Coupled cluster theory with the polarizable continuum model of solvation

The environment may significantly affect molecular properties. Thus, it is desirable to account explicitly for these effects on the wave function and its derivatives, especially when the latter are evaluated with accurate methods, such as those belonging to coupled cluster (CC) theory. In this tutorial review, we discuss how to combine CC methods with the polarizable continuum model of solvation (PCM). We describe useful approximations that include the solvent response to the correlation and excited state equations while maintaining the computational cost comparable to in vacuo calculations. Although applied to PCM, the theoretical framework presented in this review is general and can be used with any polarizable embedding model. Representative applications of the CC-PCM method to ground and excited state properties of solvated molecules are presented, and comparisons with experiment, and between the full and approximate schemes are discussed.     

Parallel variable selection of molecular dynamics clusters as a tool for calculation of spectroscopic properties

Clusters of a solute and a few solvent molecules obtained from molecular dynamics (MD) are a powerful tool to study solvation effects by advanced quantum chemical (QC) methods. For spectroscopic properties strongly dependent on the solvation, however, a large number of clusters are needed for a good convergence. In this work, a parallel variable selection (PVS) method is proposed that in some cases efficiently reduces the number of clusters needed for the averaging. The mass, charge, or atomic density MD distributions are used as a secondary variable to preselect the most probable cluster geometries used for averaging of solute spectral properties. When applied to nuclear magnetic resonance chemical shift of a model alcohol, the method allowed one to significantly reduce the total computational time, by a factor of 10. Even larger savings were achieved for the modeling of Raman and Raman optical activity spectra of (S)‐lactamide molecule dissolved in water. The results thus suggest that the PVS method can be generally used for simulations of spectroscopic properties of solvated molecules and makes multiscale MD/QC computations more affordable. © 2012 Wiley Periodicals, Inc.     

How to Predict Excited State Geometry by Using Empirical Parameters Obtained from Franck-Condon Analysis of Optical Spectrum

Excited state geometries of molecules can be calculated with highly reliable wavefunction schemes. Most of such schemes, however, are applicable to small molecules and can hardly be viewed as error-free for excited state geometries. In this study, a theoretical approach is presented in which the excited state geometries of molecules can be predicted by using vibrationally resolved experimental absorption spectrum in combination with the theoretical modelling of vibrational pattern based on Franck-Condon approximation. Huang-Rhys factors have been empirically determined and used as input for revealing the structural changes occurring between the ground and the excited state geometries upon photoexcitation. Naphthalene molecule has been chosen as a test case to show the robustness of the proposed theoretical approach. Predicted 1B_2u excited state geometry of the naphthalene has similar but slightly different bond length alternation pattern when compared with the geometries calculated with CIS, B3LYP, and CC2 methods. Excited state geometries of perylene and pyrene molecules are also determined with the presented theoretical approach. This powerful method can be applied to other molecules and specifically to relatively large molecules rather easily as long as vibrationally resolved experimental spectra are available to use.     

Understanding excited-state structure in metal polypyridyl complexes using resonance Raman excitation profiles,time-resolved resonance Raman spectroscopy and density functional theory

This article discusses the use of Raman spectroscopy, in concert with density functional theory, as a strategy for understanding excited-state structure in metal polypyridyl complexes. The first sections of the article discuss how one can use resonance Raman spectra of the ground-state molecule to understand the resonant Franck-Condon excited state. The theories behind these analyses are based on the sum-over-states and time-dependent approaches; a brief introduction to each of these methods is given. The use of density functional theory and its use in the determination of normal modes of vibration and infrared and Raman band intensities are discussed, with reference to a number of recent papers. The application of these methods is illustrated through the analysis of a number of selected examples which exemplify the strategies used to extract data from probing the Franck-Condon region. These data include the displacements of the resonant excited state with respect to the electronic ground state, the reorganisation energies associated with photoexcitation, bond length changes with excitation and other electronic parameters. The use, and limitations, of these methods are discussed. The direct calculation of resonance Raman band intensities is introduced. The direct measurement of excited-state vibrational spectra through time-resolved methods is discussed in the latter section of the article; with particular regard to the use of transient resonance Raman and time-resolved resonance Raman techniques to probe structural changes in metal polypyridyl complexes.     

Simultaneous resonance Raman optical activity involving two electronic states

In the present work, the first observation of strong resonance Raman optical activity (RROA) involving more that one resonant electronic state is reported. The chiral transition metal complex bis-(trifluoroacetylcamphorato) copper(II), abbreviated Cu(tfc)(2), exhibits both resonance Raman (RR) and RROA spectra with laser excitation at 532 nm. Vibrational assignments for this complex were carried out by comparing the non-RR spectra of Cu(tfc)(2) excited at 1024 nm to density functional theory (DFT) calculations. The theory of the single-electronic-state (SES) RROA is extended to the next simplest level of theory involving two resonant electronic states (TES) without interstate vibronic coupling as an aide to the interpretation of the observed TES-RROA spectra. Based on measured UV-vis electronic absorbance spectra and corresponding TD-DFT calculations, the most likely two states associated with the RROA spectra are identified.     

Peculiarities of the environmental influence on the optical properties of push-pull nonlinear optical molecules: a theoretical study

Gas-phase geometry optimization of NLO-active molecules is one of the standard approaches in the first principle computational methodology, whereas the important role of the environment is usually not considered during the evaluation of structural parameters. With a wide variety of environmentally influenced models in most cases only the high quality single point calculations are prepared. Among different approaches, the most used polarizable continuum model (PCM) seems to be promising. In this study, we have compared the electronic properties of gas-phase optimized geometries of imidazole-derived push-pull compounds with those optimized using PCM solvation approach including CH(2)Cl(2) and PMMA as media. We have focused particularly on the linear optical properties of investigated molecules, namely on the UV-vis absorption spectra. The analysis of presented results shows the applicability of the different quantum chemical (QC) methods for the UV-vis spectra calculations of linear NLO molecules. Herein we also present the need of molecule geometry optimization affected by the environment. Following the performed calculations, the electronic properties of gas-phase optimized molecules give conformable results with respect to those obtained by more time-consuming continuum optimizations. All computational data are supported by experimental investigations.     

Ab initio calculation of resonance Raman cross sections based on excited state geometry optimization

A method for the calculation of resonance Raman cross sections is presented on the basis of calculation of structural differences between optimized ground and excited state geometries using density functional theory. A vibrational frequency calculation of the molecule is employed to obtain normal coordinate displacements for the modes of vibration. The excited state displacement relative to the ground state can be calculated in the normal coordinate basis by means of a linear transformation from a Cartesian basis to a normal coordinate one. The displacements in normal coordinates are then scaled by root-mean-square displacement of zero point motion to calculate dimensionless displacements for use in the two-time-correlator formalism for the calculation of resonance Raman spectra at an arbitrary temperature. The method is valid for Franck-Condon active modes within the harmonic approximation. The method was validated by calculation of resonance Raman cross sections and absorption spectra for chlorine dioxide, nitrate ion, trans-stilbene, 1,3,5-cycloheptatriene, and the aromatic amino acids. This method permits significant gains in the efficiency of calculating resonance Raman cross sections from first principles and, consequently, permits extension to large systems (>50 atoms).     

Structural and spectral properties of 4-bromo-1-naphthyl chalcones: a quantum chemical study

The structural and optical properties of 4-bromo-1-naphthyl chalcones (BNC) have been studied by using quantum chemical methods. The density functional theory (DFT) and the singly excited configuration interaction (CIS) methods were employed to optimize the ground and excited state geometries of unsubstituted and substituted BNC with different electron withdrawing and donating groups in both gas and solvent phases. Based on the ground and excited state geometries, the absorption and emission spectra of BNC molecules were calculated using the time-dependent density functional theory (TDDFT) method. The solvent phase calculations were performed using the polarizable continuum model (PCM). The geometrical parameters, vibrational frequencies, and relative stability of cis- and trans-isomers of unsubstituted and substituted BNC molecules have been studied. The results from the TDDFT calculations reveal that the substitution of electron withdrawing and electron donating groups affects the absorption and emission spectra of BNC.     

Electronic g-tensors of solvated molecules using the polarizable continuum model

We present the implementation of density functional response theory combined with the polarizable continuum model (PCM), enabling first principles calculations of molecular g-tensors of solvated molecules. The calculated g-tensor shifts are compared with experimental g-tensor shifts obtained from electron paramagnetic resonance spectra for a few solvated species. The results indicate qualitative agreement between the calculations and the experimental data for aprotic solvents, whereas PCM fails to reproduce the electronic g-tensor behavior for protic solvents. This failure of PCM for protic solvents can be resolved by including into the model those solvent molecules which are involved in hydrogen bonding with the solute. The results for the protic solvents show that the explicit inclusion of the solvent molecules of the first solvation sphere is not sufficient in order to reproduce the behavior of the electronic g-tensor in protic solvents, and that better agreement with experimental data can be obtained by including the long-range electrostatic effects accounted for by the PCM approach on top of the explicit hydrogen-bonded complexes.     

Preparation and dynamics of vibrational hot spots in polyatomics via raman scttering

We exploit a recent time dependent formulation of resonance Raman scattering to examine vibrational hot spot production in molecules which have dissociative excited states. The excited-state dynamics are described by a Raman wavefunction which is used to obtain the resonance Raman (RR) spectrum. The RR spectrum will contain the spectral signature of the subsequent dynamics and decay of the hot spot initial condition.     

Ground and excited state resonance Raman spectra of an azacrown-substituted [(bpy)Re(CO)3L]+ complex: characterization of excited states, determination of structure and bonding, and observation of metal cation release from the azacrown

A [(bpy)Re(CO)3L+] complex (bpy = 2,2'-bipyridine) in which L contains a phenyl-azacrown ether that is attached to Re via an amidopyridyl linking group has been studied by steady state and nanosecond time-resolved resonance Raman spectroscopy. Vibrational band assignments have been aided by studies of model complexes in which a similar electron-donating dimethylamino group replaces the azacrown or in which an electron-donor group is absent, and by density functional theory calculations. The ground state resonance Raman spectra show nu(bpy) and nu(CO) bands of the (bpy)Re(CO)3 group when excitation is exclusively in resonance with the Re --> bpy metal-to-ligand charge-transfer (MLCT) transition, whereas L ligand bands are dominant when it is in resonance with the strong intra-ligand charge-transfer (ILCT) transition present for L ligands with electron-donor groups. Transient resonance Raman (RR) spectra obtained on single color (385 nm) pulsed excitation of the complexes in which an electron-donor group is absent show bpy*- bands of the MLCT excited state, whereas those of the complexes with electron-donor groups show both bpy*- bands and a down-shifted nu(CO) band that together are characteristic of an L-to-bpy ligand-to-ligand charge-transfer (LLCT) excited state. Samples in which a metal cation (Li+, Na+, Ca2+, Ba2+) is bound to the azacrown in the ground state show bands from both excited states, consistent with a mechanism in which the LLCT state forms after metal cation release from the MLCT state. Nanosecond time-resolved RR spectra from two-color (355 nm pump, 500 nm probe) experiments on the electron-donor systems show L-ligand bands characteristic of the LLCT state; the same bands are observed from samples in which a metal cation is bound to the azacrown in the ground state, and their time dependence is consistent with the proposed mechanism in which the rate constant for ion release in the MLCT state depends on the identity of the metal cation.     

Probing the excited states of Ru(II) complexes with dipyrido[2,3-a:3',2'-c]phenazine: a transient resonance raman spectroscopy and computational study

The lifetimes and transient resonance Raman spectra for Ru(II) complexes with the dipyrido[2,3-a:3',2'-c]phenazine (ppb) ligand and substituted analogues have been measured. The effect of altering the Ru(II) center ([Ru(CN)4]2- versus [Ru(bpy)2]2+), of the complex, on the excited-state lifetimes and spectra has been considered. For [Ru(bpy)2L]2+ complexes the excited-state lifetimes range from 124 to 600 ns in MeCN depending on the substituents on the ppb ligand. For the [Ru(CN)4L]2- complexes the lifetimes in H2O are approximately 5 ns. The transient resonance Raman spectra for the MLCT excited states of these complexes have been measured. The data are analyzed by comparison with the resonance Raman spectra of the electrochemically reduced [(PPh3)2Cu(mu-L*-)Cu(PPh3)2]+ complexes. The vibrational spectra of the complexes have been modeled using DFT methods. For experimental ground-state vibrational spectra of the complexes the data may be compared to calculated spectra of the ligand or metal complex. It is found that the mean absolute deviation between experimental and calculated frequencies is less for the calculation on the respective metal complexes than for the ligand. For the transient resonance Raman spectra of the complexes the observed vibrational bands may be compared with those of the calculated ligand radical anion, the reduced complex [Ru(CN)4L*-]3-, or the triplet state of the complex. In terms of a correlation with the observed transient RR spectra, calculations on the metal complex models offered no significant improvement compared to those based on the ligand radical anion alone. In all cases small structural changes are predicted on going from the ground to excited state.     

Density functional theory studies on the structure,spectra (FT-IR,FT-Raman,and UV) and first order molecular hyperpolarizability of 2-hydroxy-3-methoxy-N-(2-chloro-benzyl)-benzaldehyde-imine: Comparison to experimental data

The infrared and Raman spectra of 2-hydroxy-3-methoxy-N-(2-chloro-benzyl)-benzaldehyde-imine (HMCBI) have been recorded and analyzed. Density functional calculations at B3LYP/6-311++G(d,p) level were carried out to study the equilibrium geometries and vibrational spectra of HMCBI. The calculations revealed that the optimized geometry closely resembled the experimental XRD data. The calculated vibrational spectra were analyzed on the basis of the potential energy distribution (PED) of each vibrational mode, which allowed us to obtain a quantitative as well as qualitative interpretation of IR and Raman spectra. The ¹H nuclear magnetic resonance (NMR) chemical shifts of the molecule in the ground state were calculated by Gauge independent atomic orbital (GIAO) method. Information about size, shape, charge density distribution and site of chemical reactivity of the molecules has been obtained by mapping electron density isosurface with electrostatic potential surface. Based on optimized ground state geometries, the NBO analysis has been done to study donor–acceptor (bond–antibond) interactions. The TD-DFT method has been used to calculate energies, oscillator strengths of electronic singlet–singlet transitions and the absorption wavelengths. Solvent effects were considered using the polarizable continuum model (PCM). Good consistency is found between the calculated results and experimental data for the electronic absorption. The calculated first hyperpolarizability may be attractive for further studies on non-linear optical properties of materials.     

Resonance Raman scattering of rhodamine 6G as calculated by time-dependent density functional theory: vibronic and solvent effects

The geometries, UV-vis absorption spectra, and resonance Raman (RR) intensities have been determined for the S1 and S3 excited states of rhodamine 6G (R6G) in vacuum and ethanol by means of DFT/TDDFT methodologies with the aim of better understanding the structures and properties of the excited states. The RR spectra have been simulated from the vibronic theory of RR scattering as well as within the short-time approximation, while the solvent effects have been modeled using the polarizable continuum model. The S1 and S3 states of R6G present UV-vis absorption bands with similar vibronic structure, i.e., a shoulder at smaller wavelengths, although this shoulder is relatively more intense and more sensitive to the solvent in the case of S3. These differences are corroborated by the larger geometry relaxations upon excitation for S3 and the fact that the charge transfer of S3 is reduced in ethanol. Moreover, the differences between S1 and S3 are magnified when considering the RR spectra. On one hand, the RR spectrum of R6G in resonance with the S0 --> S1 transition presents many transitions of which the relative intensities strongly vary when the excitation wavelength gets closer to the maximum of absorption. The RR spectrum of R6G in resonance with S1 is however little influenced by the solvent. On the other hand, the RR spectrum of R6G in resonance with the S0 --> S3 transition displays only a few bands, strongly depends on the solvent, and is little affected when changing the excitation wavelength within the limits of the absorption band. As a consequence, the short-time approximation is suitable to reproduce the RR spectrum of R6G in resonance with S3 for a broad range of excitation wavelengths, whereas the vibronic theory approach is needed for describing the RR spectrum of R6G in resonance with S1 close to resonance.     

尿嘧啶和5-氯尿嘧啶1S0→1S2跃迁动态结构的共振拉曼光谱

采用含时量子波包理论的简单模型对5-氯尿嘧啶和尿嘧啶的共振拉曼光谱开展了强度分析拟合, 获得了1(π, π*)激发态的几何结构变化动态特征. 结果表明, 尿嘧啶1S0→1S2跃迁的动态结构特征因5-位氯原子取代而改变. 5-氯尿嘧啶的动态结构特征主要沿C5=C6伸缩振动+C6H12 弯曲振动和N3H9/N1H7弯曲振动+N1C6伸缩振动反应坐标展开, 而尿嘧啶的动态结构特征主要沿嘧啶环的伸缩振动+C5H11/C6H12/N1H7弯曲振动和C4=O10伸缩振动反应坐标展开. π和π*轨道中氯原子的pz电子参与嘧啶环的p-π共轭作用导致了在1(π, π*)激发态上5-氯尿嘧啶的振动重组能更多地配分给嘧啶环的弯曲振动模式和C5=C6伸缩振动模式. 尿嘧啶在甲醇中的激发态动态结构特征与在水中的基本一致, 但波包沿C5H11/C6H12/N1H7弯曲振动+N1C6伸缩振动(υ12)和环呼吸振动(υ17)反应坐标的运动明显增强.     

Structure and dynamics of the solvated electron in alcohols from resonance Raman spectroscopy

Resonance Raman (RR) spectroscopy is used to probe the structure and excited-state dynamics of the solvated electron in the primary liquid alcohols methanol (MeOH), ethanol (EtOH), n-propanol (n-PrOH), and n-butanol (n-BuOH). The strong resonance enhancements (>or=10(4) relative to pure solvent) of the libration, CO stretch, COH bend, CH3 bend, CH2 bend, and OH stretch reveal significant Franck-Condon coupling of the intermolecular and intramolecular vibrational modes of the solvent to the electronic excitation of the solvated electron. All enhanced bands are fully accounted for by a model of the solvated electron that is comprised of several nearby solvent molecules that are only perturbed by the presence of the electron; no new molecular species are required to explain our data. The 340 cm(-1) downshift observed for the OH stretch frequency of e-(MeOH), relative to pure solvent, strongly suggests that the methanol molecules in the first solvent shell have the hydroxyl group directed linearly toward the excess electron density. The smaller downshifts observed for e-(EtOH), e-(n-PrOH), and e-(n-BuOH) are explained in terms of a OH group that is bent 28-40 degrees from linear. The Raman cross sections and absorption spectra are modeled, lending quantitative support for the inhomogeneous origin of the broad absorption spectra, the necessity of OH local motion in all enhanced Raman modes of the alcohols, and the dominant librational response of the solvent upon photoexcitation of the electron.     

Interpretation of unusual absorption bandwidths and resonance Raman intensities in excited state mixed valence

Excited state mixed valence (ESMV) occurs in molecules in which the ground state has a symmetrical charge distribution but the excited state possesses two or more interchangeably equivalent sites that have different formal oxidation states. Although mixed valence excited states are relatively common in both organic and inorganic molecules, their properties have only recently been explored, primarily because their spectroscopic features are usually overlapped or obscured by other transitions in the molecule. The mixed valence excited state absorption bands of 2,3-di-p-anisyl-2,3-diazabicyclo[2.2.2]octane radical cation are well-separated from others in the absorption spectrum and are particularly well-suited for detailed analysis using the ESMV model. Excited state coupling splits the absorption band into two components. The lower energy component is broader and more intense than the higher energy component. The absorption bandwidths are caused by progressions in totally symmetric modes, and the difference in bandwidths is caused by the coordinate dependence of the excited state coupling. The Raman intensities obtained in resonance with the high and low energy components differ significantly from those expected based on the oscillator strengths of the bands. This unexpected observation is a result of the excited state coupling and is explained by both the averaging of the transition dipole moment orientation over all angles for the two types of spectroscopies and the coordinate-dependent coupling. The absorption spectrum is fit using a coupled two-state model in which both symmetric and asymmetric coordinates are included. The physical meaning of the observed resonance Raman intensity trends is discussed along with the origin of the coordinate-dependent coupling. The well-separated mixed valence excited state spectroscopic components enable detailed electronic and resonance Raman data to be obtained from which the model can be more fully developed and tested.     

Ab initio tools for the accurate prediction of the visible spectra of anthraquinones

The UV/vis absorption spectra of 101 anthraquinones solvated in two protic solvents (methanol and ethanol) has been theoretically predicted using the time-dependent density functional theory (TD-DFT) for the excited state calculations and the polarizable continuum model (PCM) for evaluating bulk solvent effects. Two functionals (B3LYP and PBE0) have been used and they provide similar mean absolute deviations (approximately 0.09 eV) but mean signed errors presenting opposite signs. The errors can be minimized by using simple or multiple linear regression, the latter combining the results of both functionals to reach an optimal estimation of the lambda(max) (mean absolute error 0.06 eV). Specific fittings for the two media have been performed and it turned out that our approach is even more efficient for anthraquinones solvated in ethanol.