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We extend the polarizable density embedding (PDE) model to support the calculation of nuclear magnetic resonance (NMR) shielding constants using gauge-including atomic orbitals (GIAOs) within a density functional theory (DFT) framework. The PDE model divides the total system into fragments, describing some by quantum mechanics (QM) and the others through an embedding model. The PDE model uses anisotropic polarizabilities, inter-fragment two-electron Coulomb integrals, and a non-local repulsion operator to emulate the QM effects. The terms involving Coulomb integrals are straightforwardly extended with GIAOs. In contrast, we consider two approaches to handle the gauge dependency of the non-local operator, employing either simple symmetrization or a gauge transformation. We find the latter approach to be most stable with respect to increasing the basis set size of the QM region. We examine the accuracy of the PDE model for calculating NMR shielding constants on several solutes in a water solution. The performance is compared with the classical polarizable embedding (PE) model in addition to supermolecular reference calculations. Based on these systems, we address the basis set convergence characteristics and the QM region size requirements. Furthermore, we investigate the performance of the PDE model for a system with significant electron spill-out. In many cases, we find that the PDE model outperforms the PE model, especially regarding the accuracy of nuclear shielding constants when using small QM region sizes and in systems with significant electron spill-out.

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.

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.

We present a variant of the algebraic diagrammatic construction (ADC) scheme by combining ADC with the polarizable embedding (PE) model. The presented PE-ADC method is implemented through second and third order and is designed with the aim of performing accurate calculations of excited states in large molecular systems. Accuracy and large-scale applicability are demonstrated with three case studies, and we further analyze the importance of both state-specific and linear-response-type corrections to the excitation energies in the presence of the polarizable environment. We demonstrate how our combined method can be readily applied to study photoinduced biochemical processes as we model the charge-transfer (CT) excitation which is key to the photoprotection mechanism in the dodecin protein with PE-ADC(2). Through direct access to state-of-the-art excited state analysis, we find that the polarizable environment plays a decisive role by significantly increasing the CT character of the electronic excitation in dodecin. PE-ADC is thus suited to decipher photoinduced processes in complex, biomolecular systems at high precision and at reasonable computational cost.

Quantum chemistry embedding methods have become a popular approach to calculate molecular properties of larger systems. In order to account for finite temperature effects, including both configurational and conformational averaging, embedding methods are often combined with molecular dynamics (MD) simulations either in a direct or sequential manner. One of the decisive factors for a successful application of embedding methods is that that the underlying structures provided by the MD simulation are accurate, if not this will result in low-quality prediction of the molecular properties in question. Here we investigate different approaches for generating a set of molecular structures to be used in subsequent embedding calculations ranging from classical MD using a standard molecular mechanics (MM) force field to combined quantum mechanics/molecular mechanics (QM/MM) MD. Overall, we find an intermediate approach relying on classical MD followed by a constrained QM/MM geometry optimization to be a fairly accurate and very cost-effective approach, although this procedure naturally leads to underestimation of, for example, spectral bandwidths.

We present the theory and implementation of the polarizable density embedding (PDE) model in combination with coupled cluster (CC) theory (PDE-CC). This model has been implemented in the Dalton quantum chemistry program by adapting the CC code to the polarizable embedding library (PElib). In the PDE-CC method, the smaller, but chemically important core region is described with a high-level CC method. The environment surrounding the core region can be separated into two levels of description: an inner and an outer region. The effect of the inner region on the core region is described by an embedding potential consisting of a set of fragment densities obtained from calculations on isolated fragments with a quantum-chemistry method such as Hartree-Fock (HF) or Kohn-Sham density functional theory (KS-DFT) and dressed with a set of atom-centered anisotropic dipole-dipole polarizabilities. The outer region consists of distributed atom-centered multipoles and polarizabilities, i.e., in the same way as in the polarizable embedding (PE) model. The PDE-CC method contains embedding potential operators that account for the electrostatic and polarization interactions between the core region and the environment, as well as for nonelectrostatic (also known as Pauli and exchange) repulsion. All environmental effects are included through one-electron operators and account very efficiently for the response of the environment due to the change in the electron density of the core region, e.g., upon an electronic transition.

Most chemistry, including chemistry where relativistic effects are important, occurs in an environment, and in many cases, this environment has a significant effect on the chemistry. In nonrelativistic quantum chemistry, a lot of progress has been achieved with respect to including environments such as a solvent or protein in the calculations, and now is the time to extend the possibilities for also doing this in relativistic quantum chemistry. The polarizable embedding (PE) model efficiently incorporates electrostatic effects of the environment by describing it as a collection of localized electric multipoles and polarizabilities obtained through quantum chemical calculations. In this article, we present the theory and implementation of four-and exact two-component Hamiltonians within a PE framework. We denote the methods the PE-4c-DFT and PE-X2C-DFT models. The models include a linear response formalism to calculate time-dependent (TD) properties: PE-TD-4c-DFT and PE-TD-X2C-DFT. With this first implementation, we calculate the PE-TD-4c-PBE0 excitation energies of the TcO4 - and ReO4 - ions in an explicit water solvent. This initial investigation focuses on the relative size of relativistic and solvent contributions to the excitation energies. The solvent effect is divided into an indirect solvent effect due to the structural perturbation of the XO4 - ion and a direct electrostatic effect. The relativistic effects as well as both types of solvent effects are found to contribute to a shift in the excitation energies, but they do so to different extents depending on the ion and the electronic transition in question.

In this paper we present a study of the methodological aspects regarding calculations of optical properties for DNA systems in solution. Our computational approach will be built upon a fully polarizable QM/MM/Continuum model within a damped linear response theory framework. In this approach the environment is given a highly advanced description in terms of the electrostatic potential through the polarizable embedding model. Furthermore, bulk solvent effects are included in an efficient manner through a conductor-like screening model. With the aim of reducing the computational cost we develop a set of averaged partial charges and distributed isotropic dipole-dipole polarizabilities for DNA suitable for describing the classical region in ground-state and excited-state calculations. Calculations of the UV-spectrum of the 2-aminopurine optical probe embedded in a DNA double helical structure are presented. We show that inclusion of polarizabilities in the embedding potential stemming from the DNA double helix is of crucial importance, while the water cluster surrounding the DNA system is well represented using a continuum approach.

In recent years computational methods based on embedding have become of increasing popularity when the aim is to introduce environmental effects into quantum chemistry calculations of molecular properties. This is due in particular to the efficiency of such methods while still retaining a high degree of accuracy compared to full quantum chemistry treatments. In the present paper we compare two popular embedding methods - fluctuating charges (FQ) and polarizable embedding (PE) - highlighting their similar mathematical structure. Furthermore, based on a unified formulation of the two embedding methods, we present theory and implementation of these embedding methods within resonant-convergent response theory up to the level of quadratic response. A numerical comparison between FQ and PE is presented for a set of solute-solvent systems based on calculations of UV/vis and magnetic circular dichroism spectra. Overall, we find in the cases considered the FQ and PE models to perform rather similarly, especially upon introducing effects of explicit conformational sampling into the theoretical predictions.

Quantum-mechanical embedding methods have in recent years gained significant interest and may now be applied to predict a wide range of molecular properties calculated at different levels of theory. To reach a high level of accuracy in embedding methods, both the electronic structure model of the active region and the embedding potential need to be of sufficiently high quality. In fact, failures in quantum mechanics/molecular mechanics (QM/MM)-based embedding methods have often been associated with the QM/MM methodology itself; however, in many cases the reason for such failures is due to the use of an inaccurate embedding potential. In this paper, we investigate in detail the quality of the electronic component of embedding potentials designed for calculations on protein biostructures. We show that very accurate explicitly polarizable embedding potentials may be efficiently designed using fragmentation strategies combined with single-fragment ab initio calculations. In fact, due to the self-interaction error in Kohn-Sham density functional theory (KS-DFT), use of large full-structure quantum-mechanical calculations based on conventional (hybrid) functionals leads to less accurate embedding potentials than fragment-based approaches. We also find that standard protein force fields yield poor embedding potentials, and it is therefore not advisable to use such force fields in general QM/MM-type calculations of molecular properties other than energies and structures.

The calculation of spectral properties for photoactive proteins is challenging because of the large cost of electronic structure calculations on large systems. Mixed quantum mechanical (QM) and molecular mechanical (MM) methods are typically employed to make such calculations computationally tractable. This study addresses the connection between the minimal QM region size and the method used to model the MM region in the calculation of absorption properties-here exemplified for calculations on the green fluorescent protein. We find that polarizable embedding is necessary for a qualitatively correct description of the MM region, and that this enables the use of much smaller QM regions compared to fixed charge electrostatic embedding. Furthermore, absorption intensities converge very slowly with system size and inclusion of effective external field effects in the MM region through polarizabilities is therefore very important. Thus, this embedding scheme enables accurate prediction of intensities for systems that are too large to be treated fully quantum mechanically.

We present a combination of the polarizable embedding (PE) scheme with the complex polarization propagator (CPP) method with the aim of calculating response properties including relaxation for large and complex systems. This new approach, termed PE-CPP, will benefit from the highly advanced description of the environmental electrostatic potential and polarization in the PE method as well as the treatment of near-resonant effects in the CPP approach. The PE-CPP model has been implemented in a Kohn-Sham density functional theory approach, and we present pilot calculations exemplifying the implementation for the UV/vis and carbon K-edge X-ray absorption spectra of the protein plastocyanin. Furthermore, technical details associated with a PE-CPP calculation are discussed.

Imaging of metal ion concentration, distribution, and dynamics can pave the way to diagnose a number of diseases and to identify the normal functioning of the human body. Recently, two-photon microscopy-based imaging of metal ions has become popular due to several favorable factors as compared to fluorescence-based imaging. However, much has to be investigated in order to design probes with large two-photon absorption cross sections and yet with selective binding affinity toward metal ions. In particular, it is crucial to recognize the mechanisms of metal ion-induced changes of the two-photon absorption intensity. The present paper contributes to this effort and reports on the results of extensive studies carried out to define a reliable computational protocol that can account for sampling, solvent, and finite temperature effects for one- and two-photon properties of metal probes, using azacrown ether substituted distyrylbenzene embedded in solvents as a testbed. We employ a selection of theoretical approaches to model the structure of the probe alone and in the presence of Mg 2+ ion in acetonitrile solvent, including static quantum-chemical calculations, rigid- and flexible-body molecular dynamics, and hybrid QM/MM molecular dynamics. For a set of solute-solvent configurations, the one- and the two-photon properties are computed using the recently developed polarizable embedding response approach. It is found that the hybrid QM/MM molecular dynamics based approach is the most successful one among other employed computational strategies, viz. reproduction of the metal ion-induced blue shift in the absorption wavelength and decrease in the two-photon absorption cross section, which actually is in excellent agreement with experimental data. The mechanism for such metal ion-induced changes in the optical properties is put forward using a few-state model. Possible design principles to tune the two-photon absorption properties of probes are also discussed.

Published version available in J. Chem. Theory Comput., 2016, 12 (4), pp 1684–1695. 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 de- velopment of general embedding parameters for biomolecules, where the reduction in computational cost can be considerable.

Electron paramagnetic resonance (EPR) imaging techniques provide a promising approach to detect amyloid structures which are of paramount importance in early-stage diagnosis of conformational diseases. Here, we report a combined molecular dynamics and density functional theory/molecular mechanics computational scheme for evaluation of the binding mechanism between a multifunctional spin label and the target amyloid protein. In addition, we consider evaluation of EPR spin Hamiltonian parameters with the aim of providing a better microscopic understanding and interpretation of EPR spectroscopy. The results from molecular dynamics simulations suggest that the oligothiophene conjugate part of the spin label interacts with hydrophobic residues of the amyloid protein through hydrophobic attraction and that both the N-O bond length and the N-O out-of-plane tilt angle in the nitroxide group are slightly diminished after complexation with the protein. The translational and rotational motions of the protein-bound spin label are considerably slowed compared to those of the free spin label in aqueous solution, but interestingly, hydrogen bonds formed between the nitroxide oxygen group and the surrounding water molecules are hardly affected by the presence of the amyloid protein. First-principles calculations suggest that EPR spin Hamiltonian parameters including the nitroxide nitrogen hyperfine coupling tensor A(N) and electronic g tensor suffer noticeable changes upon complexation with the protein. The magnitude of the A(N) tensor is found to be closely related to the nitroxide N-O out-of-plane tilt angle, while the g tensor is affected by both the nitroxide N-O bond length as well as the interaction between the spin label and the amyloid protein. With this work we show that state-of-the-art simulation techniques represent a promising way of providing a detailed understanding of the microscopic mechanisms responsible for the formation and stability of a spin label complexed with amyloid structures as well as the magnetic properties of the free and protein-bound spin label.

We present a combination of the polarizable embedding (PE) method with the resolution-of-the-identity implementation of the approximate coupled-cluster singles and doubles method CC2. The new approach, termed PERI-CC2, allows one to study excited state phenomena of large solvated molecular systems with an accurate correlated wave function method. Central to the PE approach is the advanced description of the environmental electrostatic potential and inclusion of polarization, and the quintessence of RI-CC2 is efficient access to excited state properties while retaining the accuracy associated with CC theory. To maintain efficiency, an approximate truncated CC2 density is introduced to calculate the PE contributions. Explicitly, we derive the central equations and outline an implementation of polarizable embedding for the RI-CC2 approach. The new method is tested against previous PE-CC2 and PE-CCSD results for solvatochromic shifts, demonstrating how the important effects of polarization are incorporated well with PERI-CC2 but with a dramatically reduced overall computational cost. A follow-up investigation of the solvatochromic shift of uracil in aqueous solution further illustrates the potential of PERI-CC2. We discuss the need to explicitly incorporate several water molecules into the region treated by quantum mechanics in order to obtain a reliable and accurate description of the physical effects when specific solute/solvent interactions as, e.g., hydrogen-bonds are involved.

We present the first systematic investigation of shifts in the nuclear magnetic resonance (NMR) shielding constant due to hydrogen bonding using either the series of wave function based methods, Hartree-Fock (HF), second-order Moller-Plesset perturbation theory (MP2), Coupled Cluster Singles and Doubles (CCSD) and CCSD extended with an approximate description of triples (CCSD(T)), or Density Functional Theory (DFT) employing either the B3LYP, PBE0, or KT3 exchange correlation (xc) functionals. The molecular systems considered are (i) the water dimer and (ii) formaldehyde in complex with two water molecules. Specially for the (17)O in formaldehyde we observe significant differences between the DFT and CCSD(T) predictions. However, the extent of these deviations depends crucially on the applied xc functional. Compared to CCSD(T) we find the KT3 functional to provide accurate results, whereas both B3LYP and PBE0 are in significant error. Potential consequences of this observation are discussed in the context of general predictions of NMR shielding constants in condensed phase.

We have developed a method to dock a transition-state structure into the active site of an enzyme. Such an approach is more discriminative than standard docking when looking for substrates of an enzyme, because a transition state has more sterical restrictions than a nonreactive state. We use an accurate and tailored force field for the transition-state for the hydroxylation reaction in cytochrome P450, obtained with the Q2MM method. We apply this method to the docking of two drugs, progesterone and flunitrazepam, to the active sites of two human cytochromes P450, 2C9 and 3A4. We obtain a qualitative agreement compared to experiments, both for hydrogen atoms bound to the same carbon atom (for which the force-field energies are directly comparable) and for general sites on the drug molecules, if the method is combined with an estimate of the intrinsic reactivity of the various sites. However, the method does not rank all the sites correctly. It is not significantly improved if the proteins are allowed to relax locally or if it is combined with the MM/PBSA approach, which fully accounts for the protein flexibility and explicitly treats solvation and entropy effects. On the other hand our method performs. better than standard docking with the GOLD software or predictions of metabolic sites with the MetaSite software.

Uracil is a commonly occurring pyrimidine derivative found in RNA where it base pairs with adenine. Rationalizing the electronic properties of uracil in both gas phase and aqueous solution is of fundamental importance because of the significant biological role played by this molecule. This paper presents accurate predictions of the solvatochromic shifts of the lowest π → π* and n → π* vertical electronic excitation energies in uracil due to an aqueous solution. The calculations are conducted using a recently developed combined quantum mechanics/molecular mechanics (QM/MM) method, and nuclear dynamical effects are accounted for through molecular dynamics simulations. The electronic structure is described using either density functional theory employing the CAM-B3LYP exchange-correlation functional or the coupled cluster singles and approximate doubles (CC2) method. The predicted solvatochromic shifts using CAM-B3LYP/MM and CC2/MM are -0.12 ± 0.01 eV and -0.20 ± 0.01 eV, respectively, for the π → π* transition and 0.42 ± 0.03 eV and 0.43 ± 0.03 eV, respectively, for the n → π* transition. Our best estimate of the solvatochromic shifts are derived using a self-consistent polarizable model in both the MD and QM/MM simulations and are -0.29 ± 0.01 eV and 0.45 ± 0.03 eV for the π → π* and n → π* transitions, respectively. The estimate is based on CC2 with electrostatic corrections defined from CAM-B3LYP and dispersion corrections derived from CC2 model system calculations. These solvatochromic shifts are in excellent agreement with experimental data, indicating the importance of explicit inclusion of polarization effects in MD-based QM/MM methods.

Even for pure substances, the deduction of the absolute configuration is not always straightforward since there is no direct link between the magnitude and sign of the optical rotation and the absolute configuration. It would be very useful to use computations of the optical rotation to link experimentally measured optical rotations to an absolute configuration. Such electronic structure calculations of the optical rotation typically employ regular energy optimized basis sets from wave function theory, and especially the aug-cc-pVDZ basis set has been popular. Here, we have carried out extrapolation of the optical rotation to the basis set limits for nine small or medium sized molecules, using basis sets developed specifically for DFT and magnetic properties (aug-pcS-n series). We suggest that assignment of absolute configuration by comparisons between theoretical and experimental optical rotations may be improved by employing different wavelengths, and accordingly the optical rotation at two wavelengths (589.3 and 355.0 nm) has been investigated. Several fitting schemes were used to estimate the optical rotations at the basis set limit. It was found that use of the aug-cc-pVDZ basis set often leads to results that deviate significantly form the basis set limit results, especially at 355.0 nm but also at 589.3 nm. The double-ζ aug-pcS-1 basis set usually provides results which are closer to the limiting values. The basis set requirements are generally more severe at 355.0 nm, where also the aug-cc-pVTZ and 6-311++G(3fd,3dp) basis sets show significant deviations from the basis set limit results, while the aug-pcS-2 basis set always leads to results within an acceptable deviation.

A density functional restricted-unrestricted approach, capable of evaluating hyperfine coupling constants with the inclusion of spin polarization effects in a spin-restricted Kohn-Sham method, has been extended to incorporate environmental effects. This is accomplished by means of a hybrid quantum mechanics/molecular mechanics formalism which allows for a granular representation of the polarization and electrostatic interactions with the classically described medium. By this technique, it is possible to trace the physical origin of hyperfine coupling constants in terms of spin polarization and spin density contributions and disentangle the dependence of these contributions on molecular geometry and solvent environment, something that increases the prospects for optimal design of spin labels for particular applications. A demonstration is given for the nitrogen isotropic hyperfine coupling constant in di-tert-butyl nitroxide solvated in water. The results indicate that the direct spin density contribution is about 5 times smaller than the spin polarization contribution to the nitrogen isotropic hyperfine coupling constant and that the latter contribution is solely responsible for the solvent shift of the constant. The developed approach is found capable of achieving satisfactory accuracy in prediction of the hyperfine coupling constants of solvated di-tert-butyl nitroxide and other similar nitroxides without the inclusion of solvent molecules in the quantum region provided polarizable force fields are used for the description of these molecules.

Encapsulation of a nitroxide spin label into a host cavity can prolong the lifetime of the spin label in biological tissues and other environments. Although such paramagnetic supramolecular complexes have been extensively studied experimentally, there is yet little understanding of the role of the encapsulation on the magnetic properties of the spin labels and their performance at the atomistic level. In this work, we approach this problem by modeling encapsulation induced changes of the magnetic properties of spin labels for a prototypical paramagnetic guest-host complex, 2,2,6,6-tetramethyl-4-methoxypiperidine-1-oxyl, enclosed in the hydrophobic cavity of cucurbit[8]uril, using state-of-the-art hybrid quantum mechanics/molecular mechanics methodology. The results allow a decomposition of the encapsulation shift of the electronic g-tensor and the nitrogen isotropic hyperfine coupling constant of nitroxide radical into a set of distinct contributions associated with the host cavity confinement and with changes of the local solvent environment of the spin label upon encapsulation. It is found that the hydrophobic cavity of cucurbit[8]uril only weakly influences the electronic g-tensor of the 2,2,6,6-tetramethyl-4-methoxypiperidine-1-oxyl but induces a significant encapsulation shift of the nitrogen hyperfine coupling constant. The latter is caused by the change of topology of the hydrogen bonding network and the nature of the hydrogen bonds around the spin label induced by the hydrophobic cavity of the inclusion host. This indirect effect is found to be more important than the direct influence of the cavity exerted on the radical. The ramification of this finding for the use of approximate methods for computing electron paramagnetic resonance spectra of spin labels and for designing optimal spin labels based on guest-host templates is discussed.

Presently, there is a great demand for small probe molecules that can be used for two-photon excitation microscopy (TPM)-based monitoring of intracellular and intraorganelle activity and pH. The candidate molecules should ideally possess a large two-photon absorption cross section with optical properties sensitive to pH changes. In the present work, we investigate the potential of a methoxy napthalene (MONAP) derivative for its suitability to serve as a pH sensor using TPM. Using an integrated approach rooted in hybrid quantum mechanics/molecular mechanics, the structures, dynamics, and the one- and two-photon properties of the probe in dimethylformamide solvent are studied. It is found that the protonated form is responsible for the optical property of MONAP at moderately low pH, for which the calculated pH-induced red shift is in good agreement with experiments. A 2-fold increase in the two-photon absorption cross section in the IR region of the spectrum is predicted for the moderately low pH form of the probe, suggesting that this can be a potential probe for pH monitoring of living cells. We also propose some design principles aimed at obtaining control of the absorption spectral range of the probe by structural tuning. Our work indicates that the integrated approach employed is capable of capturing the pH-induced changes in structure and optical properties of organic molecular probes and that such in silico tools can be used to draw structure-property relationships to design novel molecular probes suitable for a specific application.

This paper focuses on the calculation of the (isotropic) hyperfine coupling tensor, AisoK, which consists of the Fermi contact term (AFCK) and a spin orbit correction, the pseudocontact term (APCK). Using the aug-cc-pVTZ-J basis set, we test a range of correlation exchange functionals against experimental values for a series of first row transition metal complexes. This has been done both with (AisoK = AFCK + APCK) and without (AisoK = AFCK) spin orbit coupling included. Overall, hybrid functionals perform best, although some exceptions are found. Furthermore, we analyze molecular orbital contributions to the Fermi contact term. We find a great difference in the relative magnitude of contributions from frontier orbitals and inner or outer-core orbitals. Complexes, where the frontier orbital contribution exceeds the core-orbital contributions, are always small, ionic complexes (“class 1”). For these complexes, the computational requirements with respect to the one-electron basis set are not severe, and reg...

We present an evaluation of the performance of various single-reference QM methods for the prediction of the relative site energies and transition moments of the Q bands in the bacteriochlorophyll a (BChl a) pigments of the Fenna-Matthew-Olson (FMO) complex. We examine the relative merits of ZINDO, CIS, TD-DFT (with the functionals PBE, BLYP, PBE0, B3LYP, and CAM-B3LYP) and RI-CC2 in reproducing the variations across the pigments that occur as a consequence of geometrical and electrostatic effects of the FMO complex by comparison to DFT-BHLYP/MRCI. We find that these pigments are near-multiconfigurational in nature and, thus, constitute critical cases for the RI-CC2 method. The commonly used ZINDO method is fairly reliable for the site energies of the isolated pigments; however, it overestimates the coupling to the environment, thereby leading to variations across the embedded pigments that are too drastic. The overall best performance is provided by the investigated TD-DFT methods, where PBE0 is found to be slightly superior to the other functionals tested.