A variational reformulation of molecular properties in electronic-structure theory.

Conventional quantum-mechanical calculations of molecular properties, such as dipole moments and electronic excitation energies, give errors that depend linearly on the error in the wave function. An exception is the electronic energy, whose error depends quadratically on the error in wave function. We here describe how all properties may be calculated with a quadratic error, by setting up a variational Lagrangian for the property of interest. Because the construction of the Lagrangian is less expensive than the calculation of the wave function, this approach substantially improves the accuracy of quantum-chemical calculations without increasing cost. As illustrated for excitation energies, this approach enables the accurate calculation of molecular properties for larger systems, with a short time-to-solution and in a manner well suited for modern computer architectures.

Dynamical Effects of Solvation on Norbornadiene/Quadricyclane Systems.

Molecules that can undergo reversible chemical transformations following the absorption of light, the so-called molecular photoswitches, have attracted increasing attention in technologies, such as solar energy storage. Here, the optical and thermochemical properties of the photoswitch are central to its applicability, and these properties are influenced significantly by solvation. We investigate the effects of solvation on two norbornadiene/quadricyclane photoswitches. Emphasis is put on the energy difference between the two isomers and the optical absorption as these are central to the application of the systems in solar energy storage. Using a combined classical molecular dynamics and quantum mechanical/molecular mechanical computational scheme, we showcase that the dynamic effects of solvation are important. In particular, it is found that standard implicit solvation models generally underestimate the energy difference between the two isomers and overestimate the strength of the absorption, while the explicit solvation spectra are also less red-shifted than those obtained using implicit solvation models. We also find that the absorption spectra of the two systems are strongly correlated with specific dihedral angles. Altogether, this highlights the importance of including the dynamic effects of solvation.

Cluster perturbation theory IX: Perturbation series for the coupled cluster singles and doubles ground state energy.

In this paper, we develop and analyze a number of perturbation series that target the coupled cluster singles and doubles (CCSD) ground state energy. We show how classical Møller-Plesset perturbation theory series can be restructured to target the CCSD energy based on a reference CCS calculation and how the corresponding cluster perturbation series differs from the classical Møller-Plesset perturbation series. Subsequently, we reformulate these series using the coupled cluster Lagrangian framework to obtain series, where fourth and fifth order energies are determined only using parameters through second order. To test the methods, we perform a series of test calculations on molecular photoswitches of both total energies and reaction energies. We find that the fifth order reaction energies are of CCSD quality and that they are of comparable accuracy to state-of-the-art approximations to the CCSD energy based on local pair natural orbitals. The advantage of the present approach over local correlation methods is the absence of user defined threshold parameters for neglecting or approximating contributions to the correlation energy. Fixed threshold parameters lead to discontinuous energy surfaces, although this effect is often small enough to be ignored, but the present approach has a differentiable energy that will facilitate derivation and implementation of gradients and higher derivatives. A further advantage is that the calculation of the perturbation correction is non-iterative and can, therefore, be calculated in parallel, leading to a short time-to-solution.

Tensor Hypercontraction of Cluster Perturbation Theory: Quartic Scaling Perturbation Series for the Coupled Cluster Singles and Doubles Ground-State Energies.

Even though cluster perturbation theory has been shown to be a robust noniterative alternative to coupled cluster theory, it is still plagued by high order polynomial computational scaling and the storage of higher order tensors. We present a proof-of-concept strategy for implementing a cluster perturbation theory ground-state energy series for the coupled cluster singles and doubles energy with N4 computational scaling using tensor hypercontraction (THC). The reduction in computational scaling by two orders is achieved by decomposing two electron repulsion integrals, doubles amplitudes and multipliers, as well as selected double intermediates to the THC format. Using the outlined strategy, we showcase that the THC pilot implementations retain numerical accuracy to within 1 kcal/mol relative to corresponding conventional and density fitting implementations, and we empirically verify the N4 scaling.

Investigation of Solvent Effects on the Molecular Energy Storage and Optical Properties of Bicyclooctadiene/Tetracyclooctane Photoswitches.

In this paper, we investigate the effects of solvation on the solar energy storage properties of bicyclooctadiene/tetracyclooctane (BOD/TCO) photoswitches. The solvent effects on the thermochemical and optical properties are studied in cyclohexane, toluene, dichloromethane, ethanol, acetonitrile, and a vacuum using density functional theory and coupled cluster theory. Our results show that the energy storage capacity of the BOD/TCO system increases as the solvent polarity increases, and the change is more significant with an unsubstituted system. The energy storage capacity of the substituted system is not dependent on the polarity of the solvent. As the solvent polarity increases, the absorption peaks shift away from each other and the absorption intensities increase. Overall, the solvents improve the performance of the optical properties and the energy storage capacities of the BOD/TCO molecular solar thermal systems.

Corrigendum: Coupled cluster theory on modern heterogeneous supercomputers.

[This corrects the article DOI: 10.3389/fchem.2023.1154526.].

The Effects of Solvent Dynamics on the Back Reaction of Solar-Thermal Energy Storage Systems.

We have investigated dynamic solvent effects on molecular solar-thermal energy storage systems using models describing the effects of frequency dependent viscosities and dielectric constants on chemical reaction rates. We have utilized the generalized Langevin model for understanding how the reactions are affected by the frequency dependent viscosities and dielectric constants. Our results show that the rate constants of the molecular solar-thermal energy storage systems depend strongly on the dielectric electric solvent properties and the frequency dependent viscosities of the solvents.

Computational investigation of photoswitch conjugates for molecular solar energy storage.

Solar energy conversion and storage are vital for combating climate change. Molecular solar thermal systems offer a promising solution, where energy is stored in molecular compounds. This study investigates dyad molecular photoswitches by combining bicyclooctadiene/tetracyclooctane and dihydroazulene/vinylheptafulvene systems with phenyl and cyano groups. Density functional theory calculations were employed to determine molecular properties and consider solvation effects in toluene and dichloromethane. The results show that the combined systems have a predicted storage energy of up to 206.14 kJ mol-1 and an absorption peak at 390.26 nm with appreciable intensity. These dyad photoswitches exhibit favorable properties for molecular solar thermal storage and other applications. A comparison with individual photoswitches reveals advantages and disadvantages. The most effective conjugate has a slightly lower storage density than an equal mixture of individual systems, but it demonstrates better absorption characteristics, with improved overlap with the solar spectrum and higher absorption intensity. These findings contribute to the understanding of dyad molecular photoswitches, showcasing their potential for advanced energy storage and conversion technologies.

Searching the Chemical Space of Bicyclic Dienes for Molecular Solar Thermal Energy Storage Candidates.

Photoswitches are molecular systems that are chemically transformed subsequent to interaction with light and they find potential application in many new technologies. The design and discovery of photoswitch candidates require intricate molecular engineering of a range of properties to optimize a candidate to a specific applications, a task which can be tackled efficiently using quantum chemical screening procedures. In this paper, we perform a large scale screening of approximately half a million bicyclic diene photoswitches in the context of molecular solar thermal energy storage using ab initio quantum chemical methods. We further device an efficient strategy for scoring the systems based on their predicted solar energy conversion efficiency and elucidate potential pitfalls of this approach. Our search through the chemical space of bicyclic dienes reveals systems with unprecedented solar energy conversion efficiencies and storage densities that show promising design guidelines for next generation molecular solar thermal energy storage systems.

Coupled cluster theory on modern heterogeneous supercomputers.

This study examines the computational challenges in elucidating intricate chemical systems, particularly through ab-initio methodologies. This work highlights the Divide-Expand-Consolidate (DEC) approach for coupled cluster (CC) theory-a linear-scaling, massively parallel framework-as a viable solution. Detailed scrutiny of the DEC framework reveals its extensive applicability for large chemical systems, yet it also acknowledges inherent limitations. To mitigate these constraints, the cluster perturbation theory is presented as an effective remedy. Attention is then directed towards the CPS (D-3) model, explicitly derived from a CC singles parent and a doubles auxiliary excitation space, for computing excitation energies. The reviewed new algorithms for the CPS (D-3) method efficiently capitalize on multiple nodes and graphical processing units, expediting heavy tensor contractions. As a result, CPS (D-3) emerges as a scalable, rapid, and precise solution for computing molecular properties in large molecular systems, marking it an efficient contender to conventional CC models.

Elucidating the Mystery of DNA-Templating Effects on a Silver Nanocluster.

This presentation considers the effects that DNA-templating has on the optical properties of a 16-atom silver cluster. To accomplish this, hybrid quantum mechanical and molecular mechanical simulations of a Ag16-DNA complex have been carried out and compared with pure time-dependent density functional theory calculations of two Ag16 clusters in vacuum. The presented results show that the templating DNA polymers both red-shift the one-photon absorption of the silver cluster and increase its intensity. This occurs through a change in cluster shape prompted by the structural constraints of the DNA ligands combined with silver-DNA interactions. The overall charge of the cluster also contributes to the observed optical response, as oxidation of the cluster results in a simultaneous blue-shift of the one-photon absorption and a decrease in intensity. Additionally, the changes in shape and environment also lead to a blue-shift and enhancement of the two-photon absorption.

Indirect nuclear spin-spin couplings with third-order contributions added to the SOPPA method.

In this article, a modification of the second-order polarization propagator approximation (SOPPA) method is introduced and illustrated for the calculation of the indirect nuclear spin-spin couplings. The standard SOPPA method, although cheaper in terms of computational cost, offers less accurate results than the ones obtained with coupled cluster methods. A new method, named SOPPA+A3-3, was therefore developed by adding the terms of the third-order A matrix that rely on the second-order double amplitudes. The performance of this third-order contribution was studied using the coupled cluster singles and doubles method as a reference, calculating the spin-spin couplings of molecules of diverse sizes and compositions, and comparing them to the SOPPA method. The results show that inclusion of this third-order contribution gives more accurate results than the standard SOPPA method with a level of accuracy close to that of the coupled cluster method with only a small increase in the computational cost of the response calculation that dominates the computational cost for small- to medium-sized molecules. The implementation of the first contributions to the third-order polarization propagator approximation in the Dalton program, thus, already shows a significant change in these molecular properties over those obtained with the standard SOPPA method.

Massively parallel GPU enabled third-order cluster perturbation excitation energies for cost-effective large scale excitation energy calculations.

We present here a massively parallel implementation of the recently developed CPS(D-3) excitation energy model that is based on cluster perturbation theory. The new algorithm extends the one developed in Baudin et al. [J. Chem. Phys., 150, 134110 (2019)] to leverage multiple nodes and utilize graphical processing units for the acceleration of heavy tensor contractions. Furthermore, we show that the extended algorithm scales efficiently with increasing amounts of computational resources and that the developed code enables CPS(D-3) excitation energy calculations on large molecular systems with a low time-to-solution. More specifically, calculations on systems with over 100 atoms and 1000 basis functions are possible in a few hours of wall clock time. This establishes CPS(D-3) excitation energies as a computationally efficient alternative to those obtained from the coupled-cluster singles and doubles model.

Excited state dynamics and conjugation effects of the photoisomerization reactions of dihydroazulene.

Herein, we present an investigation of the excited state dynamics of the dihydroazulene photoswitch and its photoinduced reaction to vinylheptafulvene. The focus is on how the introduction of a benzannulated ring in different sites of the structure can modify the excited state topology and thus the kinetics of the ring opening reaction of DHA by alteration of the excited state conjugation of the system. The dynamics of the systems is obtained utilizing ab initio density functional theory calculations in different solvents coupled with unimolecular reaction theory. To accompany these results, the electron delocalization is investigated using the quantum theory of atoms in molecules partitioning to follow the trends induced by the benzannulated ring. It is observed that the introduction of a benzannulated ring can both enhance and diminish the rate of the photoinduced ring opening of dihydroazulene and that certain patterns of conjugation are consistent with the rate constants. Lastly, we find good agreement with earlier experimental studies indicating that the chosen approach could be used to predict whether photochromic systems lose their photoswitchability upon being optimized for specific applications via functionalization.

High throughput screening of norbornadiene/quadricyclane derivates for molecular solar thermal energy storage.

We present a procedure for performing high throughput screening of molecular compounds for molecular solar thermal energy storage devices using extended tight binding (xTB) methods. In order to validate our approach, we performed screening of 3230 norbornadiene/quadricyclane (NBD/QC) derivatives in terms of storage energies, activation barriers and absorption of solar radiation using our approach, and compared it to high level density functional theory (DFT) and cluster perturbation (CP) theory calculations. Our comparisons show that the xTB screening framework correlates very well with DFT and CP theory in that it predicts the same relative trends in the studied parameters although the storage energies and thermal reaction barriers are significantly offset. Utilizing the screening methodology, we have been able to locate compounds that would either be excellent candidates or compounds that should not be considered further for molecular solar thermal energy storage devices. This methodology can readily be extended and applied to screening other molecular motifs for molecular solar energy storage.

Modeling Absorption and Emission Spectroscopies of Symmetric and Asymmetric Azaoxahelicenes in Vacuum and Solution.

Helicenes are of general interest due to the significant chiral signals in both absorption- and emission-based spectroscopy. Herein, the spectroscopic properties of four recently synthesized azaoxahelicenes are studied using density functional theory methods. The azaoxahelicenes have 7, 9, 10, and 13 units and one to two complete turns of the structure. UV-vis absorption and electronic circular dichroism spectra are determined both in vacuum and in solution using explicit solvation through a combined molecular dynamics/polarizable embedding framework. Additionally, emission and circularly polarized luminescence spectra are determined based on vibronic calculations. The resulting spectra are in good agreement with the experimentally available data, highlighting that both absorption- and emission-based spectra of the systems can be modeled computationally such that reliable predictions can be made for systems that are yet to be synthesized.

Cluster perturbation theory. VIII. First order properties for a coupled cluster state.

We have extended cluster perturbation (CP) theory to comprehend the calculation of first order properties (FOPs). We have determined CP FOP series where FOPs are determined as a first energy derivative and also where the FOPs are determined as a generalized expectation value of the external perturbation operator over the coupled cluster state and its biorthonormal multiplier state. For S(D) orbital excitation spaces, we find that the CP series for FOPs that are determined as a first derivative, in general, in second order have errors of a few percent in the singles and doubles correlation contribution relative to the targeted coupled cluster (CC) results. For a SD(T) orbital excitation space, we find that the CP series for FOPs determined as a generalized expectation value in second order have errors of about ten percent in the triples correlation contribution relative to the targeted CC results. These second order models, therefore, constitute viable alternatives for determining high quality FOPs.

Cluster perturbation theory. VII. The convergence of cluster perturbation expansions.

The convergence of the recently developed cluster perturbation (CP) expansions [Pawlowski et al., J. Chem. Phys. 150, 134108 (2019)] is analyzed with the double purpose of developing the mathematical tools and concepts needed to describe these expansions at general order and to identify the factors that define the rate of convergence of CP series. To this end, the CP energy, amplitude, and Lagrangian multiplier equations as a function of the perturbation strength are developed. By determining the critical points, defined as the perturbation strengths for which the Jacobian becomes singular, the rate of convergence and the intruder and critical states are determined for five small molecules: BH, CO, H2O, NH3, and HF. To describe the patterns of convergence for these expansions at orders lower than the high-order asymptotic limit, a model is developed where the perturbation corrections arise from two critical points. It is shown that this model allows for rationalization of the behavior of the perturbation corrections at much lower order than required for the onset of the asymptotic convergence. For the H2O, CO, and HF molecules, the pattern and rate of convergence are defined by critical states where the Fock-operator underestimates the excitation energies, whereas the pattern and rate of convergence for BH are defined by critical states where the Fock-operator overestimates the excitation energy. For the NH3 molecule, both forms of critical points are required to describe the convergence behavior up to at least order 25.

Cluster perturbation theory. VI. Ground-state energy series using the Lagrangian.

We have extended cluster perturbation (CP) theory to comprehend the Lagrangian framework of coupled cluster (CC) theory and derived the CP Lagrangian energy series (LCP) where the 2n + 1/2n + 2 rules for the cluster amplitudes and multipliers are used to get the energy corrections. We have also developed the variational CP (LCP) series, where the total cluster amplitudes and multipliers are determined through the same orders as in the LCP series, but the energy is obtained by inserting the total cluster amplitudes and multipliers in the Lagrangian. The energies of the LCP series have errors that are bilinear in the errors of the total cluster amplitudes and multipliers. Test calculations have been performed for S(D) and SD(T) orbital excitation spaces. With the exception of molecular systems that have a low lying doubly excited state compared to the electronic ground state configuration, we find that the fourth order models LCPS (D-4), LCPSD (T-4), and LCPSD(T-4) give energies of CC target state quality. For the LCPS (D-4) model, CC target state quality is obtained as the LCPS (D-4) calculation determines more than 99.7% of the coupled cluster singles and doubles (CCSD) correlation energy as the numerical deviations of the LCPS (D-4) energy from the CCSD energy were more than an order of magnitude smaller than the triples correlation contribution. For the LCPSD (T-4) and LCPSD(T-4) models, CC target state quality was obtained, given that the LCPSD (T-4) and LCPSD(T-4) calculations recover more than 99% of the coupled cluster singles doubles and triples (CCSDT) correlation contribution and as the numerical deviations of the LCPSD (T-4) and LCPSD(T-4) energies from the CCSDT energy were nearly and order of magnitude smaller than the quadruples correlation contribution. We, thus, suggest that the fourth order models may replace the full target CC models with no or very limited loss of accuracy.

Electric Properties of Photochromic Molecules Physisorbed on Silver and Copper Nanoparticles.

This paper investigates the electric properties of the photochromic dihydroazulene/vinylheptafulvene system as it is physisorbed onto silver and copper nanoparticles. Our focus is on how the polarizability and hyperpolarizability of the dihydroazulene, s-cis-vinylheptafulvene, and s-trans-vinylheptafulvene molecules depend on molecular orientation with respect to the nanoparticles, the molecule-cluster separation, and the type of nanoparticle. The computational approach utilizes a combined quantum mechanical/molecular mechanical method in which the molecules are treated quantum mechanically while the nanoparticles are treated with a simpler classical method. The molecules are described with density functional theory. The electric properties are calculated using response theory utilizing the long-range-corrected functional CAM-B3LYP and the correlation consistent basis set aug-cc-pVDZ. The atoms of the nanoparticles are represented using atomic polarizabilities. The interactions between the nanoparticles and the molecular systems are calculated using a polarizable embedding scheme after which the molecular properties are calculated with time-dependent density functional theory. The results show that the electric properties are indeed affected by the presence of the nanoparticles. It is also clear that it is the hyperpolarizabilities that change the most while the polarizabilities are less affected. Furthermore, the influence of the nanoparticles on the molecules depends heavily on the relative molecular orientation with respect to the nanoparticles and molecular conformation. Finally, it is observed that a copper nanoparticle has a larger influence on the molecular systems than a silver nanoparticle.