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Two strategies are applied to evaluate the effect of the environment on the two-photon absorption (TPA) cross sections for two characteristic excited states of C2H4 upon complexation with H2O. The supermolecular strategy provides the reference complexation-induced shifts and uses either the EOM-CCSD or ADC(2) method. The embedding strategy is based on frozen-density-embedding theory (FDET) and uses only fundamental constants. The TPA cross sections from high-level supermolecular calculations are extremely basis-set-sensitive. Literature data and the present study indicate that accuracy of the absolute TPA cross sections below 100 atomic units and their shifts below 10 atomic units remains a challenge. The obtained FDET results show a similar basis-set behavior. For the largest basis set (d-aug-cc-pVQZ), TPA cross sections obtained from these two strategies are in excellent agreement. The complexation-induced shifts have the correct sign of the effect and a small (12-33%) relative error in magnitude. The deviations of the FDET-derived shifts from the reference are of similar magnitude as the reliability threshold of the reference shifts.

In the context of employing embedding methods to study spectroscopic properties, the viability and effectiveness of replacing an ensemble of calculations by a single calculation using an average description of the system of study are evaluated. This work aims to provide a baseline of the expected fluctuations in the average description of the system obtained in the two cases: from calculations of an ensemble of geometries, and from an average environment constructed with the same ensemble. To this end, the classical molecular dynamics simulation of a very simple system was used: a rigid molecule of acetone in a solution of rigid water. We perform a careful numerical analysis of the fluctuations of the electrostatic potential felt by the solute, as well as the fluctuations in the effect on its electronic density, measure through the dipole moment and the atomic charges derived from the corresponding potential. At the same time, we inspect the accuracy of the methods used to construct average environments. Finally, the proposed approach to generate the embedding potential from an average environment density is applied to estimate the solvatochromic shift of the first excitation of acetone. In order to account for quantum-confinement effects that may be important in certain cases, the fluctuations on the shift due to the interaction with the solvent are evaluated using Frozen-Density Embedding Theory. Our results demonstrate that, for normally-behaved environments, the constructed average environment is a reasonably good representation of a discrete solvent environment.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange–correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design. This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

The emission band for Flugi-2 solvated in dimethyl sulfoxide (DMSO) is obtained from the combined quantum-classical simulations in which the quantum mechanics/molecular mechanics excitation energies are evaluated at the equilibrated segment of the classical molecular dynamics trajectory on the lowest-excited-state potential energy surface. The classical force-field parameters were obtained and validated specifically for the purpose of the present work. The calculated gas-phase to DMSO solvatochromic shift amounts to -0.21 eV, which is in line with the experimentally determined difference between the maxima of the emission bands for Flugi-2 in decane and in DMSO (-0.26 eV). The used model describes rather well the effect of DMSO on the broadening of the emission band. The solvatochromic shift in DMSO originates from two competing effects. The structural deformation of Flugi-2 due to the interaction with DMSO, which results in a positive contribution, and the negative contribution of a larger magnitude due to favorable specific interactions with the solvent. The latter is dominated by a single hydrogen bond between the oxygen atom of a DMSO molecule and the N3 hydrogen atom of the Flugi-2 molecule in which the proton of N3 acts as the donor.

The extension of the frozen-density embedding theory for nonvariational methods [J. Chem. Theory Comput.2020,16, 6880] was utilized to evaluate intermolecular interaction energies for complexes in the Zhao-Truhlar basis set. In the applied method (FDET-MP2-FAT-LDA), the same auxiliary system is used to evaluate the correlation energy by means of the second-order Moller-Plesset perturbation theory (MP2), as in our previous work [J. Chem. Phys.2019,150, 121101]. Local density approximation is used for ExcTnad[ρA,ρB] in both cases. Additionally, the contribution to the energy due to the neglected correlation potential was evaluated and analyzed. The domain of applicability of the local density approximation for ExcTnad[ρA,ρB] was determined based on deviations from the interaction energies from the conventional MP2 calculations. The local density approximation for ExcTnad[ρA,ρB] performs well for hydrogen- or dipole-bound complexes. The relative errors in the interaction energy lie within 3-30%. While for charge-transfer complexes, this approximation fails consistently, and for other types of complexes, the performance of this approximation is not systematic. The sources of error are discussed in detail.

This is the peer reviewed version of the following article: Mroginski, Adam, Amoyal, Barnoy, Bondar, ... Schapiro. (2020). Frontiers in Multiscale Modeling of Photoreceptor Proteins. Photochemistry and Photobiology, 97(2):243-269, which has been published in final form at https://doi.org/10.1111/php.13372. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited. This perspective article highlights the challenges in the theoretical description of photoreceptor proteins using multiscale modeling, as discussed at the CECAM workshop in Tel Aviv, Israel. The participants have identified grand challenges and discussed the development of new tools to address them. Recent progress in understanding representative proteins such as green fluorescent protein, photoactive yellow protein, phytochrome, and rhodopsin is presented, along with methodological developments.

The correlation functional Ec[ρ] known in Levy's constrained search formulation of density functional theory is also one of the components of the energy functional in Frozen-Density Embedding Theory (FDET) [Wesolowski, Phys. Rev. A, 77 (2008) 012504] if the embedded wavefunction has the single determinant form. The relation between the FDET energy and quantities available from an auxiliary system is derived. In the auxiliary system, Ec[ρ] and its functional derivative (correlation potential) are entirely neglected. The relation is exact up to the quadratic terms density changes caused by electron-electron correlation. It is discussed in view of its practical applica- tions in modelling electronic structure of embedded species.

For the first time, the use of experimentally derived molecular electron densities as ρB(r) in calculations based on frozen-density embedding theory (FDET) of environment-induced shifts of electronic excitations for chromophores in clusters is demonstrated. ρB(r) was derived from X-ray restrained molecular wavefunctions of glycylglycine to obtain environment densities for simulating electronic excitations in clusters., The basic idea of frozen-density embedding theory (FDET) is the constrained minimization of the Hohenberg–Kohn density functional E HK[ρ] performed using the auxiliary functional , where ΨA is the embedded N A-electron wavefunction and ρB(r) is a non-negative function in real space integrating to a given number of electrons N B. This choice of independent variables in the total energy functional makes it possible to treat the corresponding two components of the total density using different methods in multi-level simulations. The application of FDET using ρB(r) reconstructed from X-ray diffraction data for a molecular crystal is demonstrated for the first time. For eight hydrogen-bonded clusters involving a chromophore (represented as ΨA) and the glycylglycine molecule [represented as ρB(r)], FDET is used to derive excitation energies. It is shown that experimental densities are suitable for use as ρB(r) in FDET-based simulations.

We present a thorough investigation of the errors in results obtained with the combination of frozen-density embedding theory and the algebraic diagrammatic construction scheme for the polarization propagator of second order (FDE-ADC(2)). The study was carried out on a set of 52 intermolecular complexes with varying interaction strength, each consisting of a chromophore of fundamental interest and a few small molecules in its environment. The errors emerging in frozen-density embedding theory-based methods originate from (a) the solver of the quantum many-body problem used to obtain the embedded wave function (ΨAemb), (b) the approximation for the explicit density functional for the embedding potential, and (c) the choice of the density representing the environment (ρB( r)). The present work provides a comprehensive analysis of the errors in the excitation energies based on the last two factors. Furthermore, a density-overlap-based parameter is proposed to be used as an a priori criterion of applicability.

In the original formulation, frozen-density embedding theory [T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050–8053 (1993); T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] concerns multi-level simulation methods in which variational methods are used to obtain the embedded NA-electron wavefunction. In this work, an implicit density functional for the total energy is constructed and used to derive a general expression for the total energy in methods in which the embedded NA electrons are treated non-variationally. The formula is exact within linear expansion in density perturbations. Illustrative numerical examples are provided.In the original formulation, frozen-density embedding theory [T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050–8053 (1993); T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] concerns multi-level simulation methods in which variational methods are used to obtain the embedded NA-electron wavefunction. In this work, an implicit density functional for the total energy is constructed and used to derive a general expression for the total energy in methods in which the embedded NA electrons are treated non-variationally. The formula is exact within linear expansion in density perturbations. Illustrative numerical examples are provided.

We performed a detailed deconvolution analysis of ATR-FTIR peaks of a common diacetylene, 10,12-tricosadiynoic acid (TRCDA) during the polymerization and the blue-to-red transition. Based on the analysis and the solvent dependence on the IR signals, we found that the triple peak from C C stretching mode that has been previously suspected as a consequence of Fermi resonance is rather associated with the macromolecular assembly of TRCDA. Besides these C C triple peaks, we found that the background in the region increased during the UV exposure due to the C C signals from polymers. In addition, the anisotropic compression during polymerization was also detected, which supports the proposed interpretation of X-ray data reported previously. These results are the benefits from the deconvolution analysis.

In this article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimization of conical intersections, the simulation of adiabatic and nonadiabatic molecular dynamics, and interfaces to tools for semiclassical and quantum mechanical nuclear dynamics. Furthermore, the article describes features unique to simulations of spectroscopic and magnetic phenomena such as the exact semiclassical description of the interaction between light and matter, various X-ray processes, magnetic circular dichroism, and properties. Finally, the paper describes a number of built-in and add-on features to support the OpenMolcas platform with postcalculation analysis and visualization, a multiscale simulation option using frozen-density embedding theory, and new electronic and muonic basis sets.

Terpyridine derivatives are of great interest due to their unique photophysical properties when used as antennas in metallic complexes. Several experimental and theoretical studies indicate strong charge-transfer character of the lowest electronic excited state, which could be exploited for predicting fluorescence quantum yields from the magnitude of the charge separation induced by electronic transitions. Focusing on substituted 4'-phenyl-2,2':6'2''-terpyridyl, we report on two measures of the charge separation obtained from high-level calculations in ground and excited states (length of the change of the dipole moment and the electron-hole distance). Our refined model confirms that the fluorescence quantum yield shows a global S-shape dependence on the magnitude of the charge separation, which can be quantified either by the change in dipole moments between the ground and excited states or by the associated charge-hole distances. This approach provides a remarkable tool for the molecular design of a fluorescent polyaromatic antenna.

Using MP2, CCSD, and B3LYP methods of computational chemistry, we show length dependence in the intrinsic elastic properties of short alkane fragments. For isolated alkane fragments of finite length in the gas phase and zero temperature, the intrinsic elasticity constants are found to vary with the number of carbon atoms and its parity. From extrapolation of the elasticity constants calculations to infinite chain length, and by comparing with in-situ elasticity constant of single poly(ethylene) molecule obtained with atomic force microscopy, we estimate the softening effect of environment on the extension response of the polymer. Electronic supplementary material The online version of this article (10.1007/s00894-017-3572-9) contains supplementary material, which is available to authorized users.

In numerical simulations, based on frozen-density embedding theory, the independent variables describing the total system are the embedded wave function (ΨA) and the density representing the environment. Due to inhomogeneity of the non-electrostatic component of the total energy: ), the expectation value of the embedding potential is not equal to the corresponding component of the total energy. The differences are evaluated using local and semi-local approximations for the functional EnadxcT[ρA, ρB] in two model systems representing embedded species weakly interacting with the environment. It is found that ΔnadxcT is typically one order of magnitude smaller than EnadxcT[ρA, ρB] and decreases with the overlap between and . The kinetic- and exchange-correlation contributions to ΔnadxcT cancel partially reducing its magnitude to mHartrees. Compared to local approximation for EnadxcT[ρA, ρB], the inhomogeneity is more pronounced in semi-local functionals.

We report that anion−π and cation−π interactions can occur on the same aromatic surface. Interactions of this type are referred to as ion pair−π interactions. Their existence, nature, and significance are elaborated in the context of spectral tuning, ion binding in solution, and activation of cell-penetrating peptides. The origin of spectral tuning by ion pair−π interactions is unraveled with energy-minimized excited-state structures: The solvent- and pH-independent red shift of absorption and emission of push–pull fluorophores originates from antiparallel ion pair−π attraction to their polarized excited state. In contrast, the complementary parallel ion pair−π repulsion is spectroscopically irrelevant, in part because of charge neutralization by intriguing proton and electron transfers on excited push–pull surfaces. With time-resolved fluorescence measurements, very important differences between antiparallel and parallel ion pair−π interactions are identified and quantitatively dissected from interference by aggregation and ion pair dissociation. Contributions from hydrogen bonding, proton transfer, π–π interactions, chromophore twisting, ion pairing, and self-assembly are systematically addressed and eliminated by concise structural modifications. Ion-exchange studies in solution, activation of cell-penetrating peptides in vesicles, and computational analysis all imply that the situation in the ground state is complementary to spectral tuning in the excited state; i.e., parallel rather than antiparallel ion pair−π interactions are preferred, despite repulsion from the push–pull dipole. The overall quite complete picture of ion pair−π interactions provided by these remarkably coherent yet complex results is expected to attract attention throughout the multiple disciplines of chemistry involved.

A series of long-tail alkyl ethanolamine analogs containing amide-, urea-, and thiourea moieties was synthesized and the behavior of the corresponding monolayers was assessed on the Langmuir-Pockels trough combined with grazing incidence X-ray diffraction experiments and complemented by computer simulations. All compounds form stable monolayers at the soft air/water interface. The phase behavior is dominated by strong intermolecular headgroup hydrogen bond networks. While the amide analog forms well-defined monolayer structures, the stronger hydrogen bonds in the urea analogs lead to the formation of small three-dimensional crystallites already during spreading due to concentration fluctuations. The hydrogen bonds in the thiourea case form a two-dimensional network, which ruptures temporarily during compression and is recovered in a self-healing process, while in the urea clusters the hydrogen bonds form a more planar framework with gliding planes keeping the structure intact during compression. Because the thiourea analogs are able to self-heal after rupture, such compounds could have interesting properties as tight, ordered, and self-healing monolayers.

Implementation, benchmarking, and representative applications of the new FDE-ADC(3) method for describing environmental effects on excited states as a combination of frozen density embedding (FDE) and the algebraic-diagrammatic construction scheme for the polarization propagator of third order (ADC(3)) are presented. Results of FDE-ADC(3) calculations are validated with respect to supersystem calculations on test systems with varying molecule-environment interaction strengths from dispersion up to multiple hydrogen bonds. The overall deviation compared to the supersystem calculations is as small as 0.029 eV for excitation energies, which is even smaller than the intrinsic error of ADC(3). The dependence of the accuracy on the choice of method and functional for the calculation of the environment and the nonelectrostatic part of the system-environment interaction is evaluated. In three representative examples, the FDE-ADC method is applied to investigate larger systems and to analyze excited state properties using visualization of embedded densities and orbitals.

The combination of Frozen Density Embedding Theory (FDET) and the Algebraic Diagrammatic Construction (ADC) scheme for the polarization propagator for describing environmental effects on electronically excited states is presented. Two different ways of interfacing and expressing the so-called embedding operator are introduced. The resulting excited states are compared with supermolecular calculations of the total system at the ADC(2) level of theory. Molecular test systems were chosen to investigate molecule–environment interactions of varying strength from dispersion interaction up to multiple hydrogen bonds. The overall difference between the supermolecular and the FDE-ADC calculations in excitation energies is lower than 0.09 eV (max) and 0.032 eV in average, which is well below the intrinsic error of the ADC(2) method itself.

The basic concept of allosteric cooperativity used in biology, chemistry and physics states that any change in the intermolecular host–guest interactions operating in multisite receptors can be assigned to intersite interactions. Using lanthanide metals as guests and linear multi-tridentate linear oligomers of variable lengths and geometries as hosts, this work shows that the quantitative modeling of metal loadings requires the consideration of a novel phenomenon originating from solvation processes. It stepwise modulates the intrinsic affinity of each isolated site in multisite receptors, and this without resorting to allosteric cooperativity. An easy-to-handle additive model predicts a negative power law dependence of the intrinsic affinity on the length of the linear metallopolymer. Applied to lanthanidopolymers, the latter common analysis overestimates cooperativity factors by more than two orders of magnitude.

Besides molecular electron densities obtained within the Born-Oppenheimer approximation (ρB(r)) to represent the environment, the ensemble averaged density (〈ρB〉(r)) is also admissible in frozen-density embedding theory (FDET) [Wesolowski, Phys. Rev. A, 2008, 77, 11444]. This makes it possible to introduce an approximation in the evaluation of the solvent effect on quantum mechanical observables consisting of replacing the ensemble averaged observable by the observable evaluated at ensemble averaged ρB(r). This approximation is shown to affect negligibly the solvatochromic shift in the absorption of hydrated acetone. The proposed model provides a continuum type of representation of the solvent, which reflects nevertheless its local structure, and it is to be applied as a post-simulation analysis tool in atomistic level simulations.

Shifts in the excitation energy of the organic chromophore, cis-7-hydroxyquinoline (cis-7HQ), corresponding to the π→π* transition in cis-7HQ and induced by the complexation with a variety of small hydrogen-bonded molecules, obtained with the frozen-density embedding theory (FDET), are compared with the results of the supermolecular equation-of-motion coupled-cluster (EOMCC) calculations with singles, doubles, and non-iterative triples, which provide the reference theoretical data, the supermolecular time-dependent density functional theory (TDDFT) calculations, and experiment. Unlike in the supermolecular EOMCC and TDDFT cases, where each complexation-induced spectral shift is evaluated by performing two separate calculations, one for the complex and another one for the isolated chromophore, the FDET shifts are evaluated as the differences of the excitation energies determined for the same many-electron system, representing the chromophore fragment with two different effective potentials. By considering eight complexes of cis-7HQ with up to three small hydrogen-bonded molecules, it is shown that the spectral shifts resulting from the FDET calculations employing non-relaxed environment densities and their EOMCC reference counterparts are in excellent agreement with one another, whereas the analogous shifts obtained with the supermolecular TDDFT method do not agree with the EOMCC reference data. The average absolute deviation between the complexation-induced shifts, which can be as large, in absolute value, as about 2000 cm-1, obtained using the non-relaxed FDET and supermolecular EOMCC approaches that represent two entirely different computational strategies, is only about 100 cm-1, i.e., on the same order as the accuracy of the EOMCC calculations. This should be contrasted with the supermolecular TDDFT calculations, which produce the excitation energy shifts that differ from those resulting from the reference EOMCC calculations by about 700 cm-1 on average. Among the discussed issues are the choice of the electronic density defining the environment with which the chromophore interacts, which is one of the key components of FDET considerations, the basis set dependence of the FDET, supermolecular TDDFT, and EOMCC results, the usefulness of the monomer vs supermolecular basis expansions in FDET considerations, and the role of approximations that are used to define the exchange-correlation potentials in FDET and supermolecular TDDFT calculations.

Conventionally, solving one-electron equations for embedded orbitals [Eqs. (20) and (21) in Wesolowski and Warshel, J Phys Chem, 1993, 97, 8050] proceeds by a self-consistent procedure in which the whole effective potential, including its embedding component, is updated in each iteration. We propose an alternative scheme (splitSCF), which uses the linearized embedding potential in the inner iterative loop and the outer-loop is used to account for its deviations from linearity. The convergence of the proposed scheme is investigated for a set of weakly bound intermolecular complexes representing typical interactions with the environment. The outer loop is shown to converge very fast. No more than 3-4 iterations are needed. Errors due to skipping the outer loop completely and using the electron density obtained in the absence of the environment in the linearized embedding potential are investigated in detail. It is shown that this computationally attractive simplification, used already in numerical simulations by others, is adequate not only for van der Waals and hydrogen-bonded complexes but even if the complex comprises charged components, i.e., where strong electronic polarization takes place. In charge-transfer type of complexes, larger changes of electron of density upon complex formation occur and the above simplification is not recommended.

The bifunctional of the nonadditive kinetic energy in the reference system of noninteracting electrons ([Formula: see text] [ρA, ρB] = Ts[ρA + ρB] - Ts[ρA] - Ts[ρB]) is the key quantity in orbital-free embedding calculations because they hinge on approximations to[Formula: see text] [ρA,ρB]. Since[Formula: see text] [ρA,ρB] is not linear in ρA, the associated potential (functional derivative)[Formula: see text] [ρ,ρB]/δρ|ρ=ρA(r⃗) changes if ρA varies. In this work, for two approximations to[Formula: see text] [ρA,ρB], which are nonlinear in ρA (gradient-free and gradient-dependent), their linearized versions are constructed, and the resulting changes (linearization errors) in various properties of embedded systems (orbital energies, dipole moments, interaction energies, and electron densities) are analyzed. The considered model embedded systems represent typical nonbonding interactions: van der Waals contacts, hydrogen bonds, complexes involving charged species, and intermolecular complexes of the charge-transfer character. For van der Waals and hydrogen bonded complexes, the linearization of[Formula: see text] [ρA,ρB] affects negligibly the calculated properties. Even for complexes, for which large complexation induced changes of the electron density can be expected, such as the water molecule in the field of a cation, the linearization errors are about 2 orders of magnitude smaller than the interaction induced shifts of the corresponding properties. Linearization of[Formula: see text] [ρA,ρB] is shown to be inadequate for the complexes of a strong charge-transfer character. Compared to gradient-free approximation to[Formula: see text] [ρA,ρB], introduction of gradients increases the linearization error.

The importance of the nonelectrostatic component of the embedding potential is investigated by comparing the complexation induced shifts of the iso-g obtained in embedding calculations to its supermolecular counterparts. The analyses are made in view of such multilevel simulations, for which supermolecular strategy is either impractical or impossible, such as the planned simulations for the whole enzyme ferredoxin oxidoreductase. For the biliverdin radical surrounded by a few amino acids, it is shown that the embedding potential comprising only Coulomb terms fails to reproduce even qualitatively the shifts evaluated from supermolecular calculations. The nonelectrostatic component of the exact embedding potential is a bifunctional of two electron densities [Wesolowski and Warshel, J. Phys. Chem. 1993, 97, 8050; Wesolowski, Phys. Rev. A 2008, 77, 012504]. Therefore we analyze in detail both the quality of the approximant for the bifunctional and the importance of the choice of the electron densities at which it is evaluated in practical calculations.

Modeling properties of chemical species and chemical reactions requires usually the quantum-mechanical level of description. Methods from the ever-growing toolbox of quantum chemistry1,2 are used for this purpose. Due to unfavorable scaling of quantum chemistry methods, a compromise must be made between the accuracy of the numerical results and the size of the system described at the wave function level. The same strategy can be extended for separating molecular fragments or molecules. Nonlocal embedding operators based on either transferrable pseudopotentials or frozen orbitals obtained from localization procedures have been developed in many groups. The essential feature of all such local potentials is that they comprise a component which takes into account the intermolecular Pauli repulsion.

Experimental (IR and Raman) and theoretical (Kohn-Sham calculations) methods are used in a combined analysis aimed at refining the available structural data concerning the molecular guests in channels formed by stacked dibenzo-18-crown-6 (DB18C6) crown ether. The calculations are performed for a simplified model comprising isolated DB18C6 unit and its complexes with either H2O or H3O+ guests, which are the simplest model ingredients of a one-dimensional diluted acid chain, to get structural and energetic data concerning the formation of the complex and to assign the characteristic spectroscopic bands. The oxygen centers in the previously reported crystallographic structure are assigned to either H2O or protonated species.

The packing preferences of dimers formed by nitrogen-containing planar polycyclic aromatic hydrocarbons ((C30H15N)2 and (C36H15N)2) were studied by means of theoretical calculations. Potential energy curves corresponding to various relative motions of the monomers (vertical displacement, rotating, slipping, and combinations of them) were derived. It was found that the monomers in such π-stacked dimers are rather strongly held together (the interaction energy is about −9 kcal/mol) in an off-centered arrangement. It emerges as a general picture that the aligned structures are less stable than the ones where the nitrogen atoms, as the centers of the considered monomers, are not on top of each other but offset by 1.8−2.7 Å. Displacing the centers further results in a rapid reduction of the interaction energy. Within these relatively large relative motions (up to about 3 Å) of the monomers, however, no significant loss of stability of the dimers is noted. In the case of C30H15N, changing the orientation of the enantiotopic faces in the dimer formation leads to two nonequivalent minimum energy structures of similar energies but notably different geometries. The most stable structure of both dimers studied resembles that of two adjacent layers of graphite. We conclude, therefore, that the studied molecules could be considered as good building block candidates for the fabrication of columnar organic conductors.

By means of [1]H-NOESY- and Raman-spectroscopic analyses, we experimentally demonstrated the presence of the equatorial N—Me conformer of King's sultam 4b in solution, resulting from a rapid equilibrium. As a consequence, the value of the N lone-pair anomeric stabilization should be revised to 1.5-1.6 kcal/mol. Independently from the N tilting, natural bond orbital (NBO)-comparative analyses suggest that the S d* orbitals do not appear as primordial and stereospecific acceptors for the N lone pair. Second, the five-membered-ring sultams do not seem to be particularly well-stabilized by the S—C[sigma]* orbital in the N-substituted pseudo-axial conformation, as opposed to an idealized anti-periplanar situation for the six-membered-ring analogues. In this latter case, the other anti-periplanar C—C[sigma]* and C(1')—H/C(2')[sigma]* orbitals are as important, if not more, when compared to the S—C[sigma]* participation. In the pseudo-equatorial conformation,[upsilon]-sultams particularly benefit from the N lone-pair hyperconjugation with the anti-periplanar S—O[1][sigma]* and C(2)—H/C or C(1')—H/C[sigma]* orbitals. This is also the case for -sultams when the steric requirement of the N-substituent exceeds 1.6 kcal/mol. When both axial and equatorial conformations are sterically too exacting, the N-atom is prone to sp[2] hybridization or/and conformational changes (i.e., 12c). In that case also, the mode of stereoelectronic stabilization differs from [upsilon]- to [delta]-sultams.

The kinetic energy functional Ts[ρ] in a reference system of non-interacting electrons is a key quantity in density functional theory. Approximating it as an explicit functional of the electron density ρ is the object of continuous interest since the earliest days of quantum mechanics (Thomas–Fermi electron gas theory). A simple proof of the exact inequality Ts[ρA + ρB] − Ts[ρA] − Ts[ρB] ≥ 0 valid for a special class of spin-compensated pairs of electron densities ρA and ρB (vAB-representable pairs) is provided. The derived relation is discussed to rationalize some of the results of the past attempts to approximate Ts[ρ]. It is also discussed as a tool for deriving approximations to the functional Ts[ρ] and/or the bi-functional Tnads[ρA, ρB] = Ts[ρA + ρB] − Ts[ρA] − Ts[ρB].

Experimental and theoretical techniques have been applied to study the decomposition of the [RhCl(PF3)2]2 molecule which is known as a precursor in electron beam induced deposition (EBID) of Rh. Mass spectrometry (MS) has been carried out to study the electron ionisation and fragmentation of isolated molecules. Auger electron spectroscopy has been used to characterize the EBID deposit. The MS data indicate the presence of free phosphorus and rhodium ions. This is in agreement with the analysis of the composition of the EBID deposit containing: 60% Rh, 12–25% P, 2–13% Cl, no F, 3–20% O and N. Theoretical calculations (density functional theory) has been used to characterize the precursor molecule and to derive the enthalpies of several simple decomposition reactions. The calculated geometries are in a good agreement with the available X-ray crystallographic data. The [RhCl(PF3)2]2 appears not to be rigid: the PF3 groups can rotate with a relatively low barrier (0.6 kcal mol–1) whereas the barrier for the butterfly-like motion of (RhCl)2 moiety is only 3.5 kcal mol–1. According to the theoretical results, the lowest energy pathway of the decomposition corresponds to a consecutive loss of PF3 ligands, resulting in a (RhCl)2 moiety (without phosphorus). The same conclusion is also valid for the ionised precursor. Experimental data combined with the theoretical results concerning the energetics of the considered various simple decomposition processes indicate that the electron induced dissociation of the precursor cannot be seen as a simple one-step decomposition process.

The approximate nonempirical kinetic-energy functional proposed by Tal and Bader is analyzed for polyatomic systems. The performance of this functional and the functionals derived from the gradient expansion approximation truncated to zeroth, second, and fourth order is investigated for a testing set of 68 neutral and charged molecules. It is shown that the Tal–Bader functional, despite the simplicity of the idea behind its construction, leads to significantly better total kinetic energies than the gradient expansion approximation functionals. The local behavior of the kinetic-energy density derived from the Tal–Bader functional is also discussed.

An approach in which the total energy of interacting subsystems is expressed as a bifunctional depending explicitly on two functions: electron densities of the two molecules forming a complex (1 and 2) was used to determine the equilibrium geometry and the binding energy of several weak intermolecular complexes involving carbazole and such atoms or molecules as Ne, Ar, CH4, CO, and N2. For these complexes, the experimental dissociation energies fall within the range from 0.48 to 2.06 kcal/mol. Since the effect of the intermolecular vibrations on the dissociation energy is rather small, the experimental measurements provide an excellent reference set. The obtained interaction energies are in a good agreement with experiment and are superior to the ones derived from conventional Kohn–Sham calculations. A detailed analysis of relative contribution of the terms which are expressed using approximate functionals (i.e., exchange-correlation Exc[1 + 2] and nonadditive kinetic energy T[1,2] = Ts[1 + 2]–Ts[1]–Ts[2]) is made. The nonvariational version of the applied formalism is also discussed.

An approximate kinetic-energy functional of the generalized gradient approximation form was derived following the conjointness conjecture of Lee, Lee, and Parr. The functional shares the analytical form of its gradient dependency with the exchange-energy functionals of Becke and Perdew, Burke, and Ernzerhof. The two free parameters of this functional were determined using the exact values of the kinetic energy of He and Xe atoms. A set of 12 closed-shell atoms was used to test the accuracy of the proposed functional and more than 30 others taken from the literature. It is shown that the conjointness conjecture leads to a very good class of kinetic-energy functionals. Moreover, the functional developed in this work is shown to be one of the most accurate despite its simple analytical form.

The nonadditive kinetic potential is a key element in density-dependent embedding methods. The correspondence between the ground-state density and the total effective Kohn–Sham potential provides the basis for various methods to construct the nonadditive kinetic potential for any pair of electron densities. Several research groups used numerical or analytical inversion procedures to explore this strategy which overcomes the failures of known explicit density functional approximations. The numerical inversions, however, apply additional approximations/simplifications. The relations known for the exact quantities cannot be assumed to hold for quantities obtained in numerical inversions. The exact relations are discussed with special emphasis on such issues as: the admissibility of the densities for which the potential is constructed, the choice of densities to be used as independent variables, self-consistency between the potentials and observables calculated using the embedded wavefunction, and so forth. The review focuses on how these issues are treated in practice. The review is supplemented with the analysis of the inverted potentials for weakly overlapping pairs of electron densities—the case not studied previously.

Herein, we address the question whether anion–π and cation–π interactions can take place simultaneously on the same aromatic surface. Covalently positioned carboxylate–guanidinium pairs on the surface of 4-amino-1,8-naphthalimides are used as an example to explore push–pull chromophores as privileged platforms for such “ion pair–π” interactions. In antiparallel orientation with respect to the push–pull dipole, a bathochromic effect is observed. A red shift of 41 nm found in the least polar solvent is in good agreement with the 70 nm expected from theoretical calculations of ground and excited states. Decreasing shifts with solvent polarity, protonation, aggregation, and parallel carboxylate–guanidinium pairs imply that the intramolecular Stark effect from antiparallel ion pair–π interactions exceeds solvatochromic effects by far. Theoretical studies indicate that carboxylate–guanidinium pairs can also interact with the surfaces of π-acidic naphthalenediimides and π-basic pyrenes.

Frozen-density embedding theory (FDET) provides the formal framework for multilevel numerical simulations, such that a selected subsystem is described at the quantum mechanical level, whereas its environment is described by means of the electron density (frozen density; ${\rho _{\rm{B}} (\vec r)}$). The frozen density ${\rho _{\rm{B}} (\vec r)}$ is usually obtained from some lower-level quantum mechanical methods applied to the environment, but FDET is not limited to such choices for ${\rho _{\rm{B}} (\vec r)}$. The present work concerns the application of FDET, in which ${\rho _{\rm{B}} (\vec r)}$ is the statistically averaged electron density of the solvent ${\left\langle {\rho _{\rm{B}} (\vec r)} \right\rangle }$. The specific solute-solvent interactions are represented in a statistical manner in ${\left\langle {\rho _{\rm{B}} (\vec r)} \right\rangle }$. A full self-consistent treatment of solvated chromophore, thus involves a single geometry of the chromophore in a given state and the corresponding ${\left\langle {\rho _{\rm{B}} (\vec r)} \right\rangle }$. We show that the coupling between the two descriptors might be made in an approximate manner that is applicable for both absorption and emission. The proposed protocol leads to accurate (error in the range of 0.05 eV) descriptions of the solvatochromic shifts in both absorption and emission.

Retinal is the light-absorbing biochromophore responsible for the activation of vision pigments and light-driven ion-pumps. Nature has evolved molecular tuning mechanisms that significantly shift the optical properties of the retinal pigments to enable their ab-sorption of visible light. Using large-scale quantum chemical calculations at the density functional theory level combined with the frozen density embedding theory approach, we show here how the protein environment of vision pigments tune the absorption of retinal to the 2.3-2.6 eV (480-530 nm) region by electrostatically dominated interactions between the chromophore and the sur-rounding protein residues. The calculations accurately reproduce the experimental absorption maxima of rhodopsin (2.49 eV/498 nm), and the red, green, and blue color pigments (2.3-2.9 eV/430-530 nm). We further identify key interactions responsible for the red- and blue-shifting effects by mutating the rhodopsin structure in silico, and find that deprotonation of the retinyl is likely to be responsible for the blue shifted absorption in the blue cone vision pigment.

The density of atomic systems is analysed via the Single-Exponential Decay Detector (SEDD). SEDD is a scalar field designed to explore mathematical, rather than physical, properties of electron density. Nevertheless, it has been shown that SEDD can serve as a descriptor of bonding patterns in molecules as well as an indicator of atomic shells [P. de Silva, J. Korchowiec, and T. A. Wesolowski, ChemPhysChem 13, 3462 (2012)]. In this work, a more detailed analysis of atomic shells is done for atoms in the Li-Xe series. Shell populations based on SEDD agree with the Aufbau principle even better than those obtained from the Electron Localization Function, which is a popular indicator of electron localization. A link between SEDD and the local wave vector is given, which provides a physical interpretation of SEDD.

The density-functional approach based on the partition into subsystems was applied to study the benzene dimer. For several structures, the calculated interaction energy and intermolecular distance were compared with the previous theoretical results. A good agreement with high level ab initio correlated methods was found. For instance, the interaction energies obtained in this work and the CCSD(T) method agree within 0.1 - 0.6 kcal/mol depending on the structure of the dimer. The structure with the largest interaction energy is T-shaped, in agreement with CCSD(T) results. The T-shaped structure of benzene dimer was suggested by several experimental measurements. The calculated interaction energy of 2.09 kcal/mol agrees also well with experimental estimates based on the dissociation energy which ranges from 1.6±0.2 to 2.4±0.4 kcal/mol and the estimated zero-point vibration energy of 0.3 - 0.5 kcal/mol.

The use of hybrid ab initio QM/MM methods in studies of metalloenzymes and related systems presents a major challenge to computational chemists. Methods that include the metal ion in the quantum mechanical region should also include the ligands of the metal in this region. Such a treatment, however, should be very demanding if one is interested in performing the configurational averaging needed for proper calculations of activation free energies. In the present work we examine the ability of the frozen DFT (FDFT) and the constrained DFT (CDFT) approaches to be used in ab initio studies of metal-catalyzed reactions, while allowing for an effective QM (rather than a QM/MM) treatment of the reacting complex. These approaches allow one to treat the entire enzyme by ab initio DFT methods, while confining the SCF calculations to a relatively small subsystem and keeping the electron density of the rest of the system frozen (or constrained). It is found that the FDFT and CDFT models can reproduce the trend obtained by a full DFT calculation of a proton transfer between two water molecules in a (Im)3Zn2+(H2O)2 system. This and related test cases indicate that our approximated models should be capable of providing a reliable representation of the energetics of metalloenzymes. The reasons for the special efficiency of the FDFT approach are clarified, and the strategies that can be used in FDFT studies of metalloenzymes are outlined. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1554–1561, 2000

The formalism of the Kohn–Sham equations with constrained electron density is extended to the spin-polarized case. The isotropic hyperfine coupling constants (Aiso(Mg)) of Mg+ embedded in a Ne or Ar matrix represented using a cluster are calculated and compared to that of free Mg+. For the largest basis set used, the calculated values (222.9 and 210.4 gauss for Ar and Ne, respectively) agree with experimental measurements (222.4 and 211.6). The shifts of Aiso(Mg) relative to the values for free Mg+ are rather basis-set-independent.

In view of further application to the study of molecular and atomic sticking on dust particles, we investigated the capability of the "freeze-and-thaw" cycle of the Kohn–Sham equations with constrained electron density (KSCED) to describe potential energy surfaces of weak van der Waals complexes. We report the results obtained for C6H6[centered ellipsis]X (X = O2, N2, and CO) as test cases. In the KSCED formalism, the exchange-correlation functional is defined as in the Kohn–Sham approach whereas the kinetic energy of the molecular complex is expressed differently, using both the analytic expressions for the kinetic energy of individual fragments and the explicit functional of electron density to approximate nonadditive contributions. As the analytical form of the kinetic energy functional is not known, the approach relies on approximations. Therefore, the applied implementation of KSCED requires the use of an approximate kinetic energy functional in addition to the approximate exchange-correlation functional in calculations following the Kohn–Sham formalism. Several approximate kinetic energy functionals derived using a general form by Lee, Lee, and Parr [Lee et al., Phys. Rev. A. 44, 768 (1991)] were considered. The functionals of this type are related to the approximate exchange energy functionals and it is possible to derive a kinetic energy functional from an exchange energy functional without the use of any additional parameters. The KSCED interaction energies obtained using the PW91 [Perdew and Wang, in Electronic Structure of Solids '91, edited by P. Ziesche and H. Eschrig (Academie Verlag, Berlin, 1991), p. 11] exchange-correlation functional and the kinetic energy functional derived from the PW91 exchange functional agree very well with the available experimental results. Other considered functionals lead to worse results. Compared to the supermolecule Kohn–Sham interaction energies, the ones derived from the KSCED calculations depend less on the choice of the approximate functionals used. The presented KSCED results together with the previous Kohn–Sham ones [Weso[barred lower-case ell]owski et al., J. Phys. Chem. A 101, 7818 (1997)] support the use of the PW91 functional for studies of weakly bound systems of our interest.

The structure and stretching frequency of the CO molecule physisorbed on the MgO(100) surface were investigated using the recently developed formalism of Kohn-Sham equations with constrained electron density (KSCED). The KSCED method makes it possible to divide a large system into two subsystems and to study one of them using Kohn-Sham-like equations in which the effective potential takes into account the interactions between subsystems. Compared to the standard Kohn-Sham formalism, the KSCED method involves an additional functional due to the non-additivity of the kinetic energy. The surface was represented using a cluster ((MgO5)8− or Mg9O9) embedded in an array of electric point-charges. The KSCED calculations led to a blue-shift of the stretching frequency of the C-down adsorbed CO molecule amounting to 47–21 cm−1 depending on the distance from the surface. At the C–Mg distance of 2.42 A, which corresponds to a typical minimum of the potential energy curve derived from supermolecule Kohn-Sham calculations applying gradient-corrected functionals, the KSCED frequency shift amounts to 35 cm−1 in excellent agreement with the most recent experiments. The CO stretching frequency of the O-down adsorbed CO molecule is red-shifted. The effects of cluster size and choice of the functionals on the KSCED frequencies, geometries and energies were analyzed. For C–Mg distances varying between 2.3 and 3.0 A, changing the cluster size affects the frequencies by less than 4 cm−1 and the CO bond length by less than 0.0003 A. At C–Mg distances larger than 2.4 A, the change of the cluster size negligibly affects the KSCED interaction energies. The KSCED formalism makes it possible to study directly the effects associated with relaxation of the surface's electron density upon adsorbing CO. It is shown that these effects might contribute up to 30% of the KSCED interaction energy, but that they do not result in significant changes of either the geometries or frequencies.

Although density functional theory (DFT) is more and more commonly used as a very efficient tool for the study of molecules and bulk materials, its applications to weakly bonded systems remain rather sparse in the literature, except studies that consider hydrogen bonding. It is, however, of essential interest to be able to correctly describe weaker van der Waals complexes. This prompted us to investigate more precisely the reliability of several widely-used functionals. The equilibrium geometries and the binding energies of C6H6···X (X = O2, N2, or CO) complexes are determined within the standard Kohn−Sham approach of DFT using different exchange−correlation functionals and at the MP2 level of theory for comparison. It is comprehensively concluded that extreme care must be taken in the choice of the functional since only those that behave properly at large and intermediate values of the reduced density gradient s give relevant results. The PW91 exchange functional, the enhancement factor of which does not diverge at increasing s, appears as the most reliable for the studied systems. It is furthermore demonstrated that the quality of the DFT results is determined by the exchange energy component of the total energy functional.

We analyze differences between ground-state electron densities of a model molecular complex obtained by solving the Kohn-Sham equations with constrained electron density (KSCED) [Wesolowski and Warshel, J. Phys. Chem. 97, 8050 (1993)] and as a solution of the standard Kohn-Sham equations applied to the whole complex. The differences between KSCED and KS electron densities which result from the inaccuracy of the kinetic energy functional applied in the KSCED equations are discussed. The model molecular complex consists of collinear H2 and HCN molecules separated by a short distance. Several kinetic energy functional approximations are applied within the KSCED framework and the differences between resulting electron densities are studied. The KSCED electron densities depend directly on the functional derivative of the kinetic energy functional applied in the KSCED equations. Among the studied functionals, the one proposed by Zhao et al. [Phys. Rev. A 47, 918 (1993)] and the gradient-dependent functional proposed by Perdew and Wang [Phys. Rev. B 33, 8800 (1986)] led to the smallest differences between KS and KSCED electron densities, thus having the most accurate functional derivative. Both functionals allow one to extend the range of applicability of the KSCED equations to system geometries where an overlap of electron densities of the partners of the complex is significant.

It is shown that for pairs of electron densities (ρagr and TMPH1165math001) obtained from mixing orbital densities in a spin-compensated four-electron system, the kinetic energy functional of the non-interacting reference system (Ts[ρ]) satisfies the general inequality TMPH1165math002. This condition is discussed in the context of the gradient expansion approximation to Ts[ρ] and its possible use in variational orbital-free calculations. In particular, it is shown that the second-order term of the analytic form given by von Weizsaumlcker violates this inequality for the considered pairs.

Approximations to the non-interacting kinetic energy Ts[ρ], which take the form of semilocal analytic expressions are collected. They are grouped according to the quantities on which they explicitly depend. Additionally, the approximations for quantities related to Ts[ρ] (kinetic potential and non-additive kinetic energy), for which the analytic expressions for the "parent" approximation for the functional Ts[ρ] are unknown, are also given.