Generating Function Approach to Single Vibronic Level Fluorescence Spectra

TURBOMOLE: Today and Tomorrow

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Applicability of the Thawed Gaussian Wavepacket Dynamics to the Calculation of Vibronic Spectra of Molecules with Double-Well Potential Energy Surfaces

Simulating vibrationally resolved electronic spectra of anharmonic systems, especially those involving double-well potential energy surfaces, often requires expensive quantum dynamics methods. Here, we explore the applicability and limitations of the recently proposed single-Hessian thawed Gaussian approximation for the simulation of spectra of systems with double-well potentials, including 1,2,4,5-tetrafluorobenzene, ammonia, phosphine, and arsine. This semiclassical wavepacket approach is shown to be more robust and to provide more accurate spectra than the conventional harmonic approximation. Specifically, we identify two cases in which the Gaussian wavepacket method is especially useful due to the breakdown of the harmonic approximation: (i) when the nuclear wavepacket is initially at the top of the potential barrier but delocalized over both wells, e.g., along a low-frequency mode, and (ii) when the wavepacket has enough energy to classically go over the low potential energy barrier connecting the two wells. The method is efficient and requires only a single classical ab initio molecular dynamics trajectory, in addition to the data required to compute the harmonic spectra. We also present an improved algorithm for computing the wavepacket autocorrelation function, which guarantees that the evaluated correlation function is continuous for arbitrary size of the time step.

Reliable TDDFT Protocol Based on a Local Hybrid Functional for the Prediction of Vibronic Phosphorescence Spectra Applied to Tris(2,2'-bipyridine)-Metal Complexes

An efficient computational protocol for the prediction of vibrationally resolved phosphorescence spectra is developed and validated for five tris(2,2'-bipyridine)-metal complexes ([M(bpy)₃]ⁿ⁺, where M = Zn, Ru, Rh, Os, Ir). The outstanding feature of this protocol is the use of full linear-response time-dependent density functional theory (TDDFT) for the excited-state triplet calculation, i.e., the commonly seen strategies employing the Tamm-Dancoff approximation (TDA) or unrestricted density functional theory (DFT) calculations for the T₁ state are not needed. This is achieved by the use of a local hybrid functional (LH12ct-SsirPW92) that features a real-space dependent admixture of exact exchange governed by a local mixing function. The excellent performance of this LH for triplet excitation energies known from previous studies transfers to a remarkable mean absolute error of 0.06 eV for the phosphorescence 0-0 energies investigated herein, while the popular B3PW91 functional gives an error of 0.27 eV in TDDFT and 0.09 eV in unrestricted DFT calculations, respectively. The advantages of the local hybrid are particularly apparent for excited states with a mixed-valence character. The influence of spin-orbit coupling was found to be significant for [Os(bpy)₃]²⁺ red-shifting the 0-0 energy for phosphorescence by 0.17 eV, while the effect is negligible for the other complexes (<0.03 eV). The influence of the basis-set and integration-grid sizes is evaluated, and a computationally lighter protocol is validated that leads to drastic savings in computation time with negligible loss in accuracy.

Elucidating an Atmospheric Brown Carbon Species-Toward Supplanting Chemical Intuition with Exhaustive Enumeration and Machine Learning

Brown carbon (BrC) is involved in atmospheric light absorption and climate forcing and can cause adverse health effects. Understanding the formation mechanisms and molecular structure of BrC is of key importance in developing strategies to control its environment and health impact. Structure determination of BrC is challenging, due to the lack of experiments providing molecular fingerprints and the sheer number of molecular candidates with identical mass. Suggestions based on chemical intuition are prone to errors due to the inherent bias. We present an unbiased algorithm, using graph-based molecule generation and machine learning, which can identify all molecular structures of compounds involved in biomass burning and the composition of BrC. We apply this algorithm to C₁₂H₁₂O₇, a light-absorbing "test case" molecule identified in chamber experiments on the aqueous photo-oxidation of syringol, a prevalent marker in wood smoke. Of the 260 million molecular graphs, the algorithm leaves only 36,518 (0.01%) as viable candidates matching the spectrum. Although no unique molecular structure is obtained from only a chemical formula and a UV/vis absorption spectrum, we discuss further reduction strategies and their efficacy. With additional data, the method can potentially more rapidly identify isomers extracted from lab and field aerosol particles without introducing human bias.

First principles theoretical spectroscopy of methylene blue: Between limitations of time-dependent density functional theory approximations and its realistic description in the solvent

Methylene blue [3,7-Bis(di-methylamino) phenothiazin-5-ium chloride] is a phenothiazine dye with applications as a sensitizer for photodynamic therapy, photoantimicrobials, and dye-sensitized solar cells. Time-dependent density functional theory (TDDFT), based on (semi)local and global hybrid exchange-correlation functionals, fails to correctly describe its spectral features due to known limitations for describing optical excitations of π-conjugated systems. Here, we use TDDFT with a non-empirical optimally tuned range-separated hybrid functional to explore the optical excitations of gas phase and solvated methylene blue. We compute solvated configurations using molecular dynamics and an iterative procedure to account for explicit solute polarization. We rationalize and validate that by extrapolating the optimized range separation parameter to an infinite amount of solvating molecules, the optical gap of methylene blue is well described. Moreover, this method allows us to resolve contributions from solvent-solute intermolecular interactions and dielectric screening. We validate our results by comparing them to first-principles calculations based on the GW+Bethe-Salpeter equation approach and experiment. Vibronic calculations using TDDFT and the generating function method account for the spectra's subbands and bring the computed transition energies to within 0.15 eV of the experimental data. This methodology is expected to perform equivalently well for describing solvated spectra of π-conjugated systems.

On-the-fly ab initio semiclassical evaluation of vibronic spectra at finite temperature

To compute and analyze vibrationally resolved electronic spectra at zero temperature, we have recently implemented the on-the-fly ab initio extended thawed Gaussian approximation [A. Patoz et al., J. Phys. Chem. Lett. 9, 2367 (2018)], which accounts for anharmonicity, mode-mode coupling, and Herzberg-Teller effects. Here, we generalize this method in order to evaluate spectra at non-zero temperature. In line with thermo-field dynamics, we transform the von Neumann evolution of the coherence component of the density matrix to the Schrödinger evolution of a wavefunction in an augmented space with twice as many degrees of freedom. Due to the efficiency of the extended thawed Gaussian approximation, this increase in the number of coordinates results in nearly no additional computational cost. More specifically, compared to the original, zero-temperature approach, the finite-temperature method requires no additional ab initio electronic structure calculations. At the same time, the new approach allows for a clear distinction among finite-temperature, anharmonicity, and Herzberg-Teller effects on spectra. We show, on a model Morse system, the advantages of the finite-temperature thawed Gaussian approximation over the commonly used global harmonic methods and apply it to evaluate the symmetry-forbidden absorption spectrum of benzene, where all of the aforementioned effects contribute.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Semiclassical Approach to Photophysics Beyond Kasha's Rule and Vibronic Spectroscopy Beyond the Condon Approximation. The Case of Azulene

Azulene is a prototypical molecule with an anomalous fluorescence from the second excited electronic state, thus violating Kasha's rule, and with an emission spectrum that cannot be understood within the Condon approximation. To better understand the photophysics and spectroscopy of azulene and other nonconventional molecules, we developed a systematic, general, and efficient computational approach combining the semiclassical dynamics of nuclei with ab initio electronic structure. First, to analyze the nonadiabatic effects, we complement the standard population dynamics by a rigorous measure of adiabaticity, estimated with the multiple-surface dephasing representation. Second, we propose a new semiclassical method for simulating non-Condon spectra, which combines the extended thawed Gaussian approximation with the efficient single-Hessian approach. S₁ ← S₀ and S₂ ← S₀ absorption and S₂ → S₀ emission spectra of azulene, recorded in a new set of experiments, agree very well with our calculations. We find that accuracy of the evaluated spectra requires the treatment of anharmonicity, Herzberg-Teller, and mode-mixing effects.