Gas-Phase Retinal Spectroscopy: Temperature Effects Are But a Mirage

We employ state-of-the-art first-principle approaches to investigate whether temperature effects are responsible for the unusually broad and flat spectrum of protonated Schiff base retinal observed in photodissociation spectroscopy, as has recently been proposed. We first carefully calibrate how to construct a realistic geometrical model of retinal and show that the exchange–correlation M06-2X functional yields an accurate description while the commonly used complete active space self-consistent field method (CASSCF) is not adequate. Using modern multiconfigurational perturbative methods (NEVPT2) to compute the excitations, we then demonstrate that conformations with different orientations of the β-ionone ring are characterized by similar excitations. Moreover, other degrees of freedom identified as active in room-temperature molecular dynamics simulations do not yield the shift required to explain the anomalous spectral shape. Our findings indicate that photodissociation experiments are not representative of the optical spectrum of retinal in the gas phase and call for further experimental characterization of the dissociation spectra

Ground- and Excited-State Geometry Optimization of Small Organic Molecules with Quantum Monte Carlo

We present a comparative study of the geometry optimization in the gas phase of acrolein, acetone, methylenecyclopropene, and the propenoic acid anion with special emphasis on their excited-state structures, using quantum Monte Carlo (QMC), multireference perturbation theory (CASPT2 and NEVPT2), second-order approximate coupled cluster (CC2), and time-dependent density functional theory (TDDFT). We find that, for all molecules, the geometries optimized with QMC in its simplest variational (VMC) flavor are in very good agreement with the perturbation results both in the ground and the excited states of either <i>n</i> → π* or π → π* character. Furthermore, the quality of the QMC structures is superior to those obtained with the CC2 method, which overestimates the CO bond in all <i>n</i> → π* excitations, or to the symmetry-adapted-cluster configuration interaction (SAC–CI) approach, which gives a poorer description of the CC bonds in the excited states. Finally, the spread in the TDDFT structures obtained with several current exchange-correlation functionals is large and does not reveal a clear relation between the defining features of the functionals and the quality of the optimized structures. In summary, our findings demonstrate the good performance of QMC in optimizing the geometries of these molecules, also in cases where other correlated or TDDFT approaches are inaccurate, and indicate that the method represents a robust reference approach for future structural studies also of larger systems

Size-Extensive Wave Functions for Quantum Monte Carlo: A Linear Scaling Generalized Valence Bond Approach

We propose a new class of multideterminantal Jastrow–Slater wave functions constructed with localized orbitals and designed to describe complex potential energy surfaces of molecular systems for use in quantum Monte Carlo (QMC). Inspired by the generalized valence bond formalism, we elaborate a coupling scheme between electron pairs which progressively includes new classes of excitations in the determinantal component of the wave function. In this scheme, we exploit the local nature of the orbitals to construct wave functions which have increasing complexity but scale linearly. The resulting wave functions are compact, can correlate all valence electrons, and are size extensive. We assess the performance of our wave functions in QMC calculations of the homolytic fragmentation of N–N, N–O, C–O, and C–N bonds, very common in molecules of biological interest. We find excellent agreement with experiments, and, even with the simplest forms of our wave functions, we satisfy chemical accuracy and obtain dissociation energies of equivalent quality to the CCSD­(T) results computed with the large cc-pV5Z basis set

Scalar Relativistic All-Electron and Pseudopotential <i>Ab Initio</i> Study of a Minimal Nitrogenase [Fe(SH)₄H]⁻ Model Employing Coupled-Cluster and Auxiliary-Field Quantum Monte Carlo Many-Body Methods

Nitrogenase is the only enzyme that can cleave the triple bond in N2, making nitrogen available to organisms. The detailed mechanism of this enzyme is currently not known, and computational studies are complicated by the fact that different density functional theory (DFT) methods give very different energetic results for calculations involving nitrogenase models. Recently, we designed a [Fe(SH)4H]− model with the fifth proton binding either to Fe or S to mimic different possible protonation states of the nitrogenase active site. We showed that the energy difference between these two isomers (ΔE) is hard to estimate with quantum-mechanical methods. Based on nonrelativistic single-reference coupled-cluster (CC) calculations, we estimated that the ΔE is 101 kJ/mol. In this study, we demonstrate that scalar relativistic effects play an important role and significantly affect ΔE. Our best revised single-reference CC estimates for ΔE are 85–91 kJ/mol, including energy corrections to account for contributions beyond triples, core–valence correlation, and basis-set incompleteness error. Among coupled-cluster approaches with approximate triples, the canonical CCSD(T) exhibits the largest error for this problem. Complementary to CC, we also used phaseless auxiliary-field quantum Monte Carlo calculations (ph-AFQMC). We show that with a Hartree–Fock (HF) trial wave function, ph-AFQMC reproduces the CC results within 5 ± 1 kJ/mol. With multi-Slater-determinant (MSD) trials, the results are 82–84 ± 2 kJ/mol, indicating that multireference effects may be rather modest. Among the DFT methods tested, τ-HCTH, r2SCAN with 10–13% HF exchange with and without dispersion, and O3LYP/O3LYP-D4, and B3LYP*/B3LYP*-D4 generally perform the best. The r2SCAN12 (with 12% HF exchange) functional mimics both the best reference MSD ph-AFQMC and CC ΔE results within 2 kJ/mol

Barrier Heights in Quantum Monte Carlo with Linear-Scaling Generalized-Valence-Bond Wave Functions

We investigate here the performance of our recently developed linear-scaling Jastrow-generalized-valence-bond (J-LGVB) wave functions based on localized orbitals, for the quantum Monte Carlo (QMC) calculation of the barrier heights and reaction energies of five prototypical chemical reactions. Using the geometrical parameters from the Minnesota database collection, we consider three hydrogen-exchanges, one heavy-atom exchange, and one association reaction and compare our results with the best available experimental and theoretical data. For the three hydrogen-exchange reactions, we find that the J-LGVB wave functions yield excellent QMC results, with average deviations from the reference values below 0.5 kcal/mol. For the heavy-atom exchange and association reactions, additional resonance structures are important, and we therefore extend our original formulation to include multiple coupling schemes characterized by different sets of localized orbitals. We denote these wave functions as J-MC-LGVB, where MC indicates the multiconfiguration generalization, and show that such a form leads to very accurate barrier heights and reaction energies also for the last two reactions. We can therefore conclude that the J-LGVB theory for constructing QMC wave functions, with its multiconfiguration generalization, is valid for the study of large portions of ground-state potential energy surfaces including, in particular, the region of transition states

Bathochromic Shift in Green Fluorescent Protein: A Puzzle for QM/MM Approaches

We present an extensive investigation of the vertical excitations of the anionic and neutral forms of wild-type green fluorescent protein using time-dependent density functional theory (TDDFT), multiconfigurational perturbation theory (CASPT2), and quantum Monte Carlo (QMC) methods within a quantum mechanics/molecular mechanics (QM/MM) scheme. The protein models are constructed via room-temperature QM/MM molecular dynamics simulations based on DFT and are representative of an average configuration of the chromophore–protein complex. We thoroughly verify the reliability of our structures through simulations with an extended QM region, different nonpolarizable force fields, as well as partial reoptimization with the CASPT2 approach. When computing the excitations, we find that wave function as well as density functional theory methods with long-range corrected functionals agree in the gas phase with the extrapolation of solution experiments but fail in reproducing the bathochromic shift in the protein, which should be particularly significant in the neutral case. In particular, while all methods correctly predict a shift in the absorption between the anionic and neutral forms of the protein, the location of the theoretical absorption maxima is significantly blue-shifted and too close to the gas-phase values. These results point to either an intrinsic limitation of nonpolarizable force-field embedding in the computation of the excitations or to the need to explore alternative protonation states of amino acids in the close vicinity of the chomophore

Bathochromic Shift in Green Fluorescent Protein: A Puzzle for QM/MM Approaches

We present an extensive investigation of the vertical excitations of the anionic and neutral forms of wild-type green fluorescent protein using time-dependent density functional theory (TDDFT), multiconfigurational perturbation theory (CASPT2), and quantum Monte Carlo (QMC) methods within a quantum mechanics/molecular mechanics (QM/MM) scheme. The protein models are constructed via room-temperature QM/MM molecular dynamics simulations based on DFT and are representative of an average configuration of the chromophore–protein complex. We thoroughly verify the reliability of our structures through simulations with an extended QM region, different nonpolarizable force fields, as well as partial reoptimization with the CASPT2 approach. When computing the excitations, we find that wave function as well as density functional theory methods with long-range corrected functionals agree in the gas phase with the extrapolation of solution experiments but fail in reproducing the bathochromic shift in the protein, which should be particularly significant in the neutral case. In particular, while all methods correctly predict a shift in the absorption between the anionic and neutral forms of the protein, the location of the theoretical absorption maxima is significantly blue-shifted and too close to the gas-phase values. These results point to either an intrinsic limitation of nonpolarizable force-field embedding in the computation of the excitations or to the need to explore alternative protonation states of amino acids in the close vicinity of the chomophore

Bathochromic Shift in Green Fluorescent Protein: A Puzzle for QM/MM Approaches

We present an extensive investigation of the vertical excitations of the anionic and neutral forms of wild-type green fluorescent protein using time-dependent density functional theory (TDDFT), multiconfigurational perturbation theory (CASPT2), and quantum Monte Carlo (QMC) methods within a quantum mechanics/molecular mechanics (QM/MM) scheme. The protein models are constructed via room-temperature QM/MM molecular dynamics simulations based on DFT and are representative of an average configuration of the chromophore–protein complex. We thoroughly verify the reliability of our structures through simulations with an extended QM region, different nonpolarizable force fields, as well as partial reoptimization with the CASPT2 approach. When computing the excitations, we find that wave function as well as density functional theory methods with long-range corrected functionals agree in the gas phase with the extrapolation of solution experiments but fail in reproducing the bathochromic shift in the protein, which should be particularly significant in the neutral case. In particular, while all methods correctly predict a shift in the absorption between the anionic and neutral forms of the protein, the location of the theoretical absorption maxima is significantly blue-shifted and too close to the gas-phase values. These results point to either an intrinsic limitation of nonpolarizable force-field embedding in the computation of the excitations or to the need to explore alternative protonation states of amino acids in the close vicinity of the chomophore

Rhodopsin Absorption from First Principles: Bypassing Common Pitfalls

Bovine rhodopsin is the most extensively studied retinal protein and is considered the prototype of this important class of photosensitive biosystems involved in the process of vision. Many theoretical investigations have attempted to elucidate the role of the protein matrix in modulating the absorption of retinal chromophore in rhodopsin, but, while generally agreeing in predicting the correct location of the absorption maximum, they often reached contradicting conclusions on how the environment tunes the spectrum. To address this controversial issue, we combine here a thorough structural and dynamical characterization of rhodopsin with a careful validation of its excited-state properties via the use of a wide range of state-of-the-art quantum chemical approaches including various flavors of time-dependent density functional theory (TDDFT), different multireference perturbative schemes (CASPT2 and NEVPT2), and quantum Monte Carlo (QMC) methods. Through extensive quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations, we obtain a comprehensive structural description of the chromophore–protein system and sample a wide range of thermally accessible configurations. We show that, in order to obtain reliable excitation properties, it is crucial to employ a sufficient number of representative configurations of the system. In fact, the common use of a single, ad hoc structure can easily lead to an incorrect model and an agreement with experimental absorption spectra due to cancelation of errors. Finally, we show that, to properly account for polarization effects on the chromophore and to quench the large blue-shift induced by the counterion on the excitation energies, it is necessary to adopt an enhanced description of the protein environment as given by a large quantum region including as many as 250 atoms

State-Specific Embedding Potentials for Excitation-Energy Calculations

Embedding potentials are frequently used to describe the effect of an environment on the electronic structure of molecules in larger systems, including their excited states. If such excitations are accompanied by significant rearrangements in the electron density of the embedded molecule, large differential polarization effects may take place, which in turn can require state-specific embedding potentials for an accurate theoretical description. We outline here how to extend wave function in density functional theory (WF/DFT) methods to compute the excitation energies of a molecule in a responsive environment through the use of state-specific density-based embedding potentials constructed within a modified subsystem DFT approach. We evaluate the general expression of the ground- and excited-state energy difference of the total system both with the use of state-independent and state-dependent embedding potentials and propose some practical recipes to construct the approximate excited-state DFT density of the active part used to polarize the environment. We illustrate these concepts with the state-independent and state-dependent WF/DFT computation of the excitation energies of <i>p</i>-nitroaniline, acrolein, methylenecyclopropene, and <i>p</i>-nitrophenolate in various solvents