Time-dependent Density Functional Theory Level Research Articles

Ultrafast Photoinduced Dynamics in 1,3-Cyclohexadiene: A Comparison of Trajectory Surface Hopping Schemes†.

Photoinduced nonadiabatic processes play a crucial role in a wide range of disciplines, from fundamental steps in biology to modern applications in advanced materials science. A theoretical understanding of these processes is highly desirable, and trajectory surface hopping (TSH) has proven to be a well-suited framework for a wide range of systems. In this work, we present a comprehensive comparison between two TSH algorithms, the conventional Tully's fewest switches surface hopping (FSSH) scheme and the Landau-Zener surface hopping (LZSH), to study the photoinduced ring-opening of 1,3-cyclohexadiene (CHD) to 1,3,5-hexatriene at the spin-flip time-dependent density functional theory (SF-TDDFT) level of theory. Additionally, we compare our results with a literature study at the extended multistate complete active space second-order perturbation theory method (XMS-CASPT2) level of theory. Our results show that the average population and lifetimes estimated with LZSH using SF-TDDFT are closer to the literature (using multireference methods) than those estimated with FSSH using SF-TDDFT. The latter speaks in favor of applying LZSH in combination with the SF-TDDFT method to study larger and more complex systems such as molecular photoswitches where the CHD molecule acts as a backbone. In addition, we present an implementation of Tully's FSSH algorithm as an extension to the PySurf software package.

Ultrafast Excited-State Nonadiabatic Dynamics in Pt(II) Donor-Bridge-Acceptor Assemblies: A Quantum Approach for Optical Control.

The ultrafast nonadiabatic excited state dynamics of (PTZ-N-benzyl-acetylide) (trans-bis-trimethylphosphine) Pt(II) (acetylide-NDI-bis-methyl) 1, representative of a series of Pt(II) donor-bridge-acceptor assemblies experimentally studied by the Weinstein group, University of Sheffield, is investigated by means of wavepacket propagations based on the multiconfiguration time-dependent Hartree (MCTDH) method. On the basis of electronic structure data obtained at the time-dependent density functional theory (TD-DFT) level, the subpicosecond decay is simulated by solving an 11 electronic states multimode problem, up to 18 vibrational normal modes, including both spin-orbit coupling (SOC) and vibronic coupling. A careful analysis of the results, within the diabatic representation, provides the key features of the spin-vibronic mechanism at work in this complex, distinguishing between the spin-orbit and vibronically activated ultrafast processes within the excited states manifold. The knowledge of the key active normal modes that promote selectively the population of specific electronic excited states opens a route toward optical control by selectively exciting these modes in order to drive the associated nonadiabatic processes. Relevant simulations, over 2 ps, are proposed to assess the impact of these selective vibrational excitations on the branching ratio between the primary photoproducts, namely, bridge-acceptor charge-transfer (CT) and donor-acceptor charge-separated (CS) electronic states. Whereas the excitation of the localized acetylide bridge C≡C bond stretching does not modify drastically the population of the low-lying electronic states within the first two ps, vibrational excitation of the out-of-plane twisting motion of the N-benzyl group linked to the donor entity favors the population of the 1,3CS states at the expense of the lowest 1,3CT states. This quantum study opens the route to IR optical control experiments based on the specific alteration of vibrational normal modes that activate vibronic couplings between key electronic excited states. However, the presence of critical crossings along the PES channels associated with these normal modes and the role of concurrent SOC driven ultrafast transfers of population should not be underestimated.

Reconciling TD-DFT and CASPT2 electronic structure methods for describing the photophysics of DNA.

Time-dependent density functional theory (TD-DFT) and multiconfigurational second-order perturbation theory (CASPT2) are two of the most widely used methods to investigate photoinduced dynamics in DNA-based systems. These methods sometimes give diverse dynamics in physiological environments usually modeled by quantum mechanics/molecular mechanics (QM/MM) protocol. In this work, we demonstrate for the uridine test case that the underlying topology of the potential energy surfaces of electronic states involved in photoinduced relaxation is similar in both electronic structure methods. This is verified by analyzing surface-hopping dynamics performed at the QM/MM level on aqueous solvated uridine at TD-DFT and CASPT2 levels. By constraining the dynamics to remain on state we observe similar fluctuations in energy and relaxation lifetimes in surface-hopping dynamics in both TD-DFT and experimentally validated CASPT2 methods. This finding calls for a systematic comparison of the ES potential energy surfaces of DNA and RNA nucleosides at the single- and multi-reference levels of theory. The anomalous long excited state lifetime at the TD-DFT level is explained by trapping due to the tendency of TD-DFT in QM/MM schemes with electrostatic embedding to underestimate the energy of the state leading to a wrong energetic order. A study of the FC energetics suggests that improving the description of the surrounding environment through polarizable embedding or by the expansion of QM layer with hydrogen-bonded waters helps restore the correct state order at TD-DFT level. Thus by combining TDDFT with an accurate modeling of the environment, TD-DFT is positioned as the standout protocol to model photoinduced dynamics in DNA-based aggregates and multimers.

Intramolecular rate-constant calculations based on the correlation function using temperature dependent quantum Green's functions.

A theoretical method for calculating rate constants for internal conversion (IC), intersystem crossing (ISC) and radiative (R) electronic transitions is presented. The employed method uses temperature-dependent quantum Green's functions, which give the opportunity to consider almost any nth-order polynomial perturbation operator and the influence of external electromagnetic fields on the rate constants. The rate constants of the IC, ISC and R processes are calculated for two important indocyanine molecules namely indocyanine green (ICG) and heptamethine cyanine (IR808) at the Franck-Condon level using the temperature-dependent quantum Green's function approach. Calculations at the time-dependent density functional theory level with the MN15 functional show that ICG and IR808 have only one triplet state below the S1 state. The main deactivation channel of the S1 state is the IC process with a large (kIC(S1 → S0)) rate constant of ∼109-1011 s-1. The estimated quantum yield of fluorescence (φfl) is ∼0.001-0.24 for the two studied molecules, which agrees rather well with experimental values. Thus, the present approach enables calculations of the three kinds of rate constants and the quantum yield of fluorescence using the same computational methodology.

Unraveling the delayed fluorescence mechanism of copper(I) halide-phosphine emitters from DFT calculations

Several copper complexes exhibiting luminescent properties have been studied. In this context, the possibility of incorporating them into the architecture of organic light-emitting diode (OLED) devices has been investigated to improve their efficiency and photophysical stability for predicting the suitability and character of the emissive material. Specifically, we unraveled the excitation mechanism of the Cu(I)X(dppt)(PPh3) complex [X = Br, I, dppt = 3,4-bis(diphenylphosphino)thiophene]. Since the intersystem crossing (ISC) depicts a necessary process, where the knowledge of the rate constant value enables the assessment of the suitability of the material, we calculated the reverse and intersystem crossing rates for the Cu(I) complexes contrasting with pure organic thermally activated delayed fluorescence (TADF) emitters, with the goal to emphasize that the structural design of the mononuclear copper(I) complexes results in similar singlet–triplet gaps, ΔEST, values (∼0.1 eV). Moreover, it shows a remarkable enhancement of spin–orbit coupling, which allows achieving ISC rates in the ns scale. The calculations were made in the Time-Dependent Density Functional Theory (TD-DFT) level framework with the accurate response of large molecules studied here.

Molecular design of D-π-A-π-D small molecule donor materials with narrow energy gap for organic solar cells applications.

Developing novel materials present a great challenge to improve the photovoltaic performance of organic solar cells (OSCs). In this paper, we designed a series of the donor-π bridge-acceptor-π bridge-donor (D-π-A-π-D) structure molecules. These molecules consist of diketopyrrolopyrrole (DPP) moiety as core, 9-hexyl-carbazole moiety as terminal groups, and different planar electron-rich aromatic groups as π-bridges. The density functional theory (DFT) and time-dependent DFT (TD-DFT) computations showed that the frontier molecular orbital (FMO) energy levels, energy gaps, electron-driving forces (ΔEL-L), open-circuit voltage (Voc), fill factor (FF), reorganization energy (λ), exciton binding energy (Eb), and absorption spectra of the designed molecules can be effectively adjusted by the introduction of different π-bridges. The designed molecules have narrow energy gap and strong absorption spectra, which are beneficial for improving the photoelectric conversion efficiency of organic solar cells. In addition, the designed molecules possess large ΔEL-L, large Voc, and FF values and low Eb when the typical fullerene derivatives are used as acceptors. The FMO energy levels of the designed molecules can provide match well with the typical fullerene acceptors PC61BM, bisPC61BM, and PC71BM. Our results suggest that the designed molecules are expected to be promising donor materials for OSCs. All DFT and TD-DFT calculations were carried out using the Gaussian 09 code. The computational technique chosen was the hybrid functional B3LYP and the 6-31G(d,p) basis set. The benzene and chloroform solvent effects have been considered using the polarized continuum model (PCM) at the TD-DFT level. The simulated absorption spectra of designed molecules were plotted by using the GaussSum 1.0 program.

Hyper-Rayleigh scattering optical activity: Theory, symmetry considerations, and quantum chemistry applications.

This work reports on the first computational quantum-chemistry implementation of the hyper-Rayleigh scattering optical activity (HRS-OA), a nonlinear chiroptical phenomenon. First, from the basics of the theory, which is based on quantum electrodynamics, and focusing on the electric dipole, magnetic-dipole, and electric-quadrupole interactions, the equations for the simulation of the differential scattering ratios of HRS-OA are re-derived. Then, for the first time, computations of HRS-OA quantities are presented and analyzed. They have been enacted on a prototypical chiral organic molecule (methyloxirane) at the time-dependent density functional theory level using a broad range of atomic orbital basis sets. In particular, (i) we analyze the basis set convergence, demonstrating that converged results require basis sets with both diffuse and polarization functions, (ii) we discuss the relative amplitudes of the five contributions to the differential scattering ratios, and (iii) we study the effects of origin-dependence and derived the expression of the tensor shifts and we prove the origin-independence of the theory for exact wavefunctions. Our computations show the ability of HRS-OA as a nonlinear chiroptical method, able to distinguish between the enantiomers of the same chiral molecule.

Electronic State Spectroscopy of Nitromethane and Nitroethane.

High-resolution photoabsorption cross-sections in the 3.7-10.8 eV energy range are reinvestigated for nitromethane (CH3NO2), while for nitroethane (C2H5NO2), they are reported for the first time. New absorption features are observed for both molecules which have been assigned to vibronic excitations of valence, Rydberg, and mixed valence-Rydberg characters. In comparison with nitromethane, nitroethane shows mainly broad absorption bands with diffuse structures, which can be interpreted as a result of the side-chain effect contributing to an increased number of internal degrees of freedom. New theoretical quantum chemical calculations performed at the time-dependent density functional theory (TD-DFT) level were used to qualitatively help interpret the recorded photoabsorption spectra. From the photoabsorption cross-sections, photolysis lifetimes in the terrestrial atmosphere have been obtained for both compounds. Relevant internal conversion from Rydberg to valence character is noted for both molecules, while the nuclear dynamics of CH3NO2 and C2H5NO2 along the C-N reaction coordinate have been evaluated through potential energy curves at the TD-DFT level of theory, showing that the pre-dissociative character is more prevalent in nitromethane than in nitroethane.

Influence of the Nature of the Lipid Building Blocks on the Second-Order Nonlinear Optical Responses of an Embedded Di-8-ANEPPS Probe.

The extensive collection of lipids found in cell membranes is justified by the fact that each lipid contributes to their overall structure, dynamics, and properties and so to the biological processes taking place within them. It also showcases that, in order to deepen our understanding of membranes, we need to have a tool to differentiate lipid bilayers of varying composition. In this work, we investigate a suite of single-component saturated glycerophospholipids varying only in their headgroup structure by analyzing the second harmonic generation (SHG) nonlinear optical (NLO) response of a probe, di-8-ANEPPS, embedded into the membranes. The seven hydrophilic heads chosen (phosphatidylcholine (PC), phosphatidylethanolamine (PE), diaglycerol (GL), phosphatidylserine (PS), phosphatidylglycerol (PG), phosphatidylinositol (PI), and phosphatidyc acid (PA)) represent all the major headgroups that are part of mammalian plasma membranes and provide an assortment of neutral, zwiterrionic, and charged species. First, molecular dynamics simulations revealed that the lipidic arrangement is strongly sensitive to the nature of the hydrophilic head and less to the variety in the hydrophobic region. Membranes exhibiting drastically opposite structural properties can be pointed out: 1,2-dihexadecanoyl-rac-glycerol (DPGL) is the thickest and most ordered and aligned system, whereas 1,2-diacyl-sn-glycero-3-phospho-(1'-sn-glycerol) (DPPG) is thinnest and least ordered and aligned system. The structural analyses are then confronted with the molecular NLO responses, β, computed at the time-dependent density functional theory (TDDFT) level. As the orientation of the chromophore is impacted by the various degrees of order within the lipid bilayers, the diagonal component of the β tensor parallel to the bilayer normal, βZZZ, is as well. In the end, this computational approach provides insights into the link between lipid building blocks and the NLO responses of the embedded dye.

Synthesis, crystal structure, and chromotropism properties of Dihalo N-2-ethanolpicolylamine copper(II)

Two copper (II) mononuclear complexes with the general formula [Cu(HL)X2], which L = N-2-ethanolpicolylamine and X = Cl, Br, were synthesized and characterized by elemental analysis infrared, electronic absorption spectroscopy techniques, and conductivity method. The distorted square pyramidal geometry of [Cu(HL)Cl2] was confirmed by the density functional theory level (DFT) calculation and X-ray crystallography. The complexes are soluble in polar solvents and are chromotropic. It was found both complexes have a similar identity in aqueous solution due to dissociation of halides and hydration. Their chromotropism behavior, including solvato-, thermos- and halochromism, was investigated using visible absorption spectroscopy. The original green complex displayed a reversible color change to blue in alkaline and almost colorless in acidic solutions. The pH effect on the visible absorption spectrum of the complex was studied that functions as pH-induced “off–on-off” switches triggered by the deprotonation of ligand in an alkaline aqueous solution and protonation along with loss of the ligand HL in an acidic medium. The complex also exhibited thermochromism and solvatochromism due to solvation and structural change. Further computational analysis of the electronic structure of the complex in different solvents was executed to gain a deeper insight into the properties associated with molecular orbitals. Its electronic spectrum was analyzed, and bands were assigned through the time-dependent density functional theory level (TDDFT) calculation, together with DFT-based molecular modeling

The electronic spectra of 2- chlorothiophene and 3-chlorothiophene in the vacuum ultraviolet photoabsorption energy region (3.9–10.8 eV)

The absolute photoabsorption cross-sections for 2-chlorothiophene (2-Cl-Th) and 3-chlorothiophene (3-Cl-Th), in the 3.9–10.8 eV energy range, were recorded for the first-time using synchrotron radiation. New ab initio theoretical calculations performed at the time-dependent density functional theory (TD-DFT) level were used to help interpret the photoabsorption spectra. These have provided important information on the nature of the excited states which have been assigned to valence, mixed valence-Rydberg and Rydberg transitions. The combination of high-resolution vacuum ultra-violet synchrotron radiation with TD-DFT, represents the most comprehensive and self-consistent assignment of the chlorothiophenes electronic excitation to date. Photolysis lifetimes in the Earth^{\\prime}s upper atmosphere for both chemical compounds have been estimated from the absolute photoabsorption cross-sections. Potential energy curves have been obtained at the TD-DFT level of theory, showing that the dissociative character of the lowest-lying electronic states is more efficient in 3-Cl-Th.

Generalized Energy-Based Fragmentation Approach for the Electronic Emission Spectra of Large Systems.

The excited-state (ES) geometry optimization and electronic emission (fluorescence and phosphorescence) spectra and the ES vibrational spectra of large systems are great challenges in quantum chemistry. In this work, we develop a generalized energy-based fragmentation (GEBF) approach to compute the localized ES structures and vibrational frequencies of large systems. In this approach, the ES energy derivatives (gradients or Hessians) for a localized ES of a large system can be obtained by combining the ES energy derivatives of the corresponding active subsystems (including local excitation center) and the ground-state energy derivatives of inactive subsystems. Two strategies are adopted to overcome two difficulties from state-classification and state-tracking for treating specific ESs. First, for state-classification, we develop an improved density-based spatial clustering applied with noise algorithm with a modified transition orbital projection (TOP) algorithm, which allow a certain ES energy and energy derivatives of the whole system to be calculated with different ES energies and energy derivatives of active subsystems. Furthermore, we also employ the TOP algorithm for tracking the ESs in their geometry optimizations at the time-dependent density functional theory (TDDFT) level. Then, the GEBF approach is applied to investigate the optimized ES geometries or ES vibrational frequencies for two typical systems. Our results show that the cost-effective GEBF approach can accurately reproduce the TDDFT fluorescence spectra of the cytosine derivative and the experimental phosphorescence spectra of the β-cyclodextrin derivative. The GEBF approach is expected to be routinely applied to investigate the electronic emission spectra of very large systems with local chromophores.

Spin–Orbit Couplings for Nonadiabatic Molecular Dynamics at the ΔSCF Level

A procedure for the calculation of spin-orbit coupling (SOC) at the delta self-consistent field (ΔSCF) level of theory is presented. Singlet and triplet excited electronic states obtained with the ΔSCF method are expanded into a linear combination of singly excited Slater determinants composed of ground electronic state Kohn-Sham orbitals. This alleviates the nonorthogonality between excited and ground electronic states and introduces a framework, similar to the auxiliary wave function at the time-dependent density functional theory (TD-DFT) level, for the calculation of observables. The ΔSCF observables of the formaldehyde system were compared to reference TD-DFT values. Our procedure gives all components (energies, gradients, nonadiabatic couplings, and SOC terms) at the ΔSCF level of theory for conducting efficient, full-atomistic nonadiabatic molecular dynamics with intersystem crossing, particularly in condensed phase systems.

PH-Responsive switching properties of a water-soluble dinuclear Cu(II) complex containing oximato bridges chelating ligand: Synthesis, crystal structure and computational study

This study presents a combined experimental and computational investigation on a dinuclear Cu(II) complex containing 3-[2-[(ethanol amino)ethyl]imino]-2-butanoneoxime ligand (L). The compound [CuL]2(NO3)2 was studied by IR, UV–Vis spectroscopy, thermogravimetry analysis, and molar conductance measurements. The square-pyramid geometry of the complex was confirmed by both the density functional theory level (DFT) calculation and X-ray crystallography. The complex was halochromic, and its halochromism was studied in an aqueous solution. The original green complex displayed reversible color change to blue in alkaline and colorless in acidic solutions. The pH effect on the visible absorption spectrum of the complex was studied that functions as pH-induced “off–on–off” switches triggered by the protonation and loss of the ligand L in acidic medium and deprotonation of ligand in a basic aqueous solution. Further computational analysis of the electronic structure of the complex was carried out to gain a deeper insight into the properties associated with molecular orbitals. Its electronic spectrum was analyzed, and bands were assigned through the time-dependent density functional theory level (TDDFT) calculation.

Optical Activity of Spin-Forbidden Electronic Transitions in Metal Complexes from Time-Dependent Density Functional Theory with Spin-Orbit Coupling.

The calculation of magnetic transition dipole moments and rotatory strengths was implemented at the zeroth‐order regular approximation (ZORA) two‐component relativistic time‐dependent density functional theory (TDDFT) level. The circular dichroism of the spin‐forbidden ligand‐field transitions of tris(ethylenediamine)cobalt(III) computed in this way agrees very well with available measurements. Phosphorescence dissymmetry factors glum and the corresponding lifetimes are evaluated for three N‐heterocyclic‐carbene‐based iridium complexes, two of which contain helicene moieties, and for two platinahelicenes. The agreement with experimental data is satisfactory. The calculations reproduce the signs and order of magnitude of glum , and the large variations of phosphorescence lifetimes among the systems. The electron spin contribution to the magnetic transition dipole moment is shown to be important in all of the computations.

Unveiling the relationship between structural and polarization effects on the first hyperpolarizability of a merocyanine dye.

The nonlinear optical response, more specifically the Hyper-Rayleigh Scattering (HRS) response of the Brooker's merocyanine, has been calculated at the time-dependent density functional theory level and rationalized in terms of the structural changes and polarization effects induced by applied external electric fields. The structural change leads to large changes in the HRS response, while only slight variations were observed due to the polarization effects on the fixed quinoid form. Considering both structural and polarization contributions concurrently, the HRS response is dominated by cooperative behavior of those effects for weak and intermediate electric field strengths. At the same time, the competition between both effects was a crucial factor in the region of strong electric fields. The obtained results can lead to an easier understanding for upcoming studies considering more realistic models of solvents where it is not simple to disentangle these contributions.

A tale of two vectors: A Lanczos algorithm for calculating RPA mean excitation energies.

The experimental and theoretical determination of the mean excitation energy, I(0), and the stopping power, S(v), of a material is of great interest in particle and material physics and radiation therapy. For calculations of I(0), the complete set of electronic transitions in a given basis set is required, effectively limiting such calculations to systems with a small number of electrons, even at the random-phase approximation (RPA)/time-dependent Hartree-Fock (TDHF) or time-dependent density-functional theory level. To overcome such limitations, we present here the implementation of a Lanczos algorithm adapted for the paired RPA/TDHF eigenvalue problem in the Dalton program and show that it provides good approximation of the entire RPA eigenspectra in a reduced space. We observe rapid convergence of I(0) with the number of Lanczos vectors as the algorithm favors the transitions with large contributions. In most cases, the algorithm recovers RPA I(0) values of up to 0.5% accuracy at less than a quarter of the full space size. The algorithm not only exploits the RPA paired structure to save computational resources but also preserves certain sum-over-states properties, as first demonstrated by Johnson et al. [Comput. Phys. Commun. 120, 155 (1999)]. The block Lanczos RPA solver, as presented here, thus shows promise for computing mean excitation energies for systems larger than what was computationally feasible before.

Plasmonic Circular Dichroism in Chiral Gold Nanowire Dimers.

We report a computational study at the time-dependent density functional theory (TDDFT) level of the chiro-optical spectra of chiral gold nanowires coupled in dimers. Our goal is to explore whether it is possible to overcome destructive interference in single nanowires that damp chiral response in these systems and to achieve intense plasmonic circular dichroism (CD) through a coupling between the nanostructures. We predict a huge enhancement of circular dichroism at the plasmon resonance when two chiral nanowires are intimately coupled in an achiral relative arrangement. Such an effect is even more pronounced when two chiral nanowires are coupled in a chiral relative arrangement. Individual component maps of rotator strength, partial contributions according to the magnetic dipole component, and induced densities allow us to fully rationalize these findings, thus opening the way to the field of plasmonic CD and its rational design.

Effect of donor and acceptor on optoelectronic properties of benzo[1,2-b:4,5-b′]dithiophene

A series of acceptor and donor groups anchored to benzo[1,2-b:4,5-b′]dithiophene (BDT) molecule have been systematically investigated at the density functional theory (DFT) and time-dependent density functional theory (TDDFT) level to reveal structure–property relationships, charge transfer, and fluorescence lifetimes. The DFT optimization shows that the hetero atom in the ring induces the polarity from central ring to both ends of the thiophene ring, participating in the conjugation. The donor and acceptor groups were anchored at the terminals of the BDT at two different positions to fine-tune the properties according to the requirement and study the push–pull effect. All the models studied in this work retain their aromaticity as estimated from NICS(0) and NICS(1) aromaticity index in ground and excited states. The results show that the hardness, softness, HOMO–LUMO gaps, ionization potentials (IP), and electron affinities (EA) of the BDTs are significantly affected by the electron-withdrawing and electron-donating groups. The 1H and 13C NMR chemical shift values have been computed to quantify the push–pull effect. Further, the charge transfer properties in these BDTs were explored based on reorganization energies and diagnostic descriptors derived from hole–electron theory that present different electron excitation behavior. The relationship between the computed variables such as highest occupied molecular orbital, lowest unoccupied molecular orbital, oscillator strength, dipole moment, absorption, and fluorescence energy correlates the system with one another and also to extend the possible applications of the system in optical devices. Structure–property relationship of various BDTs reveal that, upon optical excitation, the resonance effect plays an important role changing the bonding character between the substituent and BDT unit, enabling efficient electron delocalization. The examination of TDDFT results indicates that among the various models studied in this work, nitro-substituted model is better candidate for optoelectronic properties with relatively large absorption wavelength and long fluorescence lifetime.

Modeling Spectral Tuning in Red Fluorescent Proteins Using the Dipole Moment Variation upon Excitation.

We describe a model for spectral tuning in red fluorescent proteins (RFPs) based on the relation between an electronic structure descriptor, the dipole moment variation upon excitation (DMV), and the excitation energy of a protein. This approach aims to overcome the problem of accurate prediction of excitation energies in RFPs, which span a very narrow window of band maxima. The latter roughly corresponds to the energy range of 0.1 eV, which is comparable with typical errors in calculations of the excitation energy by conventional quantum chemistry methods. In this work, we demonstrate a strong quantitative correlation between DMV values, obtained computationally with modest efforts, and excitation energies ΔEex at the experimental excitation band maxima for a series of RFPs with bands between 570 and 605 nm. Protein models are constructed by motifs of the relevant crystal structures, and atomic coordinates are optimized in quantum mechanics/molecular mechanics (QM/MM) calculations with QM-subsystems composed of large chromophore-containing regions. DMV values are evaluated with the electron density computed at the time-dependent density functional theory (TDDFT) level using several functionals and basis sets. We show that the results obtained with the CAM-B3LYP, BHHLYP, and M06-2X functionals demonstrate favorable correlations between DMV and ΔEex with the mean absolute error less than 0.01 eV. Taking into account the solid theoretical grounds of the relation between the DMV and the excitation energy in fluorescent proteins, the described modeling strategy presents a rational tool for spectral tuning in these efficient markers for in vivo imaging.