Luke Roskop

Accurate methods for large molecular systems.

Three exciting new methods that address the accurate prediction of processes and properties of large molecular systems are discussed. The systematic fragmentation method (SFM) and the fragment molecular orbital (FMO) method both decompose a large molecular system (e.g., protein, liquid, zeolite) into small subunits (fragments) in very different ways that are designed to both retain the high accuracy of the chosen quantum mechanical level of theory while greatly reducing the demands on computational time and resources. Each of these methods is inherently scalable and is therefore eminently capable of taking advantage of massively parallel computer hardware while retaining the accuracy of the corresponding electronic structure method from which it is derived. The effective fragment potential (EFP) method is a sophisticated approach for the prediction of nonbonded and intermolecular interactions. Therefore, the EFP method provides a way to further reduce the computational effort while retaining accuracy by treating the far-field interactions in place of the full electronic structure method. The performance of the methods is demonstrated using applications to several systems, including benzene dimer, small organic species, pieces of the alpha helix, water, and ionic liquids.

Systematic Fragmentation Method and the Effective Fragment Potential: An Efficient Method for Capturing Molecular Energies

The systematic fragmentation method fragments a large molecular system into smaller pieces, in such a way as to greatly reduce the computational cost while retaining nearly the accuracy of the parent ab initio electronic structure method. In order to attain the desired (sub-kcal/mol) accuracy, one must properly account for the nonbonded interactions between the separated fragments. Since, for a large molecular species, there can be a great many fragments and therefore a great many nonbonded interactions, computations of the nonbonded interactions can be very time-consuming. The present work explores the efficacy of employing the effective fragment potential (EFP) method to obtain the nonbonded interactions since the EFP method has been shown previously to capture nonbonded interactions with an accuracy that is often comparable to that of second-order perturbation theory. It is demonstrated that for nonbonded interactions that are not high on the repulsive wall (generally >2.7 A), the EFP method appears to be a viable approach for evaluating the nonbonded interactions. The efficacy of the EFP method for this purpose is illustrated by comparing the method to ab initio methods for small water clusters, the ZOVGAS molecule, retinal, and the alpha-helix. Using SFM with EFP for nonbonded interactions yields an error of 0.2 kcal/mol for the retinal cis-trans isomerization and a mean error of 1.0 kcal/mol for the isomerization energies of five small (120-170 atoms) alpha-helices.

Side Reactions of Nitroxide-Mediated Polymerization: N-O versus O-C Cleavage of Alkoxyamines

Free energies for the homolysis of the NO-C and N-OC bonds were compared for a large number of alkoxyamines at 298 and 393 K, both in the gas phase and in toluene solution. On this basis, the scope of the N-OC homolysis side reaction in nitroxide-mediated polymerization was determined. It was found that the free energies of NO-C and N-OC homolysis are not correlated, with NO-C homolysis being more dependent upon the properties of the alkyl fragment and N-OC homolysis being more dependent upon the structure of the aminyl fragment. Acyclic alkoxyamines and those bearing the indoline functionality have lower free energies of N-OC homolysis than other cyclic alkoxyamines, with the five-membered pyrrolidine and isoindoline derivatives showing lower free energies than the six-membered piperidine derivatives. For most nitroxides, N-OC homolysis is normally favored above NO-C homolysis only when a heteroatom that is α to the NOC carbon center stabilizes the NO-C bond and/or the released alkyl radical is not sufficiently stabilized. As part of this work, accurate methods for the calculation of free energies for the homolysis of alkoxyamines were determined. Accurate thermodynamic parameters to within 4.5 kJ mol(-1) of experimental values were found using an ONIOM approximation to G3(MP2)-RAD combined with PCM solvation energies at the B3-LYP/6-31G(d) level.

A Paradigm for Blue- or Red-Shifted Absorption of Small Molecules Depending on the Site of π-Extension

Benzannulation of aromatic molecules is often used to red-shift absorption and emission bands of organic and inorganic, molecular, and polymeric materials; however, in some cases, either red or blue shifts are observed, depending on the site of benzannulation. A series of five platinum(II) complexes of the form (N(∧)N(∧)N)PtCl are reported here that illustrate this phenomenon, where N(∧)N(∧)N represents the tridentate monoanionic ligands 2,5-bis(2-pyridylimino)3,4-diethylpyrrolate (1), 1,3-bis(2-pyridylimino)isoindolate (2), 1,3-bis(2-pyridylimino)benz(f)isoindolate (3), 1,3-bis(2-pyridylimino)benz(e)isoindolate (4), and 1,3-bis(1-isoquinolylimino) isoindolate (5). For this series of molecules, either a blue shift (2 and 3) or a red shift (4 and 5) in absorption and emission maxima, relative to their respective nonbenzannulated compounds, was observed that depends on the site of benzannulation. Experimental data and first principles calculations suggest that a similar HOMO energy level and a destabilized or stabilized LUMO with benzannulation is responsible for the observed trends. A rationale for LUMO stabilization/destabilization is presented using simple molecular orbital theory. This explanation is expanded to describe other molecules with this unusual behavior.

Quasi-degenerate second-order perturbation theory for occupation restricted multiple active space self-consistent field reference functions

A multi-configuration quasi-degenerate second-order perturbation method based on the occupation restricted multiple active space (ORMAS-PT/ORMAS) reference wavefunction is presented. ORMAS gives one the ability to approximate a complete active space self-consistent field (CASSCF) wavefunction using only a subset of the configurations from the CASSCF space. The essential idea behind ORMAS-PT is to use the multi-reference Møller-Plesset formalism to correct the ORMAS reference energy. A computational scheme employing direct CI methodology is presented. Several tests are presented to demonstrate the performance of the ORMAS-PT method.

Diffusion energy profiles in silica mesoporous molecular sieves modelled with the fragment molecular orbital method

The fragment molecular orbital (FMO) method is used to model truncated portions of mesoporous silica nanoparticle (MSN) pores. The application of the FMO/RHF (restricted Hartree–Fock) method to MCM-41 type MSNs is discussed and an error analysis is given. The FMO/RHF method is shown to reliably approximate the RHF energy (error ∼0.2 kcal/mol), dipole moment (error ∼0.2 debye) and energy gradient (root mean square [RMS] error ∼0.2 × 10−3 a.u./bohr). Several FMO fragmentation schemes are employed to provide guidance for future applications to MSN models. An MSN pore model is functionalised with (phenyl)propyl substituents and the diffusion barrier for benzene passing through the pore is computed by the FMO/RHF-D method with the Grimme dispersion correction (RHF-D). For the reaction coordinates examined here, the maximum FMO/RHF-D interaction energies range from −0.3 to −5.8 kcal/mol.

Assessment of Perturbative Explicitly Correlated Methods for Prototypes of Multiconfiguration Electronic Structure

The performance of the [2]S and [2]R12 universal perturbative corrections that account for one- and many-body basis set errors of single- and multiconfiguration electronic structure methods is assessed. A new formulation of the [2]R12 methods is used in which only strongly occupied orbitals are correlated, making the approach more amenable for larger computations. Three model problems are considered using the aug-cc-pVXZ (X = D,T,Q) basis sets: the electron affinity of fluorine atom, a conformational analysis of two Si2H4 structures, and a description of the potential energy surfaces of the X 1Σg+, a 3Πu, b 3Σg-, and A 1Πu states of C2. In general, the [2]R12 and [2]S corrections enhance energy convergence for conventional multireference configuration interaction (MRCI) and multireference perturbation theory (MRMP2) calculations compared to their complete basis set limits. For the electron affinity of the F atom, [2]R12 electron affinities are within 0.001 eV of the experimental value. The [2]R12 conforme...

ORMAS-SCF Study of Silicon (100) Surface Clusters

An occupation restricted multiple active space (ORMAS) study of clusters that represent the silicon(100) surface (up to nine surface dimers) is discussed. The accuracy of three different active orbital ORMAS partition schemes for Si(100) surface clusters are compared. In addition to ORMAS-SCF calculations, generalized valence bond-perfect pairing (GVB-PP) properties are generated for comparison purposes. The ability of ORMAS to generate a reliable multiconfigurational zeroth-order wave function is systematically tested and when possible is compared to the full complete active space self-consistent field (CASSCF) method. This provides good benchmarks for the accuracy of ORMAS compared to CASSCF. It is demonstrated that ORMAS consistently provides a high degree of accuracy with a significantly reduced computational effort relative to a CASSCF calculation. For the largest cluster, for which a full CASSCF calculation is not possible, ORMAS predicts that the Si(100) surface dimers are symmetric.

Spin-Free [2]R12 Basis Set Incompleteness Correction to the Local Multireference Configuration Interaction and the Local Multireference Average Coupled Pair Functional Methods

The local multireference configuration interaction (LMRCI) and local multireference averaged coupled pair functional (LMRACPF) methods are extended to include explicit correlation via the universal spin-free [2]R12 basis set incompleteness correction. Four test cases are examined to measure the performance of the LMRCI+[2]R12 (without and with the Davidson + Q correction for size-extensivity) and LMRACPF+[2]R12 methods. These tests examine bond dissociation energies (BDEs) for ethene, perfluoroethene, propene, and 2-butene. As has been demonstrated for other methods, the LMRCI+[2]R12/LMRCI+Q+[2]R12/LMRACPF+[2]R12 BDEs are as accurate as the conventional LMRCI/LMRACPF BDEs that are computed with the basis set one cardinal number higher. It is shown that LMRCI+[2]R12/LMRCI+Q+[2]R12/LMRACPF+[2]R12 BDEs computed with the June calendar basis sets preserve the accuracy of the corresponding BDEs computed with the conventional aug-cc-pVXZ basis sets (where X = D, T, Q).