Matthew Goldey

Restricted active space spin-flip configuration interaction: theory and examples for multiple spin flips with odd numbers of electrons.

The restricted active space spin flip (RAS-SF) method is extended to allow ground and excited states of molecular radicals to be described at low cost (for small numbers of spin flips). RAS-SF allows for any number of spin flips and a flexible active space while maintaining pure spin eigenfunctions for all states by maintaining a spin complete set of determinants and using spin-restricted orbitals. The implementation supports both even and odd numbers of electrons, while use of resolution of the identity integrals and a shared memory parallel implementation allow for fast computation. Examples of multiple-bond dissociation, excited states in triradicals, spin conversions in organic multi-radicals, and mixed-valence metal coordination complexes demonstrate the broad usefulness of RAS-SF.

Beyond Energies: Geometries of Nonbonded Molecular Complexes as Metrics for Assessing Electronic Structure Approaches.

Electronic structure approaches for calculating intermolecular interactions have traditionally been benchmarked almost exclusively on the basis of energy-centric metrics. Herein, we explore the idea of utilizing a metric related to geometry. On a diverse series of noncovalently interacting systems of different sizes, from the water dimer to the coronene dimer, we evaluate a variety of electronic structure approximations with respect to their abilities to reproduce coupled-cluster-level geometries. Specifically, we examine Hartree-Fock, second-order Møller-Plesset perturbation theory (MP2), attenuated MP2, scaled MP2, and a number of density functionals, many of which include empirical or nonempirical van der Waals dispersion corrections. We find a number of trends that transcend system size and interaction type. For instance, functionals incorporating VV10 nonlocal correlation tend to yield highly accurate geometries; ωB97X-V and B97M-V, in particular, stand out. We establish that intermolecular distance, as measured by, e.g., the center-of-mass separation of two molecules, is the geometric parameter that deviates most profoundly among the various methods. This property of the equilibrium intermolecular separation, coupled with its accessibility via a small series of well-defined single-point calculations, makes it an ideal metric for the development and evaluation of electronic structure methods.

A Quasidegenerate Second-Order Perturbation Theory Approximation to RAS-nSF for Excited States and Strong Correlations.

We present a modification of the recently developed Restricted Active Space with n Spin Flips method (RAS-nSF), which provides significant efficiency advantages. In the RAS-nSF configuration interaction wave function, an arbitrary number of spin-flips are performed within an orbital active space (often simply the singly occupied orbitals), with state-specific orbital relaxation being described by single excitations into and out of the active space (termed hole and particle states, respectively). As the number of hole and particle states dominates the cost of the calculation, we present an attractive simplification in which the orbital relaxation effects (via hole and particle states) are treated perturbatively rather than variationally. The physical justification for this simplification stems from the spin-flip methodology itself, which suggests that the underlying molecular orbitals (high-spin ROHF) are capable of providing a decent description of the target (spin-flipped) electronic states. The current approach termed SF-CAS(h,p)n (Spin-Flip Complete Active-Space with perturbative Hole and Particle states) yields spin-pure energies and eigenfunctions due to the spin-free formulation. A description of the theory is presented, and a number of numerical examples are investigated to determine the accuracy of the approximation. Computational speedups of over 100 times were demonstrated on a 254 electron, 358 basis function calculation on a Cu(II) porphyrin derivatized with a verdazyl group.

Attenuating Away the Errors in Inter- and Intramolecular Interactions from Second-Order Møller-Plesset Calculations in the Small Aug-cc-pVDZ Basis Set.

Second-order Møller-Plesset perturbation theory (MP2) treats electron correlation at low computational cost, but suffers from basis set superposition error (BSSE) and fundamental inaccuracies in long-range contributions. The cost differential between complete basis set (CBS) and small basis MP2 restricts system sizes where BSSE can be removed. Range-separation of MP2 could yield more tractable and/or accurate forms for short- and long-range correlation. Retaining only short-range contributions proves to be effective for MP2 in the small aug-cc-pVDZ (aDZ) basis. Using one range-separation parameter, superior behavior is obtained versus both MP2/aDZ and MP2/CBS for inter- and intramolecular test sets. Attenuation of the long-range helps to cancel both BSSE and intrinsic MP2 errors. Direct scaling of the MP2 correlation energy proves useful as well. The resulting SMP2/aDZ, MP2(erfc, aDZ), and MP2(terfc, aDZ) methods perform far better than MP2/aDZ across systems with hydrogen-bonding, dispersion, and mixed interactions at a fraction of MP2/CBS computational cost.

Achieving High-Accuracy Intermolecular Interactions by Combining Coulomb-Attenuated Second-Order Møller–Plesset Perturbation Theory with Coupled Kohn–Sham Dispersion

The dispersion-corrected second-order Møller-Plesset perturbation theory (MP2C) approach accurately describes intermolecular interactions in many systems. MP2C, however, expends much computational effort to compute the long-range correlation with MP2, only to discard and replace those contributions with a simpler long-range dispersion correction based on intermolecular perturbation theory. Here, we demonstrate that one can avoid calculating the long-range MP2 correlation by attenuating the Coulomb operator, allowing the dispersion correction to handle the long-range interactions inexpensively. With relatively modest Coulomb attenuation, one obtains results that are very similar to those from conventional MP2C. With more aggressive attenuation, one can remove just enough short-range repulsive exchange-dispersion interactions to compensate for finite basis set errors. Doing so makes it possible to approach complete basis set limit quality results with only an aug-cc-pVTZ basis, resulting in substantial computational savings. Further computational savings could be achieved by reformulating the MP2C algorithm to exploit the increased sparsity of the two-electron integrals.

Shared memory multiprocessing implementation of resolution-of-the-identity second-order Møller–Plesset perturbation theory with attenuated and unattenuated results for intermolecular interactions between large molecules

We examine the second-order Møller–Plesset perturbation theory energy under the resolution-of-the-identity approximation (RI-MP2) and present an improved algorithm for single-node, multi-threaded computation. This algorithm is based on shared memory parallelisation of the rate-limiting steps and an overall reduction in the number of disk reads. The requisite fifth-order computation in RI-MP2 calculations is efficiently parallelised within this algorithm, with improvements in overall parallel efficiency as the system size increases. Fourth-order steps are also parallelised. As an application, we present energies and timings for several large, noncovalently interacting systems with this algorithm, and demonstrate that the RI-MP2 cost is still typically less than 40% of the underlying self consistent field (SCF) calculation. The attenuated RI-MP2 energy is also implemented with this algorithm, and some new large-scale tests of this method are reported. The attenuated RI-MP2(terfc, aug-cc-pVDZ) method yields excellent agreement with benchmark values for the L7 database (R. Sedlak et al., J. Chem. Theory Comput. 2013, 9, 3364) and 10 tetrapeptide conformers (L. Goerigk et al., Phys. Chem. Chem. Phys. 2013, 15, 7028), with at least a 90% reduction in the root-mean-squared (RMS) error versus RI-MP2/aug-cc-pVDZ.

Planarity and multiple components promote organic photovoltaic efficiency by improving electronic transport.

Establishing how the conformation of organic photovoltaic (OPV) polymers affects their electronic and transport properties is critical in order to determine design rules for new OPV materials and in particular to understand the performance enhancements recently reported for ternary blends. We report coupled classical and ab initio molecular dynamics simulations showing that polymer linkage twisting significantly reduces optical absorption efficiency, as well as hole transport rates in donor polymers. We predict that blends with components favoring planar geometries contribute to the enhancement of the overall efficiency of ternary OPVs. Furthermore, our electronic structure calculations for the PTB7-PID2-PC71BM system show that hole transfer rates are enhanced in ternary blends with respect to their binary counterpart. Finally, our results point at thermal disorder in the blend as a key reason responsible for device voltage losses and at the need to carry out electronic structure calculations at finite temperature to reliably compare with experiments.

Attenuated MP2 with a Long-Range Dispersion Correction for Treating Nonbonded Interactions.

Attenuated second order Møller-Plesset theory (MP2) captures intermolecular binding energies at equilibrium geometries with high fidelity with respect to reference methods, yet must fail to reproduce dispersion energies at stretched geometries due to the removal of fully long-range dispersion. For this problem to be ameliorated, long-range correction using the VV10 van der Waals density functional is added to attenuated MP2, capturing short-range correlation with attenuated MP2 and long-range dispersion with VV10. Attenuated MP2 with long-range VV10 dispersion in the aug-cc-pVTZ (aTZ) basis set, MP2-V(terfc, aTZ), is parametrized for noncovalent interactions using the S66 database and tested on a variety of noncovalent databases, describing potential energy surfaces and equilibrium binding energies equally well. Further, a spin-component scaled (SCS) version, SCS-MP2-V(2terfc, aTZ), is produced using the W4-11 database as a supplemental thermochemistry training set, and the resulting method reproduces the quality of MP2-V(terfc, aTZ) for noncovalent interactions and exceeds the performance of SCS-MP2/aTZ for thermochemistry.

Separate electronic attenuation allowing a spin-component-scaled second-order Møller-Plesset theory to be effective for both thermochemistry and noncovalent interactions.

Spin-component-scaled (SCS) second-order Møller-Plesset perturbation theory (MP2) improves the treatment of thermochemistry and noncovalent interactions relative to MP2, although the optimal scaling coefficients are quite different for thermochemistry versus noncovalent interactions. This work reconciles these two different scaling regimes for SCS-MP2 by using two different length scales for electronic attenuation of the two spin components. The attenuation parameters and scaling coefficients are optimized in the aug-cc-pVTZ (aTZ) basis using the S66 database of intermolecular interactions and the W4-11 database of thermochemistry. Transferability tests are performed for atomization energies and barrier heights, as well as on further test sets for inter- and intramolecular interactions. SCS dual-attenuated MP2 in the aTZ basis, SCS-MP2(2terfc, aTZ), performs similarly to SCS-MP2/aTZ for thermochemistry while frequently outperforming MP2 at the complete basis set limit (CBS) for nonbonded interactions.

Charge Transport in Nanostructured Materials: Implementation and Verification of Constrained Density Functional Theory

The in silico design of novel complex materials for energy conversion requires accurate, ab initio simulation of charge transport. In this work, we present an implementation of constrained density functional theory (CDFT) for the calculation of parameters for charge transport in the hopping regime. We verify our implementation against literature results for molecular systems, and we discuss the dependence of results on numerical parameters and the choice of localization potentials. In addition, we compare CDFT results with those of other commonly used methods for simulating charge transport between nanoscale building blocks. We show that some of these methods give unphysical results for thermally disordered configurations, while CDFT proves to be a viable and robust approach.