Density functional self-consistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties: Applications to solvated water and formaldehyde

A combined quantum mechanics/molecular mechanics (QM/MM) method is described, where the polarization between the solvent and solute is accounted for using a self-consistent scheme linear in the solvent polarization. The QM/MM method is implemented for calculation of energies and molecular response properties including the calculation of linear and quadratic response functions using the density-functional theory (DFT) and the Hartree-Fock (HF) theory. Sample calculations presented for ground-state energies, first-order ground-state properties, excitation energies, first-order excited state properties, polarizabilities, first-hyperpolarizabilities, and two-photon absorptions strengths of formaldehyde suggests that DFT may in some cases be a sufficiently reliable alternative to high-level theory, such as coupled-cluster (CC) theory, in modeling solvent shifts, whereas results obtained with the HF wave function deviate significantly from the CC results. Calculations carried out on water gives results that also are comparable with CC calculations in accuracy for ground-state and first-order properties. However, to obtain such accuracy an exchange-correlation functional capable of describing the diffuse Rydberg states must be chosen.     

Coupled cluster calculation of the n --> pi* electronic transition of acetone in aqueous solution

The combined linear response coupled cluster/molecular mechanics (CC/MM) scheme including mutual polarization effects in the coupling Hamiltonian is applied together with supermolecular CC methods to the study of the gas-to-aqueous solution blue shift of the n --> pi* excitation energy in acetone. The aug-cc-pVDZ basis set is found to be adequate for the calculation of this excitation energy. In the condensed phase, the shift in the excitation energy is obtained by statistical averaging over 800 solute-solvent configurations extracted from a molecular dynamics simulation. We find the shift to be around 1100-1200 cm(-1) depending on the specific model used to describe solvent polarization. The importance of including explicit polarization in both the molecular dynamics simulation as well as the CC/MM calculations is emphasized. Furthermore, the significant dependence of the excitation energy on the CO bond length of acetone is discussed.     

Calculations of nonlinear response properties using the intermediate state representation and the algebraic-diagrammatic construction polarization propagator approach: two-photon absorption spectra

An earlier proposed approach to molecular response functions based on the intermediate state representation (ISR) of polarization propagator and algebraic-diagrammatic construction (ADC) approximations is for the first time employed for calculations of nonlinear response properties. The two-photon absorption (TPA) spectra are considered. The hierarchy of the first- and second-order ADC∕ISR computational schemes, ADC(1), ADC(2), ADC(2)-x, and ADC(3/2), is tested in applications to H(2)O, HF, and C(2)H(4) (ethylene). The calculated TPA spectra are compared with the results of coupled cluster (CC) models and time-dependent density-functional theory (TDDFT) calculations, using the results of the CC3 model as benchmarks. As a more realistic example, the TPA spectrum of C(8)H(10) (octatetraene) is calculated using the ADC(2)-x and ADC(2) methods. The results are compared with the results of TDDFT method and earlier calculations, as well as to the available experimental data. A prominent feature of octatetraene and other polyene molecules is the existence of low-lying excited states with increased double excitation character. We demonstrate that the two-photon absorption involving such states can be adequately studied using the ADC(2)-x scheme, explicitly accounting for interaction of doubly excited configurations. Observed peaks in the experimental TPA spectrum of octatetraene are assigned based on our calculations.     

Hybrid density functional theory/molecular mechanics calculations of two-photon absorption of dimethylamino nitro stilbene in solution

The dimethylamino nitro stilbene (DANS) molecule is studied for exploring solvent effects on two-photon absorption using the quantum mechanical/molecular mechanical (QM/MM) response theory approach, where the quantum part is represented by density functional theory. We have explored the role of geometrical change of the chromophore in solution, the importance of taking a dynamical average over the sampled structures and the role of a granular representation of the polarization and electrostatic interactions with the classically described medium. The line shape function was simulated by the QM/MM technique thereby allowing for non-empirical prediction of the absolute two-photon cross section. We report a maximum in the TPA cross section for a medium of intermediate solvent polarity (i.e. in chloroform) and provide the grounds for an explanation of this effect which recently has been experimentally observed for a series of charge transfer species in solvents of different polarity. The calculations of absorption energies reproduce well the positive solvatochromic behavior of DANS and are in good agreement with experimental spectra available for the chloroform and DMSO solvents. In line with recent development of the QM/MM response technique for color modeling, we find this methodology to offer a versatile tool to predict and analyze two-photon absorption phenomena taking place within a medium.     

Effects of conjugation length and resonance enhancement on two-photon absorption in phenylene-vinylene oligomers

Two-photon excitation spectra have been recorded over the large spectral range of 540-1000 nm for five phenylene-vinylene oligomers that differ in the length of the conjugated pi system. The significant changes observed in the two-photon excitation spectra and absorption cross sections as a function of this systematic change in the chromophore are discussed in light of (1) the corresponding one-photon absorption spectra and (2) high-level density functional response theory calculations performed on analogues of these systems. The results obtained illustrate one way to exploit parameters that influence nonlinear optical properties in large organic molecules. Specifically, data are provided to indicate that when the frequency of the laser used in the two-photon experiment is nearly-resonant with an allowed one-photon transition, significant increases in the two-photon absorption cross section can be realized. This phenomenon of the so-called resonance enhancement allows for greater control in obtaining an optimal response when using existing two-photon chromophores, and provides a much-needed guide for the systematic development and efficient use of two-photon singlet oxygen sensitizers.     

Two-photon absorption in tetraphenylporphycenes: are porphycenes better candidates than porphyrins for providing optimal optical properties for two-photon photodynamic therapy?

Porphycenes are structural isomers of porphyrins that have many unique properties and features. In the present work, the resonant two-photon absorption of 2,7,12,17-tetraphenylporphycene (TPPo) and its palladium(II) complex (PdTPPo) has been investigated. The data obtained are compared to those from the isomeric compound, meso-tetraphenylporphyrin (TPP). Detection of phosphorescence from singlet molecular oxygen, O2(a(1)Delta(g)), produced upon irradiation of these compounds, was used to obtain two-photon excitation spectra and to quantify two-photon absorption cross sections, delta. In the spectral region of 750-850 nm, the two-photon absorption cross sections at the band maxima for both TPPo and PdTPPo, delta = 2280 and 1750 GM, respectively, are significantly larger than that for TPP. This difference is attributed to the phenomenon of so-called resonance enhancement; for the porphycenes, the two-photon transition is nearly resonant with a comparatively intense one-photon Q-band transition. The results of quantum mechanical calculations using density functional quadratic response theory are in excellent agreement with the experimental data and, as such, demonstrate that comparatively high-level quantum chemical methods can be used to interpret and predict nonlinear optical properties from such large molecular systems. One important point realized through these experiments and calculations is that one must exercise caution when using qualitative molecular-symmetry-derived arguments to predict the expected spectral relationship between allowed one- and two-photon transitions. From a practical perspective, this study establishes that, in comparison to porphyrins and other tetrapyrrolic macrocyclic systems, porphycenes exhibit many desirable attributes for use as sensitizers in two-photon initiated photodynamic therapy.     

Solvent effects on two-photon absorption of dialkylamino substituted distyrylbenzene chromophore

Solvent effects on the two-photon absorption of a symmetrical diamino substituted distyrylbenzene chromophore have been studied using the density functional response theory in combination with the polarizable continuum model. It is shown that the dielectric medium has a rather small effect both on the bond length alternation and on the one-photon absorption spectrum, but it affects significantly the two-photon absorption cross section. It is found that both one- and two-photon absorptions are extremely sensitive to the planarity of the molecule, and the absorption intensity can be dramatically reduced by the conformation distortion. It has led to the conclusion that the experimentally observed anomalous solvent effect on the two-photon absorption of dialkylamino substituted distyrylbenzene chromophores cannot be attributed to the intrinsic properties of a single molecule and its interaction with solvents.     

两类以芴为中心的有机分子双光子吸收特性

在密度泛函理论水平上, 利用响应函数方法研究了实验新合成的两类以芴为π中心的分子(SK-G1和NT-G1)的双光子吸收特性. 计算结果表明, 这两类有机分子都具有较大的单光子和双光子光吸收强度. 在低能量范围内, NT-G1分子的最大单光子吸收峰相对于SK-G1分子来说发生了红移, 且其最大单光子吸收强度是SK-G1分子的两倍. SK-G1和NT-G1分子的最大双光子吸收均发生在第二激发态. NT-G1分子的最大双光子吸收截面约是SK-G1分子的五倍, 并且NT-G1分子存在一个较宽的双光子吸收带. NT-G1分子的较强光学性质与分子内较大的电荷转移过程有关. 采用Onsager模型计算了溶剂分子对溶质分子单光子吸收性质的影响, 理论计算结果和实验测量结果符合得较好.     

Two-photon excitation spectroscopy of phenanthrene singlet states below 50000 cm−1

The two-photon excitation spectrum of phenanthrene in liquid solution is reported in the energy range 29000–49000 cm^?1. Comparison with the one-photon spectrum and extended CNDO/S calculations allows assignment of eight singlet states. The strongest two-photon band is assigned to the B_b state not seen directly in the UV spectrum. This high intensity and other features of the spectrum are in sharp contrast to the pairing selection rules which forbid two-proton transitions to “plus” states in alternate hydrocarbons.     

Statistical mechanically averaged molecular properties of liquid water calculated using the combined coupled cluster/molecular dynamics method

Liquid water is investigated theoretically using combined molecular dynamics (MD) simulations and accurate electronic structure methods. The statistical mechanically averaged molecular properties of liquid water are calculated using the combined coupled cluster/molecular mechanics (CC/MM) method for a large number of configurations generated from MD simulations. The method includes electron correlation effects at the coupled cluster singles and doubles level and the use of a large correlation consistent basis set. A polarizable force field has been used for the molecular dynamics part in both the CC/MM method and in the MD simulation. We describe how the methodology can be optimized with respect to computational costs while maintaining the quality of the results. Using the optimized method we study the energetic properties including the heat of vaporization and electronic excitation energies as well as electric dipole and quadrupole moments, the frequency dependent electric (dipole) polarizability, and electric-field-induced second harmonic generation first and second hyperpolarizabilities. Comparisons with experiments are performed where reliable data are available. Furthermore, we discuss the important issue on how to compare the calculated microscopic nonlocal properties to the experimental macroscopic measurements.     

Theoretical Studies on One-photon and Two-photon Absorption Properties of Pyrene-core Derivatives

The analytic response theory at density functional theory level is applied to investigate one-photon and two-photon absorption properties of a series of recently synthesized pyrene-core derivatives. The theoretical results show that there are a few charge-transfer states for each compound in the lower energy region. The one-photon absorption properties of the five investigated compounds are highly consistent with those given by experimental measure-ments. The two-photon absorption intensities of the compounds are greatly enhanced with the increments of the molecular sizes, in which the two-photon absorption cross section of the four-branched compound is about 5.6 times of that of the mono-branched molecule. Further-more, it is shown that the two-photon absorption properties are sensitive to the geometrical arrangements.     

Methodological aspects of QM/MM calculations: A case study on matrix metalloproteinase‐2

We address methodological issues in quantum mechanics/molecular mechanics (QM/MM) calculations on a zinc‐dependent enzyme. We focus on the first stage of peptide bond cleavage by matrix metalloproteinase‐2 (MMP‐2), that is, the nucleophilic attack of the zinc‐coordinating water molecule on the carbonyl carbon atom of the scissile fragment of the substrate. This step is accompanied by significant charge redistribution around the zinc cation, bond cleavage, and bond formation. We vary the size and initial geometry of the model system as well as the computational protocol to demonstrate the influence of these choices on the results obtained. We present QM/MM potential energy profiles for a set of snapshots randomly selected from QM/MM‐based molecular dynamics simulations and analyze the differences in the computed profiles in structural terms. Since the substrate in MMP‐2 is located on the protein surface, we investigate the influence of the thickness of the water layer around the enzyme on the QM/MM energy profile. Thin water layers (0–2 Å) give unrealistic results because of structural reorganizations in the active‐site region at the protein surface. A 12 Å water layer appears to be sufficient to capture the effect of the solvent; the corresponding QM/MM energy profile is very close to that obtained from QM/MM/SMBP calculations using the solvent macromolecular boundary potential (SMBP). We apply the optimized computational protocol to explain the origin of the different catalytic activity of the Glu116Asp mutant: the energy barrier for the first step is higher, which is rationalized on structural grounds. © 2016 Wiley Periodicals, Inc.     

One- and two-photon photosensitized singlet oxygen production: characterization of aromatic ketones as sensitizer standards

Singlet molecular oxygen, O2(a1Deltag), can be efficiently produced in a photosensitized process using either one- or two-photon irradiation. The aromatic ketone 1-phenalenone (PN) is an established one-photon singlet oxygen sensitizer with many desirable attributes for use as a standard. In the present work, photophysical properties of two other aromatic ketones, pyrene-1,6-dione (PD) and benzo[cd]pyren-5-one (BP), are reported and compared to those of PN. Both PD and BP sensitize the production of singlet oxygen with near unit quantum efficiency in a nonpolar (toluene) and a polar (acetonitrile) solvent. With their more extensive pi networks, the one-photon absorption spectra for PD and BP extend out to longer wavelengths than that for PN, thus providing increased flexibility for sensitizer excitation over the range approximately 300-520 nm. Moreover, PD and BP have much larger two-photon absorption cross sections than PN over the range 655-840 nm which, in turn, results in amounts of singlet oxygen that are readily detected in optical experiments. One- and two-photon absorption spectra of PD and BP obtained using high-level calculations model the salient features of the experimental data well. In particular, the ramifications of molecular symmetry are clearly reflected in both the experimental and calculated spectra. The use of PD and BP as standards for both the one- and two-photon photosensitized production of singlet oxygen is expected to facilitate the development of new sensitizers for application in singlet-oxygen-based imaging experiments.     

Spectroscopy of UO(2)Cl(4)(2)(-) in basic aluminum chloride-1-ethyl-3-methylimidazolium chloride

The optical absorption, emission, FT Raman, one-photon excitation, two-photon excitation, and luminescence lifetime measurements are reported for UO(2)Cl(4)(2)(-) in 40:60 AlCl(3)-EMIC (where EMIC identical with 1-ethyl-3-methylimidazolium chloride), a room-temperature ionic liquid. Comparison of the spectra with previous results from single crystals containing UO(2)Cl(4)(2)(-) allowed the characterization of four ground-state vibrational frequencies, two excited-state vibrational frequencies, and the location of eight electronic excited-state energy levels. The vibrational frequencies and electronic energy levels are found to be consistent with the UO(2)Cl(4)(2)(-) ion. Comparison of the one-photon and two-photon excitation spectra, and the relative intensities of the transitions in the emission spectrum indicate that the center of symmetry is perturbed by an interaction with the solvent.     

Toward a consistent treatment of polarization in model QM/MM calculations

The concept of model chemistries within hybrid QM/MM calculations has been addressed through analysis of the polarization energy determined by two distinct approaches based on (i) induced charges and (ii) induced dipoles. The quantum mechanical polarization energy for four configurations of the water dimer has been determined for a range of basis sets using Morokuma energy decomposition analysis. This benchmark value has been compared to the fully classical polarization energy determined using the induced dipole approach, and the molecular mechanics polarization energy calculated using induced charges within the MM region of hybrid QM/MM calculations. From the water dimer calculations, it is concluded that the induced charge approach is consistent with medium sized basis set calculations whereas the induced dipole approach is consistent with large basis set calculations. This result is highly relevant to the concept of QM/MM model chemistries.     

Solvent effect on the absorption spectra of coumarin 120 in water: A combined quantum mechanical and molecular mechanical study

The solvent effect on the absorption spectra of coumarin 120 (C120) in water was studied utilizing the combined quantum mechanical∕molecular mechanical (QM∕MM) method. In molecular dynamics (MD) simulation, a new sampling scheme was introduced to provide enough samples for both solute and solvent molecules to obtain the average physical properties of the molecules in solution. We sampled the structure of the solute and solvent molecules separately. First, we executed a QM∕MM MD simulation, where we sampled the solute molecule in solution. Next, we chose random solute structures from this simulation and performed classical MD simulation for each chosen solute structure with its geometry fixed. This new scheme allowed us to sample the solute molecule quantum mechanically and sample many solvent structures classically. Excitation energy calculations using the selected samples were carried out by the generalized multiconfigurational perturbation theory. We succeeded in constructing the absorption spectra and realizing the red shift of the absorption spectra found in polar solvents. To understand the motion of C120 in water, we carried out principal component analysis and found that the motion of the methyl group made the largest contribution and the motion of the amino group the second largest. The solvent effect on the absorption spectrum was studied by decomposing it in two components: the effect from the distortion of the solute molecule and the field effect from the solvent molecules. The solvent effect from the solvent molecules shows large contribution to the solvent shift of the peak of the absorption spectrum, while the solvent effect from the solute molecule shows no contribution. The solvent effect from the solute molecule mainly contributes to the broadening of the absorption spectrum. In the solvent effect, the variation in C-C bond length has the largest contribution on the absorption spectrum from the solute molecule. For the solvent effect on the absorption spectrum from the solvent molecules, the solvent structure around the amino group of C120 plays the key role.     

The two-photon excitation cross section of 6MAP, a fluorescent adenine analogue

6MAP is a fluorescent analogue of adenine that undergoes Watson-Crick base pairing and base stacking in double-stranded DNA. The one-photon absorption spectrum of 6MAP is characterized by a maximum around 330 nm with moderate quantum yield fluorescence centered at about 420 nm. To take advantage of this probe for confocal and single-molecule microscopy, it would be advantageous to be able to excite the analogue via two photons. We report the first determination of the two-photon excitation cross section and spectrum for 6MAP from 614 to 700 nm. The power dependence of the fluorescence indicates that emission results from the absorption of two photons. The one-photon and two-photon emission line shapes are identical within experimental error. A study of the concentration dependence of the fluorescence yield for one-photon excitation shows no measurable quenching up to about 5 microM. The maximum in the two-photon excitation spectrum gives a two-photon cross section, delta(TPE), of 3.4 +/- 0.1 Goeppert-Mayer (G.M.) at 659 nm, which correlates well with the one-photon absorption maximum. This compares quite favorably with cross sections of various naturally fluorescent biological molecules such as flavins and nicotiamide. In addition, we have also obtained the two-photon-induced fluorescence emission spectrum of quinine sulfate. It is approximately the same as that for one-photon excitation, suggesting that two-photon excitation of quinine sulfate may be used for calibration purposes.