Can the absolute configuration of cyclic peptides be determined with vibrational circular dichroism?

Cyclic peptides show a wide range of biological activities, among others as antibacterial agents. These peptides are often large and flexible with multiple chiral centers. The determination of the stereochemistry of molecules with multiple chiral centers is a challenging and important task in drug development. Chiroptical spectroscopies such as vibrational circular dichroism (VCD) can distinguish between different stereoisomers. The absolute configuration (AC) of a stereoisomer can be determined by comparing its experimental spectra to computed spectra of stereoisomers with known AC. In this way, the AC of rigid molecules with up to seven chiral centers has been assigned (Bogaerts et al., Phys. Chem. Chem. Phys., 2020, 22, 18014). The question arises whether this is possible with more conformationally flexible molecules such as cyclic peptides. We here investigate to what extent the AC of cyclic peptides can be determined with VCD. More specifically, we investigate the maximum number of chiral centers a cyclic peptide can have in order to be able to unambiguously assign the AC with VCD. We present experimental and computed IR and VCD spectra for a series of eight tetrapeptides and hexapeptides with two, three and four chiral centers. We use our recently developed computational protocol with a conformational search based on sampling with meta-dynamics. We use visual inspection to compare the computed spectra of different stereoisomers with an experimental spectrum of the corresponding cyclic peptide with known AC. We find that the AC of the investigated cyclic peptides with two chiral centers can be unambiguously assigned with VCD. This is however not possible for all of the cyclic peptides with three chiral centers and for none of those with four chiral centers. At best, one can limit the number of possible stereoisomers in those cases. Our work shows that other techniques are needed to assign the AC of cyclic peptides with three or more chiral centers. Our study also constitutes a warning that the spectra of all stereoisomers should be computed before attempting to match to an experimental spectrum, to avoid an accidental erroneous match.

A Computational Protocol for Vibrational Circular Dichroism Spectra of Cyclic Oligopeptides.

Cyclic peptides are a promising class of compounds for next-generation antibiotics as they may provide new ways of limiting antibiotic resistance development. Although their cyclic structure will introduce some rigidity, their conformational space is large and they usually have multiple chiral centers that give rise to a wide range of possible stereoisomers. Chiroptical spectroscopies such as vibrational circular dichroism (VCD) are used to assign stereochemistry and discriminate enantiomers of chiral molecules, often in combination with electronic structure methods. The reliable determination of the absolute configuration of cyclic peptides will require robust computational methods than can identify all significant conformers and their relative population and reliably assign their stereochemistry from their chiroptical spectra by comparison with ab initio calculated spectra. We here present a computational protocol for the accurate calculation of the VCD spectra of a series of flexible cyclic oligopeptides. The protocol builds on the Conformer-Rotamer Ensemble Sampling Tool (CREST) developed by Grimme and co-workers ( Phys. Chem. Chem. Phys. 2020, 22, 7169-7192 and J. Chem. Theory. Comput. 2019, 15, 2847-2862) in combination with postoptimizations using B3LYP and moderately sized basis sets. Our recommended computational protocol for the computation of VCD spectra of cyclic oligopeptides consists of three steps: (1) conformational sampling with CREST and tight-binding density functional theory (xTB); (2) energy ranking based on single-point energy calculations as well as geometry optimization and VCD calculations of conformers that are within 2.5 kcal/mol of the most stable conformer using B3LYP/6-31+G*/CPCM; and (3) VCD spectra generation based on Boltzmann weighting with Gibbs free energies. Our protocol provides a feasible basis for generating VCD spectra also for larger cyclic peptides of biological/pharmaceutical interest and can thus be used to investigate promising compounds for next-generation antibiotics.

Choosing Bad versus Worse: Predictions of Two-Photon-Absorption Strengths Based on Popular Density Functional Approximations.

We present a benchmark study of density functional approximation (DFA) performances in predicting the two-photon-absorption strengths in π-conjugated molecules containing electron-donating/-accepting moieties. A set of 48 organic molecules is chosen for this purpose, for which the two-photon-absorption (2PA) parameters are evaluated using different DFAs, including BLYP, PBE, B3LYP, PBE0, CAM-B3LYP, LC-BLYP, and optimally tuned LC-BLYP. Minnesota functionals and ωB97X-D are also used, applying the two-state approximation, for a subset of molecules. The efficient resolution-of-identity implementation of the coupled-cluster CC2 model (RI-CC2) is used as a reference for the assessment of the DFAs. Two-state models within the framework of both DFAs and RI-CC2 are used to gain a deeper insight into the performance of different DFAs. Our results give a clear picture of the performance of the density functionals in describing the two-photon activity in dipolar π-conjugated systems. The results show that global hybrids are best suited to reproduce the absolute values of 2PA strengths of donor-acceptor molecules. The range-separated functionals CAM-B3LYP and optimally tuned LC-BLYP, however, show the highest linear correlations with the reference RI-CC2 results. Hence, we recommend the latter DFAs for structure-property studies across large series of dipolar compounds.

Harmonic Infrared and Raman Spectra in Molecular Environments Using the Polarizable Embedding Model.

We present a fully analytic approach to calculate infrared (IR) and Raman spectra of molecules embedded in complex molecular environments modeled using the fragment-based polarizable embedding (PE) model. We provide the theory for the calculation of analytic second-order geometric derivatives of molecular energies and first-order geometric derivatives of electric dipole moments and dipole-dipole polarizabilities within the PE model. The derivatives are implemented using a general open-ended response theory framework, thus allowing for an extension to higher-order derivatives. The embedding-potential parameters used to describe the environment in the PE model are derived through first-principles calculations, thus allowing a wide variety of systems to be modeled, including solvents, proteins, and other large and complex molecular environments. Here, we present proof-of-principle calculations of IR and Raman spectra of acetone in different solvents. This work is an important step toward calculating accurate vibrational spectra of molecules embedded in realistic environments.

A generalized few-state model for the first hyperpolarizability.

The properties of molecules depend on their chemical structure, and thus, structure-property relations help design molecules with desired properties. Few-state models are often used to interpret experimental observations of non-linear optical properties. Not only the magnitude but also the relative orientation of the transition dipole moment vectors is needed for few-state models of the non-linear optical properties. The effect of the relative orientation of the transition dipole moment vectors is called dipole alignment, and this effect has previously been studied for multiphoton absorption properties. However, so far, no such studies are reported for the first hyperpolarizability. Here, we present a generalized few-state model for the static and dynamic first hyperpolarizability ß, accounting for the effect of dipole alignment. The formulas derived in this work are general in the sense that they can be used for any few-state model, i.e., a two-state model, a three-state model, or, in general, an n-state model. Based on the formulas, we formulate minimization and maximization criteria for the alignment of transition dipole moment vectors. We demonstrate the importance of dipole alignment by applying the formulas to the static first hyperpolarizability of ortho-, meta-, and para-nitroaniline. The formulas and the analysis provide new ways to understand the structure-property relationship for ß and can hence be used to fine-tune the magnitude of ß in a molecule.

Benchmarking the Performance of Exchange-Correlation Functionals for Predicting Two-Photon Absorption Strengths.

The present work investigates the performance of exchange-correlation functionals in the prediction of two-photon absorption (2PA) strengths. For this purpose, we considered six common functionals used for studying 2PA processes and tested these on six organoboron chelates. The set consisted of two semilocal (PBE and BLYP), two hybrid (B3LYP and PBE0), and two range-separated (LC-BLYP and CAM-B3LYP) functionals. The RI-CC2 method was chosen as a reference level and was found to give results consistent with the experimental data that are available for three of the molecules considered. Of the six exchange-correlation functionals studied, only the range-separated functionals predict an ordering of the 2PA strengths that is consistent with experimental and RI-CC2 results. Even though the range-separated functionals predict correct relative trends, the absolute values for the 2PA strengths are underestimated by a factor of 2-6 for the molecules considered. An in-depth analysis, on the basis of the derived generalized few-state model expression for the 2PA strength for a coupled-cluster wave function, reveals that the problem with these functionals can be linked to underestimated excited-state dipole moments and, to a lesser extent, overestimated excitation energies. The semilocal and hybrid functionals exhibit less predictable errors and a variation in the 2PA strengths in disagreement with the reference results. The semilocal and hybrid functionals show smaller average errors than the range-separated functionals, but our analysis reveals that this is due to fortuitous error cancellation between excitation energies and the transition dipole moments. Our results constitute a warning against using currently available exchange-correlation functionals in the prediction of 2PA strengths and highlight the need for functionals that correctly describe the electron density of excited electronic states.

Channel interference in multiphoton absorption.

We extend the theory of channel interference to higher-order multiphoton absorption processes. We derive an explicit expression for channel interference in a three-photon absorption process and propose a general scheme for deriving such expressions for multiphoton absorption processes of any order. Based on this general scheme, we derive and analyze the simplest few-state models for multiphoton absorption in centrosymmetric molecules and discuss the criteria for maximizing the corresponding multiphoton absorption strengths.

An averaged polarizable potential for multiscale modeling in phospholipid membranes.

A set of average atom-centered charges and polarizabilities has been developed for three types of phospholipids for use in polarizable embedding calculations. The lipids investigated are 1,2-dimyristoyl-sn-glycero-3-phosphocholine, 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine, and 1-palmitoyl-2-oleoyl-sn-glycerol-3-phospho-L-serine given their common use both in experimental and computational studies. The charges, and to a lesser extent the polarizabilities, are found to depend strongly on the molecular conformation of the lipids. Furthermore, the importance of explicit polarization is underlined for the description of larger assemblies of lipids, that is, membranes. In conclusion, we find that specially developed polarizable parameters are needed for embedding calculations in membranes, while common non-polarizable point-charge force fields usually perform well enough for structural and dynamical studies. © 2017 Wiley Periodicals, Inc.

Open-ended formulation of self-consistent field response theory with the polarizable continuum model for solvation.

The study of high-order absorption properties of molecules is a field of growing importance. Quantum-chemical studies can help design chromophores with desirable characteristics. Given that most experiments are performed in solution, it is important to devise a cost-effective strategy to include solvation effects in quantum-chemical studies of these properties. We here present an open-ended formulation of self-consistent field (SCF) response theory for a molecular solute coupled to a polarizable continuum model (PCM) description of the solvent. Our formulation relies on the open-ended, density matrix-based quasienergy formulation of SCF response theory of Thorvaldsen, et al., [J. Chem. Phys., 2008, 129, 214108] and the variational formulation of the PCM, as presented by Lipparini et al., [J. Chem. Phys., 2010, 133, 014106]. Within the PCM approach to solvation, the mutual solute-solvent polarization is represented by means of an apparent surface charge (ASC) spread over the molecular cavity defining the solute-solvent boundary. In the variational formulation, the ASC is an independent, variational degree of freedom. This allows us to formulate response theory for molecular solutes in the fixed-cavity approximation up to arbitrary order and with arbitrary perturbation operators. For electric dipole perturbations, pole and residue analyses of the response functions naturally lead to the identification of excitation energies and transition moments. We document the implementation of this approach in the Dalton program package using a recently developed open-ended response code and the PCMSolver libraries and present results for one-, two-, three-, four- and five-photon absorption processes of three small molecules in solution.

Open-ended response theory with polarizable embedding: multiphoton absorption in biomolecular systems.

We present the theory and implementation of an open-ended framework for electric response properties at the level of Hartree-Fock and Kohn-Sham density functional theory that includes effects from the molecular environment modeled by the polarizable embedding (PE) model. With this new state-of-the-art multiscale functionality, electric response properties to any order can be calculated for molecules embedded in polarizable atomistic molecular environments ranging from solvents to complex heterogeneous macromolecules such as proteins. In addition, environmental effects on multiphoton absorption (MPA) properties can be studied by evaluating single residues of the response functions. The PE approach includes mutual polarization effects between the quantum and classical parts of the system through induced dipoles that are determined self-consistently with respect to the electronic density. The applicability of our approach is demonstrated by calculating MPA strengths up to four-photon absorption for the green fluorescent protein. We show how the size of the quantum region, as well as the treatment of the border between the quantum and classical regions, is crucial in order to obtain reliable MPA predictions.

Averaged Solvent Embedding Potential Parameters for Multiscale Modeling of Molecular Properties.

We derive and validate averaged solvent parameters for embedding potentials to be used in polarizable embedding quantum mechanics/molecular mechanics (QM/MM) molecular property calculations of solutes in organic solvents. The parameters are solvent-specific atom-centered partial charges and isotropic polarizabilities averaged over a large number of geometries of solvent molecules. The use of averaged parameters reduces the computational cost to obtain the embedding potential, which can otherwise be a rate-limiting step in calculations involving large environments. The parameters are evaluated by analyzing the quality of the resulting molecular electrostatic potentials with respect to full QM potentials. We show that a combination of geometry-specific parameters for solvent molecules close to the QM region and averaged parameters for solvent molecules further away allows for efficient polarizable embedding multiscale modeling without compromising the accuracy. The results are promising for the development of general embedding parameters for biomolecules, where the reduction in computational cost can be considerable.

Correction: Analysis of computational models for an accurate study of electronic excitations in GFP.

Correction for 'Analysis of computational models for an accurate study of electronic excitations in GFP' by Tobias Schwabe et al., Phys. Chem. Chem. Phys., 2015, 17, 2582-2588.

Benchmarking two-photon absorption cross sections: performance of CC2 and CAM-B3LYP.

We investigate the performance of CC2 and TDDFT/CAM-B3LYP for the calculation of two-photon absorption (TPA) strengths and cross sections and contrast our results to a recent coupled cluster equation-of-motion (EOM-EE-CCSD) benchmark study [K. D. Nanda and A. I. Krylov, J. Chem. Phys., 2015, 142, 064118]. In particular, we investigate whether CC2 TPA strengths are significantly overestimated compared to higher-level coupled-cluster calculations for fluorescent protein chromophores. Our conclusion is that CC2 TPA strengths are only slightly overestimated compared to the reference EOM-EE-CCSD results and that previously published overestimated cross sections are a result of inconsistencies in the conversion of the TPA strengths to macroscopic units. TDDFT/CAM-B3LYP TPA strengths, on the other hand, are found to be 1.5 to 3 times smaller than the coupled-cluster reference for the molecular systems considered. The unsatisfactory performance of TDDFT/CAM-B3LYP can be linked to an underestimation of excited-state dipole moments predicted by TDDFT/CAM-B3LYP.

Open-Ended Recursive Approach for the Calculation of Multiphoton Absorption Matrix Elements.

We present an implementation of single residues for response functions to arbitrary order using a recursive approach. Explicit expressions in terms of density-matrix-based response theory for the single residues of the linear, quadratic, cubic, and quartic response functions are also presented. These residues correspond to one-, two-, three- and four-photon transition matrix elements. The newly developed code is used to calculate the one-, two-, three- and four-photon absorption cross sections of para-nitroaniline and para-nitroaminostilbene, making this the first treatment of four-photon absorption in the framework of response theory. We find that the calculated multiphoton absorption cross sections are not very sensitive to the size of the basis set as long as a reasonably large basis set with diffuse functions is used. The choice of exchange-correlation functional, however, significantly affects the calculated cross sections of both charge-transfer transitions and other transitions, in particular, for the larger para-nitroaminostilbene molecule. We therefore recommend the use of a range-separated exchange-correlation functional in combination with the augmented correlation-consistent double-ζ basis set aug-cc-pVDZ for the calculation of multiphoton absorption properties.

Electronic circular dichroism of fluorescent proteins: a computational study.

The electronic circular dichroism (ECD) properties of the green fluorescent protein and other fluorescent proteins have been calculated with density functional theory. The influence of different embedding models on the ECD signal of the chromophore has been investigated by modeling the protein environment by the polarizable continuum model (QM/PCM), by the polarizable embedding model (PE-QM/MM), by treating the minimal environment quantum mechanically at the same footing as the chromophore (QM/QM), and by adding the remaining part of the protein by means of PCM (QM/QM/PCM). The rotatory strength is found to be more sensitive than the oscillatory strength to changes in the geometry of the chromophore and its surroundings and to the type of embedding model used. In general, explicit embedding of the surrounding protein (PE-QM/MM or QM/QM) induces an increase in the rotatory strength of the chromophore. Explicit inclusion of the whole protein through polarizable embedding is found to be an affordable embedding model that gives the correct sign of the rotatory strength for all fluorescent proteins. PCM is useful as a first approximation to protein environment effects, but as a rule seems to underestimate the rotatory strength.

Molecular quantum mechanical gradients within the polarizable embedding approach--application to the internal vibrational Stark shift of acetophenone.

We present an implementation of analytical quantum mechanical molecular gradients within the polarizable embedding (PE) model to allow for efficient geometry optimizations and vibrational analysis of molecules embedded in large, geometrically frozen environments. We consider a variational ansatz for the quantum region, covering (multiconfigurational) self-consistent-field and Kohn-Sham density functional theory. As the first application of the implementation, we consider the internal vibrational Stark effect of the C=O group of acetophenone in different solvents and derive its vibrational linear Stark tuning rate using harmonic frequencies calculated from analytical gradients and computed local electric fields. Comparisons to PE calculations employing an enlarged quantum region as well as to a non-polarizable embedding scheme show that the inclusion of mutual polarization between acetophenone and water is essential in order to capture the structural modifications and the associated frequency shifts observed in water. For more apolar solvents, a proper description of dispersion and exchange-repulsion becomes increasingly important, and the quality of the optimized structures relies to a larger extent on the quality of the Lennard-Jones parameters.

Analysis of computational models for an accurate study of electronic excitations in GFP.

Using the chromophore of the green fluorescent protein (GFP), the performance of a hybrid RI-CC2/polarizable embedding (PE) model is tested against a quantum chemical cluster approach. Moreover, the effect of the rest of the protein environment is studied by systematically increasing the size of the cluster and analyzing the convergence of the excitation energies. It is found that the influence of the environment of the chromophore can accurately be described using a polarizable embedding model with only a minor error compared to a full quantum chemical description. It is also shown that the treatment of only a small region around the chromophore is only by coincidence a good approximation. Therefore, such cluster approaches should be used with care. Based on our results, we suggest that polarizable embedding models, including a large part of the environment to describe its effect on biochromophores on top of an accurate way of describing the central subsystem, are both accurate and computationally favourable in many cases.

Rotational averaging of multiphoton absorption cross sections.

Rotational averaging of tensors is a crucial step in the calculation of molecular properties in isotropic media. We present a scheme for the rotational averaging of multiphoton absorption cross sections. We extend existing literature on rotational averaging to even-rank tensors of arbitrary order and derive equations that require only the number of photons as input. In particular, we derive the first explicit expressions for the rotational average of five-, six-, and seven-photon absorption cross sections. This work is one of the required steps in making the calculation of these higher-order absorption properties possible. The results can be applied to any even-rank tensor provided linearly polarized light is used.

Intermolecular charge transfer enhances two-photon absorption in yellow fluorescent protein.

We present a quantum chemical study of the two-photon absorption (TPA) properties of yellow fluorescent protein (YFP), a mutant of the extensively studied green fluorescent protein. The aromatic chromophore of YFP has a π-stacking interaction with the aromatic ring of a tyrosine residue (Tyr203) in a parallel-displaced structure with a distance of about 3.4 Å. We study the TPA spectrum of the π-stacking system of YFP using the well-established Coulomb-attenuated B3LYP density functional (CAM-B3LYP) and the second-order approximate coupled-cluster model CC2. This work presents both the first comprehensive study of the two-photon absorption spectrum of YFP and the largest-scale coupled-cluster calculation of two-photon absorption that has ever been performed. We analyze the intermolecular charge-transfer (ICT) transitions in this stacked system and show that the ICT transitions are an important mechanism for enhancing the TPA cross sections in YFP. We investigate the distance dependence of the ICT transitions and show that their TPA cross sections are strongly dependent on the separation of the aromatic moieties. This provides a means for tuning the TPA properties of YFP and other structurally related fluorescent proteins through molecular engineering.

A polarizable embedding DFT study of one-photon absorption in fluorescent proteins.

A theoretical study of the one-photon absorption of five fluorescent proteins (FPs) is presented. The absorption properties are calculated using a polarizable embedding approach combined with density functional theory (PE-DFT) on the wild-type green fluorescent protein (wtGFP) and several of its mutants (BFP, eGFP, YFP and eCFP). The observed trends in excitation energies among the FPs are reproduced by our approach when performing calculations directly on the crystal structures or when using structures extracted from molecular dynamics simulations. However, in the former case, QM/MM geometry optimization of the chromophores within a frozen protein environment is needed in order to reproduce the experimental trends. An explicit account of polarization in the force field is not needed to yield the correct trend between the different FPs, but it is necessary for reproducing the experimentally observed red shift from vacuum to protein. This is the first computational study of a range of fluorescent proteins using a polarizable embedding potential.