Analytic first derivatives of floating occupation molecular orbital-complete active space configuration interaction on graphical processing units

Prediction challenge: First principles simulation of the ultrafast electron diffraction spectrum of cyclobutanone

Computer simulation has long been an essential partner of ultrafast experiments, allowing the assignment of microscopic mechanistic detail to low-dimensional spectroscopic data. However, the ability of theory to make a priori predictions of ultrafast experimental results is relatively untested. Herein, as a part of a community challenge, we attempt to predict the signal of an upcoming ultrafast photochemical experiment using state-of-the-art theory in the context of preexisting experimental data. Specifically, we employ ab initio Ehrenfest with collapse to a block mixed quantum-classical simulations to describe the real-time evolution of the electrons and nuclei of cyclobutanone following excitation to the 3s Rydberg state. The gas-phase ultrafast electron diffraction (GUED) signal is simulated for direct comparison to an upcoming experiment at the Stanford Linear Accelerator Laboratory. Following initial ring-opening, dissociation via two distinct channels is observed: the C3 dissociation channel, producing cyclopropane and CO, and the C2 channel, producing CH2CO and C2H4. Direct calculations of the GUED signal indicate how the ring-opened intermediate, the C2 products, and the C3 products can be discriminated in the GUED signal. We also report an a priori analysis of anticipated errors in our predictions: without knowledge of the experimental result, which features of the spectrum do we feel confident we have predicted correctly, and which might we have wrong?

Simulating the Excited-State Dynamics of Polaritons with Ab Initio Multiple Spawning

Over the past decade, there has been a growth of interest in polaritonic chemistry, where the formation of hybrid light-matter states (polaritons) can alter the course of photochemical reactions. These hybrid states are created by strong coupling between molecules and photons in resonant optical cavities and can even occur in the absence of light when the molecule is strongly coupled with the electromagnetic fluctuations of the vacuum field. We present a first-principles model to simulate nonadiabatic dynamics of such polaritonic states inside optical cavities by leveraging graphical processing units (GPUs). Our first implementation of this model is specialized for a single molecule coupled to a single-photon mode confined inside the optical cavity but with any number of excited states computed using complete active space configuration interaction (CASCI) and a Jaynes-Cummings-type Hamiltonian. Using this model, we have simulated the excited-state dynamics of a single salicylideneaniline (SA) molecule strongly coupled to a cavity photon with the ab initio multiple spawning (AIMS) method. We demonstrate how the branching ratios of the photodeactivation pathways for this molecule can be manipulated by coupling to the cavity. We also show how one can stop the photoreaction from happening inside of an optical cavity. Finally, we also investigate cavity-based control of the ordering of two excited states (one optically bright and the other optically dark) inside a cavity for a set of molecules, where the dark and bright states are close in energy.

What Controls the Quality of Photodynamical Simulations? Electronic Structure Versus Nonadiabatic Algorithm

The field of nonadiabatic dynamics has matured over the last decade with a range of algorithms and electronic structure methods available at the moment. While the community currently focuses more on developing and benchmarking new nonadiabatic dynamics algorithms, the underlying electronic structure controls the outcome of nonadiabatic simulations. Yet, the electronic-structure sensitivity analysis is typically neglected. In this work, we present a sensitivity analysis of the nonadiabatic dynamics of cyclopropanone to electronic structure methods and nonadiabatic dynamics algorithms. In particular, we compare wave function-based CASSCF, FOMO-CASCI, MS- and XMS-CASPT2, density-functional REKS, and semiempirical MRCI-OM3 electronic structure methods with the Landau-Zener surface hopping, fewest switches surface hopping, and ab initio multiple spawning with informed stochastic selection algorithms. The results clearly demonstrate that the electronic structure choice significantly influences the accuracy of nonadiabatic dynamics for cyclopropanone even when the potential energy surfaces exhibit qualitative and quantitative similarities. Thus, selecting the electronic structure solely on the basis of the mapping of potential energy surfaces can be misleading. Conversely, we observe no discernible differences in the performance of the nonadiabatic dynamics algorithms across the various methods. Based on the above results, we discuss the present-day practice in computational photodynamics.

Efficient quantum analytic nuclear gradients with double factorization

Efficient representations of the Hamiltonian, such as double factorization, drastically reduce the circuit depth or the number of repetitions in error corrected and noisy intermediate-scale quantum (NISQ) algorithms for chemistry. We report a Lagrangian-based approach for evaluating relaxed one- and two-particle reduced density matrices from double factorized Hamiltonians, unlocking efficiency improvements in computing the nuclear gradient and related derivative properties. We demonstrate the accuracy and feasibility of our Lagrangian-based approach to recover all off-diagonal density matrix elements in classically simulated examples with up to 327 quantum and 18 470 total atoms in QM/MM simulations with modest-sized quantum active spaces. We show this in the context of the variational quantum eigensolver in case studies, such as transition state optimization, ab initio molecular dynamics simulation, and energy minimization of large molecular systems.

SQMBox: Interfacing a semiempirical integral library to modular ab initio electronic structure enables new semiempirical methods

Ab initio and semiempirical electronic structure methods are usually implemented in separate software packages or use entirely different code paths. As a result, it can be time-consuming to transfer an established ab initio electronic structure scheme to a semiempirical Hamiltonian. We present an approach to unify ab initio and semiempirical electronic structure code paths based on a separation of the wavefunction ansatz and the needed matrix representations of operators. With this separation, the Hamiltonian can refer to either an ab initio or semiempirical treatment of the resulting integrals. We built a semiempirical integral library and interfaced it to the GPU-accelerated electronic structure code TeraChem. Equivalency between ab initio and semiempirical tight-binding Hamiltonian terms is assigned according to their dependence on the one-electron density matrix. The new library provides semiempirical equivalents of the Hamiltonian matrix and gradient intermediates, corresponding to those provided by the ab initio integral library. This enables the straightforward combination of semiempirical Hamiltonians with the full pre-existing ground and excited state functionality of the ab initio electronic structure code. We demonstrate the capability of this approach by combining the extended tight-binding method GFN1-xTB with both spin-restricted ensemble-referenced Kohn-Sham and complete active space methods. We also present a highly efficient GPU implementation of the semiempirical Mulliken-approximated Fock exchange. The additional computational cost for this term becomes negligible even on consumer-grade GPUs, enabling Mulliken-approximated exchange in tight-binding methods for essentially no additional cost.

TeraChem protocol buffers (TCPB): Accelerating QM and QM/MM simulations with a client-server model

The routine use of electronic structures in many chemical simulation applications calls for efficient and easy ways to access electronic structure programs. We describe how the graphics processing unit (GPU) accelerated electronic structure program TeraChem can be set up as an electronic structure server, to be easily accessed by third-party client programs. We exploit Google's protocol buffer framework for data serialization and communication. The client interface, called TeraChem protocol buffers (TCPB), has been designed for ease of use and compatibility with multiple programming languages, such as C++, Fortran, and Python. To demonstrate the ease of coupling third-party programs with electronic structures using TCPB, we have incorporated the TCPB client into Amber for quantum mechanics/molecular mechanics (QM/MM) simulations. The TCPB interface saves time with GPU initialization and I/O operations, achieving a speedup of more than 2× compared to a prior file-based implementation for a QM region with ∼250 basis functions. We demonstrate the practical application of TCPB by computing the free energy profile of p-hydroxybenzylidene-2,3-dimethylimidazolinone (p-HBDI^-)-a model chromophore in green fluorescent proteins-on the first excited singlet state using Hamiltonian replica exchange for enhanced sampling. All calculations in this work have been performed with the non-commercial freely-available version of TeraChem, which is sufficient for many QM region sizes in common use.

Computation of NMR shieldings at the CASSCF level using gauge-including atomic orbitals and Cholesky decomposition

We present an implementation of coupled-perturbed complete active space self-consistent field (CP-CASSCF) theory for the computation of nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals and Cholesky decomposed two-electron integrals. The CP-CASSCF equations are solved using a direct algorithm where the magnetic Hessian matrix-vector product is expressed in terms of one-index transformed quantities. Numerical tests on systems with up to about 1300 basis functions provide information regarding both the computational efficiency and limitations of our implementation.

Photochemical Deracemization of Chiral Alkenes via Triplet Energy Transfer

A visible-light-mediated, enantioselective approach to axially chiral alkenes is described. Starting from a racemic mixture, a major alkene enantiomer is formed due to selective triplet energy transfer from a catalytically active chiral sensitizer. A catalyst loading of 2 mol % was sufficient to guarantee consistently high enantioselectivities and yields (16 examples, 51%-quant., 81-96% ee). NMR studies and DFT computations revealed that triplet energy transfer is more rapid within the substrate-catalyst complex of the minor alkene enantiomer. Since this enantiomer is continuously racemized, the major enantiomer is enriched in the photostationary state.

InteraChem: Exploring Excited States in Virtual Reality with Ab Initio Interactive Molecular Dynamics

InteraChem is an ab initio interactive molecular dynamics (AI-IMD) visualizer that leverages recent advances in virtual reality hardware and software, as well as the graphical processing unit (GPU)-accelerated TeraChem electronic structure package, in order to render quantum chemistry in real time. We introduce the exploration of electronically excited states via AI-IMD using the floating occupation molecular orbital-complete active space configuration interaction method. The optimization tools in InteraChem enable identification of excited state minima as well as minimum energy conical intersections for further characterization of excited state chemistry in small- to medium-sized systems. We demonstrate that finite-temperature Hartree-Fock theory is an efficient method to perform ground state AI-IMD. InteraChem allows users to track electronic properties such as molecular orbitals and bond order in real time, resulting in an interactive visualization tool that aids in the interpretation of excited state chemistry data and makes quantum chemistry more accessible for both research and educational purposes.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

Photochemical Deracemization of Primary Allene Amides by Triplet Energy Transfer: A Combined Synthetic and Theoretical Study

The photochemical deracemization of 2,4-disubstituted 2,3-butadienamides (allene amides) was investigated both experimentally and theoretically. The reaction was catalyzed by a thioxanthone which is covalently linked to a chiral 1,5,7-trimethyl-3-azabicyclo[3.3.1]nonan-2-one skeleton providing a U-shaped arrangement of the sensitizing unit relative to a potential hydrogen-bonding site. Upon irradiation at λ = 420 nm in the presence of the sensitizer (2.5 mol %), the amides reached at -10 °C a photostationary state in which one enantiomer prevailed. The enantioenriched allene amides (70-93% ee) were isolated in 74% to quantitative yield (19 examples). Based on luminescence data and DFT calculations, energy transfer from the thioxanthone to the allene amides is thermodynamically feasible, and the achiral triplet allene intermediate was structurally characterized. Hydrogen bonding of the amide enantiomers to the sensitizer was monitored by NMR titration. The experimental association constants (K_a) were similar (59.8 vs 25.7 L·mol^-1). DFT calculations, however, revealed a significant difference in the binding properties of the two enantiomers. The major product enantiomer exhibits a noncovalent dispersion interaction of its arylmethyl group to the external benzene ring of the thioxanthone, thus moving away the allene from the carbonyl chromophore. The minor enantiomer displays a CH-π interaction of the hydrogen atom at the terminal allene carbon atom to the same benzene ring, thus forcing the allene into close proximity to the chromophore. The binding behavior explains the observed enantioselectivity which, as corroborated by additional calculations, is due to a rapid triplet energy transfer within the substrate-catalyst complex of the minor enantiomer.

CAS without SCF-Why to use CASCI and where to get the orbitals

The complete active space self-consistent field (CASSCF) method has seen broad adoption due to its ability to describe the electronic structure of both the ground and excited states of molecules over a broader swath of the potential energy surface than is possible with the simpler Hartree-Fock approximation. However, it also has a reputation for being unwieldy, computationally costly, and un-black-box. Here, we discuss a class of alternatives, complete active space configuration interaction (CASCI) methods, paying particular attention to their application to electronic excited states. The goal of this Perspective is fourfold. First, we argue that CASCI is not merely an approximation to CASSCF, in that it can be designed to have important qualitative advantages over CASSCF. Second, we present several insights drawn from our experience experimenting with different schemes for computing orbitals to be employed in CASCI. Third, we argue that CASCI is well suited for application to nanomaterials. Finally, we reason that, with the rise in new low-scaling approaches for describing multireference systems, there is a greater need than ever to develop new methods for defining orbitals that provide an efficient and accurate description of both static correlation and electronic excitations in a limited active space.

Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method

We present a reduced scaling and exact reformulation of state specific complete active space second-order perturbation (CASPT2) analytical gradients in terms of the MP2 and Fock derivatives using the supporting subspace method. This work follows naturally from the supporting subspace formulation of the CASPT2 energy in terms of the MP2 energy using dressed orbitals and Fock builds. For a given active space configuration, the terms corresponding to the MP2-gradient can be evaluated with O(N⁵) operations, while the rest of the calculations can be computed with O(N³) operations using Fock builds, Fock gradients, and linear algebra. When tensor-hyper-contraction is applied simultaneously, the computational cost can be further reduced to O(N⁴) for a fixed active space size. The new formulation enables efficient implementation of CASPT2 analytical gradients by leveraging the existing graphical processing unit (GPU)-based MP2 and Fock routines. We present benchmark results that demonstrate the accuracy and performance of the new method. Example applications of the new method in ab initio molecular dynamics simulation and constrained geometry optimization are given.

Reduced scaling extended multi-state CASPT2 (XMS-CASPT2) using supporting subspaces and tensor hyper-contraction

We present a reduced scaling formulation of the extended multi-state CASPT2 (XMS-CASPT2) method, which is based on our recently developed state-specific CASPT2 (SS-CASPT2) formulation using supporting subspaces and tensor hyper-contraction. By using these two techniques, the off-diagonal elements of the effective Hamiltonian can be computed with only O(N³) operations and O(N²) memory, where N is the number of basis functions. This limits the overall computational scaling to O(N⁴) operations and O(N²) memory. Thus, excited states can now be obtained at the same reduced (relative to previous algorithms) scaling we achieved for SS-CASPT2. In addition, we also investigate how the energy denominators can be factorized with the Laplace quadrature when some of the denominators are negative, which is critical for excited state calculations. An efficient implementation of the method has been developed using graphical processing units while also exploiting spatial sparsity in tensor operations. We benchmark the accuracy of the new method by comparison to non-THC formulated XMS-CASPT2 for the excited states of various molecules. In our tests, the THC approximation introduces negligible errors (≈0.01 eV) compared to the non-THC reference method. Scaling behavior and computational timings are presented to demonstrate performance. The new method is also interfaced with quantum mechanics/molecular mechanics (QM/MM). In an example study of green fluorescent protein, we show how the XMS-CASPT2 potential energy surfaces and excitation energies are affected by increasing the size of the QM region up to 278 QM atoms with more than 2300 basis functions.

Fluorescence quenching by photoinduced electron transfer between 7-methoxycoumarin and guanine base facilitated by hydrogen bonds: an in silico study

In this study, the effects of hydrogen bond (H-bond) formation on fluorescence quenching of 7-methoxycoumarin (7MC) via photo-induced electron transfer from a guanine base (Gua) are investigated using a combined quantum mechanics/molecular mechanics simulation. The electronic structure is calculated by the floating occupation molecular orbital complete active space configuration interaction modification on a semiempirical method. Then the full multiple spawning method is employed for the dynamics simulations on multiple electronic states. The methods employed here are validated by simulating direct dynamics of 7MC (without Gua) and compared with available experimental results. Our computational results are in good agreement with the previously reported experimental results in terms of spectroscopic properties of 7MC. In the case of a H-bonded 7MC-Gua complex, the results from constrained dynamics simulations and single-point calculations suggest that the electron transfer occurs on the second excited state and it depends not only on the H-bond length but also on the intermolecular planarity between 7MC and Gua. Moreover, a proton coupled electron transfer can occur at ≈1 Å of H-bond length, where a proton from Gua is also transferred together with the electron to 7MC. The obtained simulations are expected to be greatly beneficial for designing effective fluorescently labeled nucleotide probes as well as providing information for precise fluorescence signal interpretation.

Dissociative ionization dynamics of dielectric gas C3F7CN

Fluoronitrile C₃F₇CN is a promising candidate for the replacement of SF₆ dielectric gas in high-voltage insulation.

Imaging CF3I conical intersection and photodissociation dynamics with ultrafast electron diffraction

Conical intersections play a critical role in excited-state dynamics of polyatomic molecules because they govern the reaction pathways of many nonadiabatic processes. However, ultrafast probes have lacked sufficient spatial resolution to image wave-packet trajectories through these intersections directly. Here, we present the simultaneous experimental characterization of one-photon and two-photon excitation channels in isolated CF₃I molecules using ultrafast gas-phase electron diffraction. In the two-photon channel, we have mapped out the real-space trajectories of a coherent nuclear wave packet, which bifurcates onto two potential energy surfaces when passing through a conical intersection. In the one-photon channel, we have resolved excitation of both the umbrella and the breathing vibrational modes in the CF₃ fragment in multiple nuclear dimensions. These findings benchmark and validate ab initio nonadiabatic dynamics calculations.

Dynamics of recombination via conical intersection in a semiconductor nanocrystal

Conical intersections are well known to introduce nonradiative decay pathways in molecules, but have only recently been implicated in nonradiative recombination processes in materials. Here we apply excited state ab initio molecular dynamics simulations based on a multireference description of the electronic structure to defective silicon nanocrystals up to 1.7 nm in diameter to search for accessible nonradiative recombination pathways. Dangling bond defects are found to induce conical intersections between the ground and first excited electronic states of five systems of various sizes. These defect-induced conical intersections are accessible at energies that are in the visible range (2.4-2.7 eV) and very weakly dependent on particle size. The dynamic simulations suggest that these intersections are accessed 40-60 fs after creation of a defect-localized excitation. This ultrafast recombination is attributed to the fact that Jahn-Teller distortion on the first excited state drives the defect directly towards a conical intersection with the ground electronic state.

Automated Discovery and Refinement of Reactive Molecular Dynamics Pathways

We describe a flexible and broadly applicable energy refinement method, "nebterpolation," for identifying and characterizing the reaction events in a molecular dynamics (MD) simulation. The new method is applicable to ab initio simulations with hundreds of atoms containing complex and multimolecular reaction events. A key aspect of nebterpolation is smoothing of the reactive MD trajectory in internal coordinates to initiate the search for the reaction path on the potential energy surface. We apply nebterpolation to analyze the reaction events in an ab initio nanoreactor simulation that discovers new molecules and mechanisms, including a C-C coupling pathway for glycolaldehyde synthesis. We find that the new method, which incorporates information from the MD trajectory that connects reactants with products, produces a dramatically distinct set of minimum energy paths compared to existing approaches that start from information for the reaction end points alone. The energy refinement method described here represents a key component of an emerging simulation paradigm where molecular dynamics simulations are applied to discover the possible reaction mechanisms.