Theoretical characterization of electronic states in interacting chemical systems

Unrevealing the Nitrogen Elusive Chirality of 3-Sulfanyl and 3-Sulfinyl N-Tosyl Isoindolinones by ECD Spectra: An Experimental and Theoretical Investigation

The nitrogen-hybridization/pyramidalization of two solvated N-tosylisoindolinone derivatives having chiral residues in adjacent (I) or adjacent and distal (II) position has been investigated by a theoretical-computational procedure based on Molecular Dynamics simulations and Quantum-Chemical calculations. After validation of our methodology in providing a reliable repertory of conformations by modeling the electronic circular dichroism (EDC) spectra, the electronic features associated with N-pyramidalization were further characterized through Natural Bond Order (NBO) analysis. Comparing against the N-geometry observed in crystal structures as a reference, our findings reveal that the presence of neighbouring chiral centers induces a more pronounced N-pyramidalization in solution than in the solid state, both in I and II. Furthermore, NBO analysis confirms that the N-lactam mostly retains the sp2 character but exhibits slight configurational distortion (ξI=13°; ξII=21°), which significantly influences the chiroptical activities observed in ECD spectra of I and II. This substantiates the N-lactams as configurationally stable chiral centers.

Modeling the temperature dependence of the fluorescence properties of Indole in aqueous solution

In a recent paper, we proposed a scheme to describe the relaxation mechanism of the excited Indole in aqueous solution, involving the fluctuations among the diabatic electronic states 1Lb, 1La and 1πσ∗. Such a theoretical and computational model reproduced accurately the available experimental data at room temperature. Following these results, in the present work, we model the complex temperature dependence of the fluorescence properties of Indole in aqueous solution, with results further validating the proposed relaxation scheme. This scheme is able to explain the temperature effects on the fluorescence behavior indicating the water fluctuations as the main cause of (i) the stabilization of the dark state (1πσ∗) and (ii) the increase in temperature of the kinetics of the irreversible transition towards such a state.

Evidence of a Distinctive Enantioselective Binding Mode for the Photoinduced Radical Cyclization of α-Chloroamides in Ene-Reductases

We demonstrate here through molecular simulations and mutational studies the origin of the enantioselectivity in the photoinduced radical cyclization of α-chloroacetamides catalyzed by ene-reductases, in particular the Gluconobacter oxidans ene-reductase and the Old Yellow Enzyme 1, which show opposite enantioselectivity. Our results reveal that neither the π-facial selectivity model nor a protein-induced selective stabilization of the transition states is able to explain the enantioselectivity of the radical cyclization in the studied flavoenzymes. We propose a new enantioinduction scenario according to which enantioselectivity is indeed controlled by transition-state stability; however, the relative stability of the prochiral transition states is not determined by direct interaction with the protein but is rather dependent on an inherent degree of freedom within the substrate itself. This intrinsic degree of freedom, distinct from the traditional π-facial exposure mode, can be controlled by the substrate conformational selection upon binding to the enzyme.

Plasmon-enhanced circular dichroism spectroscopy of chiral drug solutions

We investigate the potential of surface plasmon polaritons at noble metal interfaces for surface-enhanced chiroptical sensing of dilute chiral drug solutions with nl volume. The high quality factor of surface plasmon resonances in both Otto and Kretschmann configurations enables the enhancement of circular dichroism differenatial absorption thanks to the large near-field intensity of such plasmonic excitations. Furthermore, the subwavelength confinement of surface plasmon polaritons is key to attain chiroptical sensitivity to small amounts of drug volumes placed around ≃100 nm by the metal surface. Our calculations focus on reparixin, a pharmaceutical molecule currently used in clinical studies for patients with community-acquired pneumonia, including COVID-19 and acute respiratory distress syndrome. Considering realistic dilute solutions of reparixin dissolved in water with concentration ≤5 mg/ml and nl volume, we find a circular-dichroism differential absorption enhancement factor of the order ≃20 and chirality-induced polarization distortion upon surface plasmon polariton excitation. Our results are relevant for the development of innovative chiroptical sensors capable of measuring the enantiomeric imbalance of chiral drug solutions with nl volume.

Benchmarking Aspects of Ab Initio Fragment Models for Accurate Excimer Potential Energy Surfaces

While Coupled-Cluster methods have been proven to provide an accurate description of excited electronic states, the scaling of the computational costs with the system size limits the degree for which these methods can be applied. In this work different aspects of fragment-based approaches are studied on noncovalently bound molecular complexes with interacting chromophores of the fragments, such as π-stacked nucleobases. The interaction of the fragments is considered at two distinct steps. First, the states localized on the fragments are described in the presence of the other fragment(s); for this we test two approaches. One method is founded on QM/MM principles, only including the electrostatic interaction between the fragments in the electronic structure calculation with Pauli repulsion and dispersion effects added separately. The other model, a Projection-based Embedding (PbE) using the Huzinaga equation, includes both electrostatic and Pauli repulsion and only needs to be augmented by dispersion interactions. In both schemes the extended Effective Fragment Potential (EFP2) method of Gordon et al. was found to provide an adequate correction for the missing terms. In the second step, the interaction of the localized chromophores is modeled for a proper description of the excitonic coupling. Here the inclusion of purely electrostatic contributions appears to be sufficient: it is found that the Coulomb part of the coupling provides accurate splitting of the energies of interacting chromophores that are separated by more than 4 Å.

Unveiling the Excited State Dynamics of Indole in Solution

In this paper, we reconstruct in detail the dynamics of the emitting electronic excited state of aqueous indole, investigating its relaxation mechanism and kinetics to be related to the time-dependent fluorescence signal. Taking advantage of the results shown in a very recent paper, we were able to model the relaxation process in solution in terms of the transitions between two gas-phase singlet electronic states (¹L_a and ¹L_b), subsequently irreversibly relaxing to the gas-phase singlet dark state (¹πσ*). A comparison of the results with the available experimental data shows that the relaxation mechanism we obtain by our theoretical-computational model is reliable, reproducing rather accurately all the experimental observables.

Theoretical-Computational Modeling of CD Spectra of Aqueous Monosaccharides by Means of Molecular Dynamics Simulations and Perturbed Matrix Method

The electronic circular dichroism (ECD) spectra of aqueous d-glucose and d-galactose were modeled using a theoretical-computational approach combining molecular dynamics (MD) simulations and perturbed matrix method (PMM) calculations, hereafter termed MD-PMM. The experimental spectra were reproduced with a satisfactory accuracy, confirming the good performances of MD-PMM in modeling different spectral features in complex atomic-molecular systems, as already reported in previous studies. The underlying strategy of the method was to perform a preliminary long timescale MD simulation of the chromophore followed by the extraction of the relevant conformations through essential dynamics analysis. On this (limited) number of relevant conformations, the ECD spectrum was calculated via the PMM approach. This study showed that MD-PMM was able to reproduce the essential features of the ECD spectrum (i.e., the position, the intensity, and the shape of the bands) of d-glucose and d-galactose while avoiding the rather computationally expensive aspects, which were demonstrated to be important for the final outcome, such as (i) the use of a large number of chromophore conformations; (ii) the inclusion of quantum vibronic coupling; and (iii) the inclusion of explicit solvent molecules interacting with the chromophore atoms within the chromophore itself (e.g., via hydrogen bonds).

A Simplified Treatment for Efficiently Modeling the Spectral Signal of Vibronic Transitions: Application to Aqueous Indole

In this paper, we introduce specific approximations to simplify the vibronic treatment in modeling absorption and emission spectra, allowing us to include a huge number of vibronic transitions in the calculations. Implementation of such a simplified vibronic treatment within our general approach for modelling vibronic spectra, based on molecular dynamics simulations and the perturbed matrix method, provided a quantitative reproduction of the absorption and emission spectra of aqueous indole with higher accuracy than the one obtained when using the existing vibronic treatment. Such results, showing the reliability of the approximations employed, indicate that the proposed method can be a very efficient and accurate tool for computational spectroscopy.

PyMM: An Open-Source Python Program for QM/MM Simulations Based on the Perturbed Matrix Method

Quantum mechanical/molecular mechanics (QM/MM) methods are important tools in molecular modeling as they are able to couple an extended phase space sampling with an accurate description of the electronic properties of the system. Here, we describe a Python software package, called PyMM, which has been developed to apply a QM/MM approach, the perturbed matrix method, in a simple and efficient way. PyMM requires a classical atomic trajectory of the whole system and a set of unperturbed electronic properties of the ground and electronic excited states. The software output includes a set of the most common perturbed properties, such as the electronic excitation energies and the transitions dipole moments, as well as the eigenvectors describing the perturbed electronic states, which can be then used to estimate whatever electronic property. The software is composed of a simple and complete command-line interface, a set of internal input validation, and three main analyses focusing on (i) the perturbed eigenvector behavior, (ii) the calculation of the electronic absorption spectrum, and (iii) the estimation of the free energy differences along a reaction coordinate.

Modeling Charge Transfer Reactions by Hopping between Electronic Ground State Minima: Application to Hole Transfer between DNA Bases

In this paper, we extend the previously described general model for charge transfer reactions, introducing specific changes to treat the hopping between energy minima of the electronic ground state (i.e., transitions between the corresponding vibrational ground states). We applied the theoretical–computational model to the charge transfer reactions in DNA molecules which still represent a challenge for a rational full understanding of their mechanism. Results show that the presented model can provide a valid, relatively simple, approach to quantitatively study such reactions shedding light on several important aspects of the reaction mechanism.

Absorption behavior of doxorubicin hydrochloride in visible region in different environments: a combined experimental and computational study

The experimental absorption measurements in the interval 350-600 nm (Vis), molecular dynamics simulations, quantum-mechanics calculations and an advanced molecular treatment of simulation data are here combined to provide a complete picture of the absorption behavior in the visible portion of the electromagnetic spectrum of the doxorubicin hydrochloride (DX) molecule in different environments. By such an approach, we have shown that it is possible to characterize the effect of the environment on the DX absorption behavior - including the vibronic contributions - as well as to interpret such differences in terms of molecular electronic excited states, which are found to be strongly influenced by the environment.

Theoretical Modeling of Redox Potentials of Biomolecules

The estimation of the redox potentials of biologically relevant systems by means of theoretical-computational approaches still represents a challenge. In fact, the size of these systems typically does not allow a full quantum-mechanical treatment needed to describe electron loss/gain in such a complex environment, where the redox process takes place. Therefore, a number of different theoretical strategies have been developed so far to make the calculation of the redox free energy feasible with current computational resources. In this review, we provide a survey of such theoretical-computational approaches used in this context, highlighting their physical principles and discussing their advantages and limitations. Several examples of these approaches applied to the estimation of the redox potentials of both proteins and nucleic acids are described and critically discussed. Finally, general considerations on the most promising strategies are reported.

A computational insight into the relationship between side chain IR line shapes and local environment in fibril-like structures

Infrared spectroscopy is a widely used technique to characterize protein structures and protein mediated processes. While the amide I band provides information on proteins' secondary structure, amino acid side chains are used as infrared probes for the investigation of protein reactions and local properties. In this paper, we use a hybrid quantum mechanical/classical molecular dynamical approach based on the perturbed matrix method to compute the infrared band due to the C=O stretching mode of amide-containing side chains. We calculate, at first, the infrared band of zwitterionic glutamine in water and obtain results in very good agreement with the experimental data. Then, we compute the signal arising from glutamine side chains in a microcrystal of the yeast prion Sup35-derived peptide, GNNQQNY, with a fibrillar structure. The infrared bands obtained by selective isotopic labeling of the two glutamine residues, Q4 and Q5, of each peptide were experimentally used to investigate the local hydration in the fibrillar microcrystal. The experimental spectra of the two glutamine residues, which experience different hydration environments, feature different spectral signals that are well reproduced by the corresponding calculated spectra. In addition, the analysis of the simulated spectra clarifies the molecular origin of the experimentally observed spectroscopic differences that arise from the different local electric field experienced by the two glutamine residues, which is, in turn, determined by a different hydrogen bonding pattern.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

Fully Atomistic Multiscale Approach for pKa Prediction

The ionization state of titratable amino acids strongly affects proteins structure and functioning in a large number of biological processes. It is therefore essential to be able to characterize the pK_a of ionizable groups inside proteins and to understand its microscopic determinants in order to gain insights into many functional properties of proteins. A big effort has been devoted to the development of theoretical approaches for the prediction of deprotonation free energies, yet the accurate theoretical/computational calculation of pK_a values is recognized as a current challenge. A methodology based on a hybrid quantum/classical approach is here proposed for the computation of deprotonation free energies. The method is applied to calculate the pK_a of formic acid, methylammonium, and methanethiol, providing results in good agreement with the corresponding experimental estimates. The pK_a is also calculated for aspartic acid and lysine as single residues in solution and for three aspartic/glutamic acids inside a well-characterized protein: hen egg white lysozyme. While for small molecules the method is able to deal with multiple protonation states of all titratable groups, this becomes computationally very expensive for proteins. The calculated pK_a values for the single amino acids (except for the zwitterionic aspartic acid) and inside the protein display a systematic shift with respect to the experimental values that suggests that the fine balance between hydrophobic and polar interactions might be not accurately reproduced by the usual classical force-fields, thus affecting the computation of deprotonation free energies. The calculated pK_a shifts inside the protein are in good agreement with the corresponding experimental ones (within 1 pK_a unit), well reproducing the pK_a changes due to the protein environment even in the case of large pK_a shifts.

Antiadiabatic View of Fast Environmental Effects on Optical Spectra

An antiadiabatic approach is proposed to model how the refractive index of the surrounding medium affects optical spectra of molecular systems in condensed phases. The approach solves some of the issues affecting current implementations of continuum solvation models and more generally of effective models where a classical description is adopted for the molecular environment.

Modeling amino-acid side chain infrared spectra: the case of carboxylic residues

Infrared (IR) spectroscopy is commonly utilized for the investigation of protein structures and protein-mediated processes.

Evidence of a Thermodynamic Ramp for Hole Hopping to Protect a Redox Enzyme from Oxidative Damage

Redox proteins and enzymes are at risk of irreversible oxidative damage from highly oxidizing intermediates generated in the active site in the case of unsuccessful functional reaction. Chains of tyrosine and/or tryptophan residues have been recently proposed to provide protection to the active site and the whole protein by delivering oxidizing equivalents (holes) out of the protein via a multistep hopping mechanism. In the present work we use a hybrid quantum/classical theoretical-computational methodology based on the perturbed matrix method and on molecular dynamics simulations to calculate the oxidation potential difference along a chain of tyrosine and tryptophan residues in a human redox enzyme of major importance, a superoxide dismutase, which acts as antioxidant defense. We show that the hole hopping is thermodynamically favored along such a chain and that the hopping propensity is strongly affected by the protein environment and in particular by the active site and its second coordination sphere.

Extending the perturbed matrix method beyond the dipolar approximation: comparison of different levels of theory

Some years ago we developed a theoretical-computational hybrid quantum/classical methodology, the Perturbed Matrix Method (PMM), to be used in conjunction with molecular dynamics simulations for the investigation of chemical processes in complex systems, that proved to be a valuable tool for the simulation of relevant experimental observables, e.g., spectroscopic signals, reduction potentials, kinetic constants. In typical PMM calculations the quantum sub-part of the system, the quantum centre, is embedded into an external perturbing field providing a perturbation operator explicitly calculated up to the dipolar terms. In this paper we further develop the PMM approach, beyond the dipolar terms in the perturbation operator expansion, by including explicitly the quadrupolar terms and/or by expanding the perturbation operator on each atom of the quantum centre. These different levels of the perturbation operator expansion, providing different levels of theory, have been tested by calculating three different spectroscopic observables: the spectral signal of liquid water and aqueous benzene due to the lowest energy electronic excitation and the infrared amide I band of aqueous trans-N-methylacetamide. All the systems tested show that, even though the previous PMM level of theory is already capable of reproducing the main features of the spectral signal, the higher levels of theory improve the quantitative reproduction of the spectral details.

Experimental and theoretical study on structure and spectroscopic properties of 2-bromo-3-N-(N',N'-dimethylformamidino) benzanthrone

The goal of present research is a theoretical and experimental investigation of geometrical structure, electronic properties, absorption and fluorescence spectra prediction for 2-bromo-3-N-(N',N'-dimethylformamidino)benzanthrone. As a result of conformational analysis, two rotamers have been found with a rotational barrier of 5.45 kcal/mol. Absorption and fluorescence spectra maxima in the solvent (ethanol) have been calculated using the concepts of the Jablonsky diagram. The obtained values of the absorption and fluorescence maxima (437 and 679 nm, respectively) correspond to the experimental values (447 and 659 nm). The abnormally large Stokes shift is associated with the redistribution of electron density, as well as flattening of the structure of the molecule in the excited state. According to the frontal molecular orbital analysis data, the peak in the long-wave part of the absorption spectra is created by an electron transition from the highest occupied molecular orbital (HOMO) to the lowest occupied molecular orbital (LUMO) (π→π*). Substitute group does not participate in the formation of absorption and fluorescence spectra.

Theoretical-computational modeling of charge transfer and intersystem crossing reactions in complex chemical systems

In this paper we present a theoretical-computational methodology specifically aimed at describing processes involving internal conversion or intersystem crossing, from atomistic (semiclassical) simulations and, hence, very suitable for treating complex atomic-molecular systems. The core of the presented approach is the evaluation of the diabatic perturbed energy surfaces of a portion of the whole system, treated at the quantum level and therefore preventively selected, in semi-classical interaction with the atomic-molecular environment. Subsequently, the estimation of the coupling between the diabatic surfaces and the inclusion of the obtained observables within a properly designed kinetic model allows the reconstruction of the whole phenomenology directly comparable to the experimental (typically kinetic) data. Application to two systems has demonstrated that the proposed approach can represent a valuable tool, somewhat complementary to other methods based on explicit quantum-dynamical approaches, for the theoretical-computational investigations of large and complex atomic-molecular systems.

On the nature of solvatochromic effect: The riboflavin absorption spectrum as a case study

We present here the calculation of the absorption spectrum of riboflavin in acetonitrile and dimethyl sulfoxide using a hybrid quantum/classical approach, namely the perturbed matrix method, based on quantum mechanical calculations and molecular dynamics simulations. The calculated spectra are compared to the absorption spectrum of riboflavin previously calculated in water and to the experimental spectra obtained in all three solvents. The experimentally observed variations in the absorption spectra upon change of the solvent environment are well reproduced by the calculated spectra. In addition, the nature of the excited states of riboflavin interacting with different solvents is investigated, showing that environment effects determine a recombination of the gas-phase electronic states and that such a recombination is strongly affected by the polarity of the solvent inducing significant changes in the absorption spectra.

Extending the essential dynamics analysis to investigate molecular properties: application to the redox potential of proteins

Here, a methodology is proposed to investigate the collective fluctuation modes of an arbitrary set of observables, maximally contributing to the fluctuation of another functionally relevant observable. The methodology, based on the analysis of fully classical molecular dynamics (MD) simulations, exploits the essential dynamics (ED) method, originally developed to analyse the collective motions in proteins. We apply this methodology to identify the residues that are more relevant for determining the reduction potential (E(0)) of a redox-active protein. To this aim, the fluctuation modes of the single-residue electrostatic potentials mostly contributing to the fluctuations of the total electrostatic potential (the main determinant of E(0)) are investigated for wild-type azurin and two of its mutants with a higher E(0). By comparing the results here obtained with a previous study on the same systems [Zanetti-Polzi et al., Org. Biomol. Chem., 2015, 13, 11003] we show that the proposed methodology is able to identify the key sites that determine E(0). This information can be used for a general deeper understanding of the molecular mechanisms on the basis of the redox properties of the proteins under investigation, as well as for the rational design of mutants with a higher or lower E(0). From the results of the present analysis we propose a new azurin mutant that, according to our calculations, shows a further increase of E(0).

Photoexcitation and relaxation kinetics of molecular systems in solution: towards a complete in silico model

A theoretical–computational method is proposed for modelling the complete kinetics – from photo-excitation to relaxation – of a chromophore in solution.

A dynamical approach to non-adiabatic electron transfers at the bio-inorganic interface

A methodology is proposed to investigate the role of the energy fluctuations, determined by the dynamical evolution of a system, and the role of non-adiabaticity in affecting the kinetic rate of electron transfer reactions at the bio-inorganic interface.

A few key residues determine the high redox potential shift in azurin mutants

The wide range of variability of the reduction potential (E(0)) of blue-copper proteins has been the subject of a large number of studies in the past several years. In particular, a series of azurin mutants have been recently rationally designed tuning E(0) over a very broad range (700 mV) without significantly altering the redox-active site [Marshall et al., Nature, 2009, 462, 113]. This clearly suggests that interactions outside the primary coordination sphere are relevant to determine E(0) in cupredoxins. However, the molecular determinants of the redox potential variability are still undisclosed. Here, by means of atomistic molecular dynamics simulations and hybrid quantum/classical calculations, the mechanisms that determine the E(0) shift of two azurin mutants with high potential shifts are unravelled. The reduction potentials of native azurin and of the mutants are calculated obtaining results in good agreement with the experiments. The analysis of the simulations reveals that only a small number of residues (including non-mutated ones) are relevant in determining the experimentally observed E(0) variation via site-specific, but diverse, mechanisms. These findings open the path to the rational design of new azurin mutants with different E(0).

Theoretical-computational modeling of photo-induced charge separation spectra and charge recombination kinetics in solution

A computational approach, based on molecular dynamics simulations and quantum-chemical calculations, is proposed for modelling the photo-induced charge separation and the kinetics of the subsequent charge recombination (CR) processes in solution.

On the nature of DNA hyperchromic effect

A combined theoretical-experimental study of the hyperchromic effect as occurring in the denaturation of a double stranded polyA-polyT is presented. Our theoretical/computational procedure allows us to reproduce the essential features of the experimental spectra and to characterize those molecular interactions responsible for the changes in the UV absorbance. We found that although excitonic intrastrand interactions strongly affect the absorbance, they are almost fully maintained in the single-stranded DNA. Our data indicate that hyperchromic effect originates from the higher delocalization of the excitonic states in the denaturated DNA with respect to the double-stranded conformation.

A general theoretical model for electron transfer reactions in complex systems

In this paper we present a general theoretical-computational model for treating electron transfer reactions in complex atomic-molecular systems. The underlying idea of the approach, based on unbiased first-principles calculations at the atomistic level, utilizes the definition and the construction of the Diabatic Perturbed states of the involved reactive partners (i.e. the quantum centres in our perturbation approach) as provided by the interaction with their environment, including their mutual interaction. In this way we reconstruct the true Adiabatic states of the reactive partners characterizing the electron transfer process as the fluctuation of the electronic density due to the fluctuating perturbation. Results obtained by using a combination of Molecular Dynamics simulation and the Perturbed Matrix Method on a prototypical intramolecular electron transfer (from 2-(9,9'-dimethyl)fluorene to the 2-naphthalene group separated by a steroidal 5-α-androstane skeleton) well illustrate the accuracy of the method in reproducing both the thermodynamics and the kinetics of the process.