Local electric fields and molecular properties in heterogeneous environments through polarizable embedding

Color Tuning in Bovine Rhodopsin through Polarizable Embedding

Bovine rhodopsin is among the most studied proteins in the rhodopsin family. Its primary activation mechanism is the photoisomerization of 11-cis retinal, triggered by the absorption of a UV-visible photon. Different mutants of the same rhodopsin show different absorption wavelengths due to the influence of the specific amino acid residues forming the cavity in which the retinal chromophore is embedded, and rhodopsins activated at different wavelengths are, for example, exploited in the field of optogenetics. In this letter, we present a procedure for systematically investigating color tuning in models of bovine rhodopsin and a set of its mutants embedded in a membrane bilayer. Vertical excitation energy calculations were carried out with the polarizable embedding potential for describing the environment surrounding the chromophore. We show that polarizable embedding outperformed regular electrostatic embedding in determining both the vertical excitation energies and associated oscillator strengths of the systems studied.

Disentangling the molecular polarizability and first hyperpolarizability of methanol-air interfaces

Liquid-air interfaces have extensive implications in different areas of interest because the dynamical processes at the interface can be different from those in bulk. Thus, its characterization, understanding, and control may be pivotal in advancing discoveries. However, characterizing the interface requires special and selective tools to avoid signals from the bulk region. This surface specificity and versatility is achieved by using the second harmonic generation (SHG) responses. This study adopts multiscale simulation methods to evaluate the surface SHG responses of methanol-air interfaces with submonolayer resolution tackled by sequentially using classical molecular dynamics simulations under different temperatures and then employing quantum chemistry methods to compute the molecular first hyperpolarizabilities (β). This approach ensures the configurational diversity required to evaluate the average β values. The main achievements are (i) a quasi-absence of surface sensitivity of the mean polarizability 〈α〉 with values about 2% larger than those obtained in bulk, (ii) conversely, smooth variations on the polarizability anisotropy Δα are observed up to the fourth molecular layer at around 20 Å from the interface, and (iii) narrow interfacial effects on the SHG responses, β(-2ω;ω,ω), which are limited to the first molecular layer (∼3.0 Å) and characterized by a high contrast in the βZZZ(-2ω;ω,ω) tensor component between the first and the subsequent layers. Similar trends are obtained at different temperatures or when increasing the number of methanol molecules treated at the quantum chemistry level, indicating the robustness of the approach for describing the dipolar molecular responses of air-liquid interfaces.

Accuracy of One- and Two-Photon Intensities with the Extended Polarizable Density Embedding Model

The recently developed extended polarizable density embedding (PDE-X) model is evaluated for the spectroscopic properties of organic chromophores solvated in water, including both one- and two-photon absorption properties. The PDE-X embedding model systematically improves vertical excitation energies over the preceding polarizable density embedding model (PDE). PDE-X shows more modest improvements over existing embedding models for oscillator strengths and two-photon absorption cross-sections, which are more sensitive properties. We argue that the origin of these discrepancies is related to the description of polarization effects, suggesting directions for future development of the embedding model.

Polarizable Embedding Potentials through Molecular Fractionation with Conjugate Caps Including Hydrogen Bonds

Polarizable embedding (PE) refers to classical embedding approaches, such as those used in quantum mechanics/molecular mechanics (QM/MM), that allow mutual polarization between the quantum and classical regions. The quality of the embedding potential is critical to provide accurate results, e.g., for spectroscopic properties and dynamical processes. High-quality embedding-potential parameters can be obtained by dividing the classical region into smaller fragments and deriving the parameters from ab initio calculations on the fragments. For solvents and other systems composed of small molecules, the fragments can be individual molecules, while a more complicated fragmentation procedure is needed for larger molecules, such as proteins and nucleic acids. One such fragmentation strategy is the molecular fractionation with conjugate caps (MFCC) approach. As is widely known, hydrogen bonds play a key role in many biomolecular systems, e.g., in proteins, where they are responsible for the secondary structure. In this work, we assess the effects of including hydrogen-bond fragmentation in the MFCC procedure [MFCC(HB)] for deriving the embedding-potential parameters. The MFCC(HB) extension is evaluated on several molecular systems, ranging from small model systems to proteins, directly in terms of molecular electrostatic potentials and embedding potentials and indirectly in terms of selected properties of chromophores embedded in water and complex protein environments.

Polarizable Embedding without Artificial Boundary Polarization

We present a fully self-consistent polarizable embedding (PE) model that does not suffer from unphysical boundary polarization. This is achieved through the use of the minimum-image convention (MIC) in the induced electrostatics. It is a simple yet effective approach that includes a more physically accurate description of the polarization throughout the molecular system. Using PE with MIC (PE-MIC), we shed new light on the limitations of commonly employed cutoff models, such as the droplet model, when used in PE calculations. Specifically, we investigate the effects of the unphysical polarization at the outer boundary by comparing induced dipoles and the associated electrostatic potentials, as well as some optical properties of solute-solvent and biomolecular systems. We show that the magnitude of the inaccuracies caused by the unphysical polarization depends on multiple parameters: the nature of the quantum subsystem and of the environment, the cutoff model and distance, and the calculated property.

Theoretical and Numerical Comparison of Quantum- and Classical Embedding Models for Optical Spectra

Quantum-mechanical (QM) and classical embedding models approximate a supermolecular quantum-chemical calculation. This is particularly useful when the supermolecular calculation has a size that is out of reach for present QM models. Although QM and classical embedding methods share the same goal, they approach this goal from different starting points. In this study, we compare the polarizable embedding (PE) and frozen-density embedding (FDE) models. The former is a classical embedding model, whereas the latter is a density-based QM embedding model. Our comparison focuses on solvent effects on optical spectra of solutes. This is a typical scenario where super-system calculations including the solvent environment become prohibitively large. We formulate a common theoretical framework for PE and FDE models and systematically investigate how PE and FDE approximate solvent effects. Generally, differences are found to be small, except in cases where electron spill-out becomes problematic in the classical frameworks. In these cases, however, atomic pseudopotentials can reduce the electron-spill-out issue.

A method to capture the large relativistic and solvent effects on the UV-vis spectra of photo-activated metal complexes

We have recently developed a method based on relativistic time-dependent density functional theory (TD-DFT) that allows the calculation of electronic spectra in solution (Creutzberg, Hedegård, J. Chem. Theory Comput.18, 2022, 3671). This method treats the solvent explicitly with a classical, polarizable embedding (PE) description. Furthermore, it employs the complex polarization propagator (CPP) formalism which allows calculations on complexes with a dense population of electronic states (such complexes are known to be problematic for conventional TD-DFT). Here, we employ this method to investigate both the dynamic and electronic effects of the solvent for the excited electronic states of trans-trans-trans-[Pt(N₃)₂(OH)₂(NH₃)₂] in aqueous solution. This complex decomposes into species harmful to cancer cells under light irradiation. Thus, understanding its photo-physical properties may lead to a more efficient method to battle cancer. We quantify the effect of the underlying structure and dynamics by classical molecular mechanics simulations, refined with a subsequent DFT or semi-empirical optimization on a cluster. Moreover, we quantify the effect of employing different methods to set up the solvated system, e.g., how sensitive the results are to the method used for the refinement, and how large a solvent shell that is required. The electronic solvent effect is always included through a PE potential.

Assessing the quality of QM/MM approaches to describe vacuo-to-water solvatochromic shifts

The performance of different quantum mechanics/molecular mechanics embedding models to compute vacuo-to-water solvatochromic shifts is investigated. In particular, both nonpolarizable and polarizable approaches are analyzed and computed results are compared to reference experimental data. We show that none of the approaches outperform the others and that errors strongly depend on the nature of the molecular transition to be described. Thus, we prove that the best choice of embedding model highly depends on the molecular system and that the use of a specific approach as a black box can lead to significant errors and, sometimes, totally wrong predictions.

Investigation of the Second Harmonic Generation at the Water-Vacuum Interface by Using Multi-Scale Modeling Methods

The Sequential Quantum Mechanics/Molecular Mechanics scheme has been enacted to perform a systematic investigation of the polarizability (α) and first hyperpolarizability (β) responses at the water-vacuum interface. After performing classical molecular dynamics simulations to provide snapshots of the structures, quantum chemistry calculations of the linear and nonlinear optical responses have been performed for clusters of five water molecules at the time-dependent DFT level in combination with different embedding schemes, ranging from point charges to polarizable point charges, with and without local field effects. When going from the bulk to the interface, the main observations of these calculations encompass i) a modest increase of the average polarizability but an increase by about a factor of two of its anisotropy, ii) an increase by about 20 % of the β_HRS response, accompanied by a small increase of its depolarization ratio, and iii) a net increase of the component of the β tensor normal to the interface (β_zzz ) as well as of β_// . Globally, the interfacial effects on β are localized at the first molecular layer while they are observed up to the fourth molecular layer on α.

Quantum chemistry study of the multiphoton absorption in enhanced green fluorescent protein at the single amino acid residue level

The chromophore (CRO) of fluorescent proteins (FPs) is embedded in a complex environment that is a source of specific interactions with the CRO. Understanding how these interactions influence FPs spectral properties is important for a directed design of novel markers with desired characteristics. In this work, we apply computational chemistry methods to gain insight into one-, two- and three-photon absorption (1PA, 2PA, 3PA) tuning in enhanced green fluorescent protein (EGFP). To achieve this goal, we built EGFP models differing in: i) number and position of hydrogen-bonds (h-bonds) donors to the CRO and ii) the electric field, as approximated by polarizable force  field, acting on the CRO. We  find that h-bonding to the CRO's phenolate oxygen results in stronger one- and multiphoton absorption. The brighter absorption can be also achieved by creating more positive electric field near the CRO's phenolate moiety. Interestingly, while individual CRO-environment h-bonds usually enhance 1PA and 2PA, it takes a few h-bond donors to enhance 3PA. Clearly, response of the absorption intensity to many-body effects depends on the excitation mechanism.  We further employ symmetry-adapted perturbation theory (SAPT) to reveal excellent (2PA) and good (3PA) correlation of multiphoton intensity with electrostatic and induction interaction energies. This points to importance of accounting for mutual CRO-environment polarization in quantitative calculations of absorption spectra in FPs.

Polarizable Embedding Complex Polarization Propagator in Four- and Two-Component Frameworks

Explicit embedding methods combined with the complex polarization propagator (CPP) enable the modeling of spectroscopy for increasingly complex systems with a high density of states. We present the first derivation and implementation of the CPP in four- and exact-two-component (X2C) polarizable embedding (PE) frameworks. We denote the developed methods PE-4c-CPP and PE-X2C-CPP, respectively. We illustrate the methods by estimating the solvent effect on ultraviolet-visible (UV-vis) and X-ray atomic absorption (XAS) spectra of [Rh(H₂O)₆]³⁺ and [Ir(H₂O)₆]³⁺ immersed in aqueous solution. We moreover estimate solvent effects on UV-vis spectra of a platinum complex that can be photochemically activated (in water) to kill cancer cells. Our results clearly show that the inclusion of the environment is required: UV-vis and (to a lesser degree) XAS spectra can become qualitatively different from vacuum calculations. Comparison of PE-4c-CPP and PE-X2C-CPP methods shows that X2C essentially reproduces the solvent effect obtained with the 4c methods.

First Hyperpolarizability of Water in Bulk Liquid Phase: Long-Range Electrostatic Effects Included via the Second Hyperpolarizability

The molecular first hyperpolarizability β contributes to second-order optical non-linear signals collected from molecular liquids. For the Second Harmonic Generation (SHG) response, the first hyperpolarizability β (2ω,ω,ω) often depends on...

Fast Approximate but Accurate QM/MM Interactions for Polarizable Embedding

The coupling between the quantum (QM) and classical (MM) regions is often one of the computational bottlenecks when applying polarizable QM/MM to computational spectroscopy. In this Article, we explore three strategies to approximate the QM/MM coupling based on multipole expansion techniques. The implementations of these approximations are benchmarked in terms of both accuracy and computational efficiency and are furthermore applied to the calculation of spectroscopic properties including both one- and two-photon absorption strengths. We show that the proposed strategies provide significant computational savings without compromising the accuracy of the calculated spectroscopic properties.

Local-Field Effects in Linear Response Properties within a Polarizable Frozen Density Embedding Method

In this work, we present a polarizable frozen density embedding (FDE) method for calculating polarizabilities of coupled subsystems. The method (FDE-pol) combines a FDE method with an explicit polarization model such that the expensive freeze/thaw cycles can be bypassed, and approximate nonadditive kinetic potentials are avoided by enforcing external orthogonality between the subsystems. To describe the polarization of the frozen environment, we introduce a Hirshfeld partition-based density-dependent method for calculating the atomic polarizabilities of atoms in molecules, which alleviates the need to fit the atomic parameters to a specific system of interest or to a larger general set of molecules. We show that the Hirshfeld partition-based method predicts molecular polarizabilities close to the basis set limit, and thus, a single basis set-dependent scaling parameter can be introduced to improve the agreement against the reference polarizability data. To test the model, we characterized the uncoupled and coupled response of small interacting molecular complexes. Here, the coupled response properties include the perturbation of the frozen system due to the external perturbation which is ignored in the uncoupled response. We show that FDE-pol can accurately reproduce both the exact uncoupled polarizability and the coupled polarizabilities of the supermolecular systems. Using damped response theory, we also demonstrate that the coupled frequency-dependent polarizability can be described by including local field effects. The results emphasize the necessity of including local-field effects for describing the response properties of coupled subsystems, as well as the importance of accurate atomic polarizability models.

First hyperpolarizability of water at the air-vapor interface: a QM/MM study questions standard experimental approximations

Surface Second-Harmonic Generation (S-SHG) experiments provide a unique approach to probe interfaces. One important issue for S-SHG is how to interpret the S-SHG intensities at the molecular level. Established frameworks commonly assume that each molecule emits light according to an average molecular hyperpolarizability tensor β(-2ω,ω,ω). However, for water molecules, this first hyperpolarizability is known to be extremely sensitive to their environment. We have investigated the molecular first hyperpolarizability of water molecules within the liquid-vapor interface, using a quantum description with explicit, inhomogeneous electrostatic embedding. The resulting average molecular first hyperpolarizability tensor depends on the distance relative to the interface, and it practically respects the Kleinman symmetry everywhere in the liquid. Within this numerical approach, based on the dipolar approximation, the water layer contributing to the Surface Second Harmonic Generation (S-SHG) intensity is less than a nanometer. The results reported here question standard interpretations based on a single, averaged hyperpolarizability for all molecules at the interface. Not only the molecular first hyperpolarizability tensor significantly depends on the distance relative to the interface, but it is also correlated to the molecular orientation. Such hyperpolarizability fluctuations may impact the S-SHG intensity emitted by an aqueous interface.

Nitrogen K-Edge X-ray Absorption Spectra of Ammonium and Ammonia in Water Solution: Assessing the Performance of Polarizable Embedding Coupled Cluster Methods

The recent development of liquid jet and liquid leaf sample delivery systems allows for accurate measurements of soft X-ray absorption spectra in transmission mode of solutes in a liquid environment. As this type of measurement becomes increasingly accessible, there is a strong need for reliable theoretical methods for assisting in the interpretation of the experimental data. Coupled cluster methods have been extensively developed over the past decade to simulate X-ray absorption in the gas phase. Their performance for solvated species, on the contrary, remains largely unexplored. Here, we investigate the current state of the art of coupled cluster modeling of nitrogen K-edge X-ray absorption of aqueous ammonia and ammonium based on quantum mechanics/molecular mechanics, where both the level of coupled cluster calculations and polarizable embedding are scrutinized. The results are compared to existing experimental data as well as simulations based on transition potential density functional theory.

A discrete interaction model/quantum mechanical method for simulating surface-enhanced Raman spectroscopy in solution

Since surface-enhanced Raman scattering (SERS) is of considerable interest for sensing applications in aqueous solution, the role that solvent plays in the spectroscopy must be understood. However, these efforts are hindered due to a lack of simulation approaches for modeling solvent effects in SERS. In this work, we present an atomistic electrodynamics-quantum mechanical method to simulate SERS in aqueous solution based on the discrete interaction model/quantum mechanical method. This method combines an atomistic electrodynamics model of the nanoparticle with a time-dependent density functional theory description of the molecule and a polarizable embedding method for the solvent. The explicit treatment of solvent molecules and nanoparticles results in a large number of polarizable dipoles that need to be considered. To reduce the computational cost, a simple cut-off based approach has been implemented to limit the number of dipoles that need to be treated without sacrificing accuracy. As a test of this method, we have studied how solvent affects the SERS of pyridine in the junction between two nanoparticles in aqueous solution. We find that the solvent leads to an enhanced SERS due to an increased local field at the position of the pyridine. We further demonstrate the importance of both image field and local field effects in determining the enhancements and the spectral signatures. Our results show the importance of describing the local environment due to the solvent molecules when modeling SERS.

Efficient Open-Source Implementations of Linear-Scaling Polarizable Embedding: Use Octrees to Save the Trees

We present open-source implementations of the linear-scaling fast multipole method (FMM) within the polarizable embedding (PE) model for efficient treatment of large polarizable environments in computational spectroscopy simulations. The implementations are tested for accuracy, efficiency, and usability on model systems as well as more realistic biomolecular systems. We explain how FMM parameters affect the calculation of molecular properties and show that PE calculations employing FMM can be carried out in a black-box manner. The efficiency of the linear-scaling approach is demonstrated by simulating the UV/vis spectrum of a chromophore in an environment of more than 1 million polarizable sites. Our implementations are interfaced to several open-source quantum chemistry programs, making computational spectroscopy simulations within the PE model and FMM available to a large variety of methods and a broad user base.

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.

Removing artifacts in polarizable embedding calculations of one- and two-photon absorption spectra of fluorescent proteins

The multiscale calculations involving excited states may suffer from the electron spill-out (ESO) problem. This seems to be especially the case when the environment of the core region, described with the electronic structure method, is approximated by a polarizable force field. The ESO effect often leads to incorrect physical character of electronic excitations, spreading outside the quantum region, which, in turn, results in erroneous absorption spectra. In this work, we investigate means to remove the artifacts in one-photon absorption (OPA) and two-photon absorption (TPA) spectra of green and yellow fluorescent protein representatives. This includes (i) using different basis sets, (ii) extending the core subsystem beyond the chromophore, (iii) modification of polarization interaction between the core region and its environment, and (iv) including the Pauli repulsion through effective core potentials (ECPs). Our results clearly show that ESO is observed when diffuse functions are used to assemble the multielectron wave function regardless of the exchange-correlation functional used. Furthermore, extending the core region, thus accounting for exchange interactions between the chromophore and its environment, leads to even more spurious excited states. Also, damping the interactions between the core subsystem and the polarizable force field is hardly helpful. In contrast, placing ECPs in the position of sites creating the embedding potential leads to the removal of artificious excited states that presumably should not be observed in the OPA and TPA spectra. We prove that it is a reliable and cost-effective approach for systems where the covalent bond(s) between the core region and its environment must be cut.

Computational Characterization of Novel Malononitrile Variants of Laurdan with Improved Photophysical Properties for Sensing in Membranes

Fluorescent probes are powerful tools for improving our understanding of cellular membranes and other complex biological environments. Using simulations, we gain atomistic and electronic insights into the effectiveness of the probes. In the current work, we have used various computational approaches to comprehensively investigate the properties of the fluorescent probe Laurdan and two Laurdan-like probes: AADAL and ECL. In addition, we propose the development of their corresponding novel malononitrile variants, which are computationally characterized herein. For the candidate probes, electronic structure calculations were used to rationalize their optical properties, including their ability for two-photon activation, and molecular dynamics simulations were used to unravel atomistic details of their functioning within lipid bilayers. While Laurdan, AADAL, and ECL were found to have very similar optical and membrane partitioning profiles, their malononitrile variants were found to show significantly improved optical properties, especially in regard to two-photon cross sections, and they appear to retain the desired membrane characteristics of the parent Laurdan molecule.

Polarizable Density Embedding for Large Biomolecular Systems

We present an efficient and robust fragment-based quantum-classical embedding model capable of accurately capturing effects from complex environments such as proteins and nucleic acids. This is realized by combining the molecular fractionation with conjugate caps (MFCC) procedure with the polarizable density embedding (PDE) model at the level of Fock matrix construction. The PDE contributions to the Fock matrix of the core region are constructed using the local molecular basis of the individual fragments rather than the supermolecular basis of the entire system. Thereby, we avoid complications associated with the application of the MFCC procedure on environment quantities such as electronic densities and molecular-orbital energies. Moreover, the computational cost associated with solving self-consistent field (SCF) equations of the core region remains unchanged from that of purely classical polarized embedding models. We analyze the performance of the resulting model in terms of the reproduction of the electrostatic potential of an insulin monomer protein and further in the context of solving problems related to electron spill-out. Finally, we showcase the model for the calculation of one- and two-photon properties of the Nile red molecule in a protein environment. Based on our analyses, we find that the combination of the MFCC approach with the PDE model is an efficient, yet accurate approach for calculating molecular properties of molecules embedded in structured biomolecular environments.

What is the Optimal Size of the Quantum Region in Embedding Calculations of Two-Photon Absorption Spectra of Fluorescent Proteins?

We systematically investigate an impact of the size and content of a quantum (QM) region, treated at the density functional theory level, in embedding calculations on one- (OPA) and two-photon absorption (TPA) spectra of the following fluorescent proteins (FPs) models: Aequorea victoria green FP (avGFP) with neutral (avGFP-n) and anionic (avGFP-a) chromophore as well as Citrine FP. We find that amino acid (a.a.) residues as well as water molecules hydrogen-bonded (h-bonded) to the chromophore usually boost both OPA and TPA processes intensity. The presence of hydrophobic a.a. residues in the quantum region also non-negligibly affects both absorption spectra but decreases absorption intensity. We conclude that to reach a quantitative description of OPA and TPA spectra in multiscale modeling of FPs, the quantum region should consist of a chromophore and most of a.a. residues and water molecules in a radius of 0.30–0.35 nm (ca. 200–230 atoms) when the remaining part of the system is approximated by the electrostatic point-charges. The optimal size of the QM region can be reduced to 80–100 atoms by utilizing a more advanced polarizable embedding model. We also find components of the QM region that are specific to a FP under study. We propose that the F165 a.a. residue is important in tuning the TPA spectrum of avGFP-n but not other investigated FPs. In the case of Citrine, Y203 and M69 a.a. residues must definitely be part of the QM subsystem. Furthermore, we find that long-range electrostatic interactions between the QM region and the rest of the protein cannot be neglected even for the most extensive QM regions (ca. 350 atoms).

Two-Photon Absorption Cross-Sections in Fluorescent Proteins Containing Non-canonical Chromophores Using Polarizable QM/MM

Multi-photon absorption properties, particularly two-photon absorption (2PA), of fluorescent proteins (FPs) have made them attractive tools in deep-tissue clinical imaging. Although the diversity of photophysical properties for FPs is wide, there are some caveats predominant among the existing FP variants that need to be overcome, such as low quantum yields and small 2PA cross-sections. From a computational perspective, Salem et al. (2016) suggested the inclusion of non-canonical amino acids in the chromophore of the red fluorescent protein DsRed, through the replacement of the tyrosine amino acid. The 2PA properties of these new non-canonical chromophores (nCCs) were determined in vacuum, i.e., without taking into account the protein environment. However, in the computation of response properties, such as 2PA cross-sections, the environment plays an important role. To account for environment and protein-chromophore coupling effects, quantum mechanical/molecular mechanical (QM/MM) schemes can be useful. In this work, the polarizable embedding (PE) model is employed along with time-dependent density functional theory to describe the 2PA properties of a selected set of chromophores made from non-canonical amino acids as they are embedded in the DsRed protein matrix. The objective is to provide insights to determine whether or not the nCCs could be developed and, thus, generate a new class of FPs. Results from this investigation show that within the DsRed environment, the nCC 2PA cross-sections are diminished relative to their values in vacuum. However, further studies toward understanding the 2PA limit of these nCCs using different protein environments are needed.

Dalton Project: A Python platform for molecular- and electronic-structure simulations of complex systems

The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

The DIRAC code for relativistic molecular calculations

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.

Cost-Effective Potential for Accurate Polarizable Embedding Calculations in Protein Environments

The fragment-based polarizable embedding (PE) model combined with an appropriate electronic structure method constitutes a highly efficient and accurate multiscale approach for computing spectroscopic properties of a central moiety including effects from its molecular environment through an embedding potential. There is, however, a comparatively high computational overhead associated with the computation of the embedding potential, which is derived from first-principles calculations on individual fragments of the environment. To reduce the computational cost associated with the calculation of embedding potential parameters, we developed a set of amino acid-specific transferable parameters tailored for large-scale PE-based calculations that include proteins. The amino acid-based parameters are obtained by simultaneously fitting to a set of reference electric potentials based on structures derived from a backbone-dependent rotamer library. The developed cost-effective polarizable protein potential (CP³) consists of atom-centered charges and isotropic dipole-dipole polarizabilities of the standard amino acids. In terms of reproduction of electric potentials, the CP³ is shown to perform consistently and with acceptable accuracy across both small tripeptide test systems and larger proteins. We show, through applications on realistic protein systems, that acceptable accuracy can be obtained by using a pure CP³ representation of the protein environment, thus altogether omitting the cost associated with the calculation of embedding potential parameters. High accuracy comparable to that of the full fragment-based approach can be achieved through a mixed description where the CP³ is used only to describe amino acids beyond a threshold distance from the central quantum part.

Characterization of β-turns by electronic circular dichroism spectroscopy: a coupled molecular dynamics and time-dependent density functional theory computational study

Electronic circular dichroism is one of the most used spectroscopic techniques for peptide and protein structural characterization. However, while valuable experimental spectra exist for α-helix, β-sheet and random coil secondary structures, previous studies showed important discrepancies for β-turns, limiting their use as a reference for structural studies. In this paper, we simulated circular dichroism spectra for the best-characterized β-turns in peptides, namely types I, II, I' and II'. In particular, by combining classical molecular dynamics simulations and state-of-the-art quantum time-dependent density functional theory (with the polarizable embedding multiscale model) computations, two common electronic circular dichroism patterns were found for couples of β-turn types (namely, type I/type II' and type II/type I'), at first for a minimal di-peptide model (Ace-Ala-Ala-NHMe), but also for all sequences tested with non-aromatic residues in the central positions. On the other hand, as expected, aromatic substitution causes important perturbations to the previously found ECD patterns. Finally, by applying suitable approximations, these patterns were subsequently rationalized based on the exciton chirality rule. All these results provide useful predictions and pave the way for a possible experimental characterization of β-turns based on circular dichroism spectroscopy.

The key to the yellow-to-cyan tuning in the green fluorescent protein family is polarisation

Computational approaches have to date failed to fully capture the large (about 0.4 eV) excitation energy tuning displayed by the nearly identical anionic chromophore in different green fluorescent protein (GFP) variants. Here, we present a thorough comparative study of a set of proteins in this sub-family, including the most red- (phiYFP) and blue-shifted (mTFP0.7) ones. We employ a classical polarisable embedding through induced dipoles and combine it with time-dependent density functional theory and multireference perturbation theory in order to capture both state-specific induction contributions and the coupling of the polarisation of the protein to the chromophore transition density. The obtained results show that only upon inclusion of both these two effects generated by the mutual polarisation between the chromophore and the protein can the full spectral tuning be replicated. We finally discuss how this mutual polarisation affects the correlation between excitation energies, dipole moment variation, and molecular electrostatic field.

Rational design of novel fluorescent analogues of cholesterol: a “step-by-step” computational study

State-of-the-art quantum chemical and molecular dynamics simulations are used as guidelines in design of novel fluorescent analogues of cholesterol.

A quantum-mechanical perspective on linear response theory within polarizable embedding

We present a derivation of linear response theory within polarizable embedding starting from a rigorous quantum-mechanical treatment of a composite system. To this aim, two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are introduced and the pole structures as well as residues of the individual terms are discussed. In addition to providing a thorough justification for the descriptions used in polarizable embedding models, this theoretical analysis clarifies which form of the response function to use and highlights complications in separating out subsystem contributions to molecular properties. The basic features of the presented expressions and various approximate forms are illustrated by their application to a composite model system.

TD-DFT calculations of one- and two-photon absorption in Coumarin C153 and Prodan: attuning theory to experiment

We use TD-DFT to calculate the one-photon absorption (1PA) and two-photon absorption (2PA) properties of C153 and Prodan in toluene and DMSO, and benchmark different methods relative to accurate experimental data available from the literature on these particular systems. As the first step, we modify the range-separated TD-DFT to provide the best prediction for the peak 1PA wavelength, and then apply the optimized functionals to achieve quantitative predictions of the corresponding two-photon absorption cross section, σ_2PA, with an accuracy ∼10-20% in C153 and ∼20-30% in Prodan. To elucidate the origin of residual discrepancies between the theory and experimental observations, we invoked the two essential states model for σ_2PA, which allows us to verify not only the transition wavelength and the σ_2PA value, but also to quantitatively benchmark the calculation of key molecular parameters such as the transition dipole moment and the change of the permanent dipole moment. Such comprehensive cross-checking indicates that a larger discrepancy in Prodan is most likely caused by a noted failure of DFT to predict the relative intensity and relative ordering of closely lying excited states with different degrees of intramolecular charge transfer, which we further support by analyzing the predictions obtained by high-level coupled-cluster calculations in the gas phase. Our results highlight the utility of benchmarking the calculations not only relative to other theoretical methods, but also in comparison to the experimental measurements, wherever such data are available.

Polarizable Density Embedding: A Solution to the Electron Spill-Out Problem in Multiscale Modeling

We analyze the performance of the polarizable density embedding (PDE) model-a new multiscale computational approach designed for prediction and rationalization of general molecular properties of large and complex systems. We showcase how the PDE model very effectively handles the use of large and diffuse basis sets that are otherwise questionable-due to electron spill-out effects-in standard embedding models. Based on our analysis, we find the PDE model to be robust and much more systematic than less sophisticated focused embedding models, and thus outline the PDE model as a very efficient and accurate approach to describe the electronic structure of ground and excited states as well as molecular properties of complex, heterogeneous systems.

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.

Prediction of two-photon absorption enhancement in red fluorescent protein chromophores made from non-canonical amino acids

Two-photon spectroscopy of fluorescent proteins is a powerful bio-imaging tool known for deep tissue penetration and little cellular damage. Being less sensitive than the one-photon microscopy alternatives, a protein with a large two-photon absorption (TPA) cross-section is needed. Here, we use time-dependent density functional theory (TD-DFT) at the B3LYP and CAM-B3LYP/6-31+G(d,p) levels of theory to screen twenty-two possible chromophores that can be formed upon replacing the amino-acid Tyr66 that forms the red fluorescent protein (RFP) chromophore with a non-canonical amino acid. The two-level model for TPA was used to assess the properties (i.e., transition dipole moment, permanent dipole moment difference, and the angle between them) leading to the TPA cross-sections determined via response theory. Computing TPA cross-sections with B3LYP and CAM-B3LYP yields similar overall trends. Results using both functionals agree that the RFP-derived model of the Gold Fluorescent Protein chromophore (Model 20) has the largest intrinsic TPA cross-section at the optimized geometry. TPA was further computed for selected chromophores following conformational changes: variation of both the dihedral angle of the acylimine moiety and the tilt and twist angles between the rings of the chromophore. The TPA cross-section assumed an oscillatory trend with the rotation of the acylimine dihedral, and the TPA is maximized in the planar conformation for almost all models. Model 21 (a hydroxyquinoline derivative) is shown to be comparable to Model 20 in terms of TPA cross-section. The conformational study on Model 21 shows that the acylimine angle has a much stronger effect on the TPA than its tilt and twist angles. Having an intrinsic TPA ability that is more than 7 times that of the native RFP chromophore, Models 20 and 21 appear to be very promising for future experimental investigation.

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 that includes effects from the molecular environment modeled by the polarizable embedding model.

Excited states in large molecular systems through polarizable embedding

Using the polarizable embedding model enables rational design of light-sensitive functional biological materials.