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An efficient implementation of the perturb-then-diagonalize nonorthogonal configuration interaction method with second-order Møller-Plesset perturbation theory (NOCI-MP2) is presented. Relative to other low scaling multireference perturbation theories, NOCI-MP2 often requires a much smaller active space because of the use of nonorthogonal reference configurations. Reworking the NOCI-MP2 equations with the resolution of the identity (RI) approximation enables the method to have the same memory requirements and computational scaling as single reference RI-MP2. The working equations are extended to include single substitutions as required when the reference determinants do not satisfy the Hartree-Fock equations. A detailed computational algorithm is presented along with timings to establish the performance of the implementation. NOCI-MP2 is applied to the binding energy and charge resonance energy in dication and monocation π dimers, as well as didiamantane ethane, and hexaphenylethane. A well-defined set of nonorthogonal determinants are obtained using absolutely localized molecular orbitals (ALMOs), as solutions to the self-consistent field for molecular interactions (SCF-MI) equations corresponding to covalent and ionic determinants. Agreement with experimental information where available, and other multireference methods, is satisfactory, with the use of an 0.3 au level shift to guard against large MP2 amplitudes. For didiamantane ethane and hexaphenylethane, large dispersion forces help stabilize the molecules despite the steric repulsion. By contrast, in the case of hexaphenylethane, the energy penalty from the geometric distortion of the fragments significantly weakens the bond.

Singlet exciton fission (SF), the conversion of one spin-singlet exciton (S1)into two spin-triplet excitons (T1), could provide a means to overcome theShockley-Queisser limit in photovoltaics. SF as measured by the decay of S1 hasbeen shown to occur efficiently and independently of temperature even when theenergy of S1 is as much as 200 meV less than 2T1. Here, we study films ofTIPS-tetracene using transient optical spectroscopy and show that the initialrise of the triplet pair state (TT) occurs in 300 fs, matched by rapid loss ofS1 stimulated emission, and that this process is mediated by the strongcoupling of electronic and vibrational degrees of freedom. This is followed bya slower 10 ps morphology-dependent phase of S1 decay and TT growth. We observethe TT to be thermally dissociated on 10-100 ns timescales to form freetriplets. This provides a model for "temperature independent", efficient TTformation and thermally activated TT separation.

The traditional structure-function paradigm has provided significant insights for well-folded proteins in which structures can be easily and rapidly revealed by X-ray crystallography beamlines. However, approximately one-third of the human proteome is comprised of intrinsically disordered proteins and regions (IDPs/IDRs) that do not adopt a dominant well-folded structure, and therefore remain "unseen" by traditional structural biology methods. This Perspective considers the challenges raised by the "Dark Proteome", in which determining the diverse conformational substates of IDPs in their free states, in encounter complexes of bound states, and in complexes retaining significant disorder requires an unprecedented level of integration of multiple and complementary solution-based experiments that are analyzed with state-of-the art molecular simulation, Bayesian probabilistic models, and high-throughput computation. We envision how these diverse experimental and computational tools can work together through formation of a "computational beamline" that will allow key functional features to be identified in IDP structural ensembles.

In this paper we introduce two size consistent forms of the non-orthogonal configuration interaction with second-order Møller-Plesset perturbation theory method, NOCI-MP2. We show that the original NOCI-MP2 formulation [S. R. Yost, T. Kowalczyk, and T. VanVoorh, J. Chem. Phys. 193, 174104 (2013)], which is a perturb-then-diagonalize multi-reference method, is not size consistent. We also show that this causes significant errors in large systems like the linear acenes. By contrast, the size consistent versions of the method give satisfactory results for singlet and triplet excited states when compared to other multi-reference methods that include dynamic correlation. For NOCI-MP2 however, the number of required determinants to yield similar levels of accuracy is significantly smaller. These results show the promise of the NOCI-MP2 method, though work still needs to be done in creating a more consistent black-box approach to computing the determinants that comprise the many-electron NOCI basis.

In this paper we introduce two size consistent forms of the non-orthogonal configuration interaction with second-order Møller-Plesset perturbation theory method, NOCI-MP2. We show that the original NOCI-MP2 formulation [S. R. Yost, T. Kowalczyk, and T. VanVoorh, J. Chem. Phys. 193, 174104 (2013)], which is a perturb-then-diagonalize multi-reference method, is not size consistent. We also show that this causes significant errors in large systems like the linear acenes. By contrast, the size consistent versions of the method give satisfactory results for singlet and triplet excited states when compared to other multi-reference methods that include dynamic correlation. For NOCI-MP2 however, the number of required determinants to yield similar levels of accuracy is significantly smaller. These results show the promise of the NOCI-MP2 method, though work still needs to be done in creating a more consistent black-box approach to computing the determinants that comprise the many-electron NOCI basis.

The traditional structure-function paradigm has provided significant insights for well-folded proteins in which structures can be easily and rapidly revealed by X-ray crystallography beamlines. However, approximately one-third of the human proteome is comprised of intrinsically disordered proteins and regions (IDPs/IDRs) that do not adopt a dominant well-folded structure, and therefore remain "unseen" by traditional structural biology methods. This Perspective considers the challenges raised by the "Dark Proteome", in which determining the diverse conformational substates of IDPs in their free states, in encounter complexes of bound states, and in complexes retaining significant disorder requires an unprecedented level of integration of multiple and complementary solution-based experiments that are analyzed with state-of-the art molecular simulation, Bayesian probabilistic models, and high-throughput computation. We envision how these diverse experimental and computational tools can work together through formation of a "computational beamline" that will allow key functional features to be identified in IDP structural ensembles.