular mechanical, ab initio, and combined semiempirical quantum mechanical/molecular mechanical methods. It is shown that the molecular mechanical force field significantly and consistently reproduces the benchmark results with greater accuracy than the semiempirical models and our mDC model produces errors twice as small as the molecular mechanical force field. The comparisons between the methods are extended to the docking of drug candidates to the Cyclin-Dependent Kinase 2 protein receptor. We correlate the protein-ligand binding energies to their experimental inhibition constants and find that the mDC produces the best correlation. Condensed phase simulation of mDC water is performed and shown to produce O-O radial distribution functions similar to TIP4P-EW.

A variational linear-scaling framework to build practical, efficient next-generation orbital-based quantum force fields

We introduce a new hybrid molecular orbital/density-functional modified divide-and-conquer (mDC) approach that allows the linear-scaling calculation of very large quantum systems. The method provides a powerful framework from which linear-scaling force fields for molecular simulations can be developed. The method is variational in the energy, and has simple, analytic gradients and essentially no break-even point with respect to the corresponding full electronic structure calculation. Furthermore, the new approach allows intermolecular forces to be properly balanced such that non-bonded interactions can be treated, in some cases, to much higher accuracy than the full calculation. The approach is illustrated using the second-order self-consistent charge density-functional tight-binding model (DFTB2). Using this model as a base Hamiltonian, the new mDC approach is applied to a series of water systems, where results show that geometries and interaction energies between water molecules are greatly improved relative to full DFTB2. In order to achieve substantial improvement in the accuracy of intermolecular binding energies and hydrogen bonded cluster geometries, it was necessary to extend the DFTB2 model to higher-order atom-centered multipoles for the second-order self-consistent intermolecular electrostatic term. Using generalized, linear-scaling electrostatic methods, timings demonstrate that the method is able to calculate a water system of 3000 atoms in less than half of a second, and systems of up to one million atoms in only a few minutes using a conventional desktop workstation.

Multilevel X-Pol: a fragment-based method with mixed quantum mechanical representations of different fragments

The explicit polarization (X-Pol) method is a fragment-based quantum mechanical model, in which a macromolecular system or other large or complex system in solution is partitioned into monomeric fragments. The present study extends the original X-Pol method, where all fragments are treated using the same electronic structure theory, to multilevel representations, called multilevel X-Pol, in which different electronic structure methods are used to describe different fragments. The multilevel X-Pol method has been implemented into a locally modified version of Gaussian 09. A key ingredient that is used to couple interfragment electrostatic interactions at different levels of theory is the use of the response density for the post-self-consistent-field energy. (The response density is also called the generalized density.) The method is useful for treating fragments in a small region of the system such as a solute molecule or the substrate and amino acids in the active site of an enzyme with a high-level theory, and the fragments in the rest of the system by a lower-level and computationally more efficient method. Multilevel X-Pol is illustrated here by applications to hydrogen bonding complexes in which one fragment is treated with the hybrid M06 density functional, Møller-Plesset perturbation theory, or coupled cluster theory, and the other fragments are treated by Hartree-Fock theory or the B3LYP or M06 hybrid density functionals.

Optimization of the explicit polarization (X-Pol) potential using a hybrid density functional

The explicit polarization (X-Pol) method is a self-consistent fragment-based electronic structure theory in which molecular orbitals are block-localized within fragments of a cluster, macromolecule, or condensed-phase system. To account for short-range exchange repulsion and long-range dispersion interactions, we have incorporated a pairwise, empirical potential, in the form of Lennard-Jones terms, into the X-Pol effective Hamiltonian. In the present study, the X-Pol potential is constructed using the B3LYP hybrid density functional with the 6-31G(d) basis set to treat interacting fragments, and the Lennard-Jones parameters have been optimized on a dataset consisting of 105 bimolecular complexes. It is shown that the X-Pol potential can be optimized to provide a good description of hydrogen bonding interactions; the root mean square deviation of the computed binding energies from full (i.e., nonfragmental) CCSD(T)/aug-cc-pVDZ results is 0.8 kcal/mol, and the calculated hydrogen bond distances have an average deviation of about 0.1 Å from those obtained by full B3LYP/aug-cc-pVDZ optimizations.