Communication: Automatic code generation enables nuclear gradient computations for fully internally contracted multireference theory

Ultrafast and radiationless electronic excited state decay of uracil and thymine cations: computing the effects of dynamic electron correlation

In this article we characterise the radiationless decay of the first few electronic excited states of the cations of DNA/RNA nucleobases uracil and thymine, including the effects of dynamic electron correlation on energies and geometries (optimised with XMS-CASPT2). In both systems, we find that one state of ²n and another two of ²π⁺ character can be populated following photoionisation, and their different minima and interstate crossings are located. We find strong similarities between uracil and thymine cations: with accessible conical intersections suggesting that depopulation of their electronic excited states takes place on ultrafast timescales in both systems, suggesting that they are photostable in agreement with previous theoretical (uracil⁺) evidence. We find that dynamic electron correlation separates the energy levels of the "3-state" conical intersection (D₂/D₁/D₀)_CI previously located with CASSCF for uracil⁺, which will therefore have a different geometry and higher energy. Simulating the electronic and vibrational absorptions allows us to characterise spectral fingerprints that could be used to monitor these cation photo-processes experimentally.

Nonadiabatic dynamics: The SHARC approach

We review the Surface Hopping including ARbitrary Couplings (SHARC) approach for excited-state nonadiabatic dynamics simulations. As a generalization of the popular surface hopping method, SHARC allows simulating the full-dimensional dynamics of molecules including any type of coupling terms beyond nonadiabatic couplings. Examples of these arbitrary couplings include spin-orbit couplings or dipole moment-laser field couplings, such that SHARC can describe ultrafast internal conversion, intersystem crossing, and radiative processes. The key step of the SHARC approach consists of a diagonalization of the Hamiltonian including these couplings, such that the nuclear dynamics is carried out on potential energy surfaces including the effects of the couplings-this is critical in any applications considering, for example, transition metal complexes or strong laser fields. We also give an overview over the new SHARC2.0 dynamics software package, released under the GNU General Public License, which implements the SHARC approach and several analysis tools. The review closes with a brief survey of applications where SHARC was employed to study the nonadiabatic dynamics of a wide range of molecular systems. This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and KineticsSoftware > Simulation MethodsSoftware > Quantum Chemistry.

Automatic Differentiation in Quantum Chemistry with Applications to Fully Variational Hartree-Fock

Automatic differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions. Thus, AD has great potential in quantum chemistry, where gradients are omnipresent but also difficult to obtain, and researchers typically spend a considerable amount of time finding suitable analytical forms when implementing derivatives. Here, we demonstrate that AD can be used to compute gradients with respect to any parameter throughout a complete quantum chemistry method. We present DiffiQult, a Hartree-Fock implementation, entirely differentiated with the use of AD tools. DiffiQult is a software package written in plain Python with minimal deviation from standard code which illustrates the capability of AD to save human effort and time in implementations of exact gradients in quantum chemistry. We leverage the obtained gradients to optimize the parameters of one-particle basis sets in the context of the floating Gaussian framework.

Novel strategy to implement active-space coupled-cluster methods

A new approach is presented for the efficient implementation of coupled-cluster (CC) methods including higher excitations based on a molecular orbital space partitioned into active and inactive orbitals. In the new framework, the string representation of amplitudes and intermediates is used as long as it is beneficial, but the contractions are evaluated as matrix products. Using a new diagrammatic technique, the CC equations are represented in a compact form due to the string notations we introduced. As an application of these ideas, a new automated implementation of the single-reference-based multi-reference CC equations is presented for arbitrary excitation levels. The new program can be considered as an improvement over the previous implementations in many respects; e.g., diagram contributions are evaluated by efficient vectorized subroutines. Timings for test calculations for various complete active-space problems are presented. As an application of the new code, the weak interactions in the Be dimer were studied.

Accurate Excited-State Geometries: A CASPT2 and Coupled-Cluster Reference Database for Small Molecules

We present an investigation of the excited-state structural parameters determined for a large set of small compounds with the dual goals of defining reference values for further works and assessing the quality of the geometries obtained with relatively cheap computational approaches. In the first stage, we compare the excited-state geometries obtained with ADC(2), CC2, CCSD, CCSDR(3), CC3, and CASPT2 and large atomic basis sets. It is found that CASPT2 and CC3 results are generally in very good agreement with one another (typical differences of ca. 3 × 10^–3 Å) when all electrons are correlated and when the aug-cc-pVTZ atomic basis set is employed with both methods. In a second stage, a statistical analysis reveals that, on the one hand, the excited-state (ES) bond lengths are much more sensitive to the selected level of theory than their ground-state (GS) counterparts and, on the other hand, that CCSDR(3) is probably the most cost-effective method delivering accurate structures. Indeed, CCSD tends to provide too compact multiple bond lengths on an almost systematic basis, whereas both CC2 and ADC(2) tend to exaggerate these bond distances, with more erratic error patterns, especially for the latter method. The deviations are particularly marked for the polarized CO and CN bonds, as well as for the puckering angle in formaldehyde homologues. In the last part of this contribution, we provide a series of CCSDR(3) GS and ES geometries of medium-sized molecules to be used as references in further investigations.

Multiconfigurational Second-Order Perturbation Theory with Frozen Natural Orbitals Extended to the Treatment of Photochemical Problems

A new flavor of the frozen natural orbital complete active space second-order perturbation theory method (FNO-CASPT2, Aquilante et al., J. Chem. Phys. 131, 034113) is proposed herein. In this new implementation, the virtual space in Cholesky decomposition-based CASPT2 computations (CD-CASPT2) is truncated by excluding those orbitals that contribute the least toward preserving a predefined value of the trace of an approximate density matrix, as that represents a measure of the amount of dynamic correlation retained in the model. In this way, the amount of correlation included is practically constant at all nuclear arrangements, thus allowing for the computation of smooth electronic states surfaces and energy gradients-essential requirements for theoretical studies in photochemistry. The method has been benchmarked for a series of relevant biochromophores for which large speed-ups have been recorded while retaining the accuracy achieved in the corresponding CD-CASPT2 calculations. Both vertical excitation energies and gradient calculations have been carried out to establish general guidelines as to how much correlation needs to be retained in the calculation for the results to be consistent with the CD-CASPT2 findings. Our results feature errors within a tenth of an eV for the most difficult cases and have been validated to be used for gradient computations where an up to 3-fold speed-up is observed depending on the size of the system and the basis set employed.

Automated Code Engine for Graphical Processing Units: Application to the Effective Core Potential Integrals and Gradients

We present an automated code engine (ACE) that automatically generates optimized kernels for computing integrals in electronic structure theory on a given graphical processing unit (GPU) computing platform. The code generator in ACE creates multiple code variants with different memory and floating point operation trade-offs. A graph representation is created as the foundation of the code generation, which allows the code generator to be extended to various types of integrals. The code optimizer in ACE determines the optimal code variant and GPU configurations for a given GPU computing platform by scanning over all possible code candidates and then choosing the best-performing code candidate for each kernel. We apply ACE to the optimization of effective core potential integrals and gradients. It is observed that the best code candidate varies with differing angular momentum, floating point precision, and type of GPU being used, which shows that the ACE may be a powerful tool in adapting to fast evolving GPU architectures.