Calculated Transition Energies Research Articles

The effect of ruthenium on the performance of porphyrin dye and porphyrin–fullerene dyad solar cells predicted by DFT and TD-DFT calculations

The effect of ruthenium on the performance of porphyrin dye and porphyrin–fullerene (PF) dyad solar cells is investigated by using density functional theory and time-dependant density functional theory calculations. The results reveal that ruthenium facilitates rapid electron injection from porphyrin to fullerene, narrows the band gaps of porphyrin dye and PF dyad and alters the density of states near the corresponding Fermi levels. The HOMOs are localised on the donor moieties and the LUMOs on the acceptor moieties. The donor and acceptor dyads form good donor–acceptor pairs for photo-to-current conversion under the effect of ruthenium. HOMOs of porphyrin and ruthenium metalloporphyrin dyes fall within the (TiO2)60 and Ti38O76 gaps, and support the issue of typical interfacial electron transfer reaction. The calculated transition energies of porphyrin are almost insensitive to ethanol solvent effects. The introduction of ruthenium to the porphyrin ring leads to more active nonlinear optical performance, stronger response to the external electric field and induces higher photo-to-current conversion efficiency. Moreover, ruthenium shifts the absorption bands of porphyrin and makes it a potential candidate for harvesting light for photovoltaic applications.

A comparison between state-specific and linear-response formalisms for the calculation of vertical electronic transition energy in solution with the CCSD-PCM method

The calculation of vertical electronic transition energies of molecular systems in solution with accurate quantum mechanical methods requires the use of approximate and yet reliable models to describe the effect of the solvent on the electronic structure of the solute. The polarizable continuum model (PCM) of solvation represents a computationally efficient way to describe this effect, especially when combined with coupled cluster (CC) methods. Two formalisms are available to compute transition energies within the PCM framework: State-Specific (SS) and Linear-Response (LR). The former provides a more complete account of the solute-solvent polarization in the excited states, while the latter is computationally very efficient (i.e., comparable to gas phase) and transition properties are well defined. In this work, I review the theory for the two formalisms within CC theory with a focus on their computational requirements, and present the first implementation of the LR-PCM formalism with the coupled cluster singles and doubles method (CCSD). Transition energies computed with LR- and SS-CCSD-PCM are presented, as well as a comparison between solvation models in the LR approach. The numerical results show that the two formalisms provide different absolute values of transition energy, but similar relative solvatochromic shifts (from nonpolar to polar solvents). The LR formalism may then be used to explore the solvent effect on multiple states and evaluate transition probabilities, while the SS formalism may be used to refine the description of specific states and for the exploration of excited state potential energy surfaces of solvated systems.

Vertical Electronic Excitations in Solution with the EOM-CCSD Method Combined with a Polarizable Explicit/Implicit Solvent Model.

The accurate calculation of electronic transition energies and properties of isolated chromophores is not sufficient to provide a realistic simulation of their excited states in solution. In fact, the solvent influences the solute geometry, electronic structure, and response to external fields. Therefore, a proper description of the solvent effect is fundamental. This can be achieved by combining polarizable explicit and implicit representations of the solvent. The former provides a realistic description of solvent molecules around the solute, while the latter introduces the electrostatic effect of the bulk solution and reduces the need of too large a number of explicit solvent molecules. This strategy is particularly appealing when an accurate method such as equation of motion coupled cluster singles and doubles (EOM-CCSD) is employed for the treatment of the chromophore. In this contribution, we present the coupling of EOM-CCSD with a fluctuating charges (FQ) model and polarizable continuum model (PCM) of solvation for vertical excitations in a state-specific framework. The theory, implementation, and prototypical applications of the method are presented. Numerical tests on small solute-water clusters show very good agreement between full EOM-CCSD and EOM-CCSD-FQ calculations, with and without PCM, with differences ≤ 0.1 eV. Additionally, approximated schemes that further reduce the computational cost of the method are introduced and showed to perform well compared to the full method (errors ≤ 0.1 eV).

Transition energies of theDlines in Na-like ions

The NIST electron beam ion trap (EBIT) was used to measure the ${D}_{1}$(3$s$-3${p}_{1/2}$) and ${D}_{2}$(3$s$-3${p}_{3/2}$) transitions in Na-like ions of xenon, barium, samarium, gadolinium, dysprosium, erbium, tungsten, platinum, and bismuth. The wavelengths are in the range 3--12 nm. Relativistic many-body perturbation theory calculations were carried out for the ${D}_{1}$ and ${D}_{2}$ lines for every element in the isoelectronic sequence from argon ($Z$ $=$ 18) to uranium ($Z$ $=$ 92), taking into account some higher-order terms in the quantum electrodynamics (QED) expansion. Uncertainties in the calculated values were carefully assessed by considering the uncertainties in the various contributions to the total calculated transition energies. We conclude that at the current level of accuracy, the calculated values can be taken to reliably represent the isoelectronic sequence from $Z$ $=$ 18 to 92. The agreement of theory and experiment for the ${D}_{1}$ line of bismuth ($Z$ $=$ 83) provides a test of QED at the level of 0.4$%$. Our results are also sensitive to retardation effects due to the finite speed of light and to variations in the assumed nuclear size.

Tungsten L transition line shapes and energy shifts resulting from ionization in warm dense matter

Spectra of the W L transitions in the energy range 8–12 keV from warm dense plasmas generated by the Naval Research Laboratory's Gamble II pulsed power machine were recorded by a newly developed high-resolution transmission-crystal X-ray spectrometer with ±2 eV accuracy. The discharges have up to 2 MV voltage, 0.5 MA current, and produce up to 2.4 MJ/cm−3 energy density. The plasma-filled rod pinch (PFRP) diode produces a plasma with Ne ≈ 1022 cm−3 and Te ≈ 50 eV during the time of maximum X-ray emission. By analyzing the line shapes, it was determined that the Lβ2 inner-shell transition from the 4d5/2 level was shifted to higher energy by up to 23 eV relative to nearby Lβ transitions from n = 3 levels. In addition, the Lβ2 transition was significantly broader and asymmetric compared to the n = 3 transitions. The energy shift of the Lβ2 transition results from the ionization of electrons outside the 4d shell that perturbs the transition energies in the ions to higher values. The increased line width and asymmetry result from unresolved transitions from a range of ionization states up to +28. The ionization distribution was determined by comparison of the measured energy shifts and widths to calculated transition energies in W ions, and the ionization was correlated with Gamble discharge parameters such as the anode type and the high voltage delay time. This work demonstrates a new hard X-ray spectroscopic diagnostic technique for the direct measurement of the ionization distribution in warm dense plasmas of the heavy elements W through U that is independent of the other plasma parameters and does not require interpretation by hydrodynamic, atomic kinetics, and radiative simulation codes.

White Light Generation by Carbonyl Based Indole Derivatives Due to Proton Transfer: An Efficient Fluorescence Sensor

The motivation of the present work is to understand the optical, chemical, and electrical aspects of the proton transfer mechanism of indole (I) and some carbonyl based indole derivatives: indole-3-carboxaldehyde (I3C) and indole-7-carboxaldehyde (I7C) for both powder form and their liquid solution. Structural information for indole derivatives (isolated molecule and in solution) is obtained with density functional theory (DFT) and time dependent DFT (TD-DFT) methods. Calculated transition energies are used to generate UV-vis, FTIR, Raman, and NMR spectra which are later verified with the experimental spectra. The occurrence of different conformers [cis (N(c)), trans (N(t)), and zwitterion (Z*)] have been interpreted by Mulliken charge, natural bond orbital (NBO) analysis, and polarization versus electric field (P-E loop) studies. (1)H and (13)C NMR and molecular vibrational frequencies of the fundamental modes established the stability of Nc due to the presence of intramolecular hydrogen bonding (IHB) in the ground state (S0). Computed/experimental UV-vis absorption/emission studies reveal the creation of new species: zwitterion (Z*) and anion (A*) in the excited state (S1) due to excited state intramolecular and intermolecular proton transfer (ESI(ra)PT and ESI(er)PT). Increased electrical conductivity (σ(ac)) with temperature and increased ferroelectric polarization at higher field verifies proton conduction in I7C.

Photoluminescence spectroscopy study of excited states in In<SUB align="right">xGa<SUB align="right">1−xAs-capped InAs quantum dots

This study reports on photoluminescence (PL) and PL excitation (PLE) spectroscopy studies of excited state transitions in InxGa1–xAs-capped InAs quantum dots (QDs). InAs self-assembled QDs were grown on GaAs (001) wafers using 2.5 mono layer (ML) InAs deposition via molecular beam epitaxy. GaAs-capped QDs showed PL peak position at 1.182 μm at 78 K with a narrow full width at half maximum of 23 meV, indicating a highly uniform QD ensemble. The PLE spectrum of GaAs-capped QDs showed four peaks related to the QD excited state transitions at 1.117, 1.140, 1.192 and 1.224 eV at 8 K. Both ground state and excited state interband transitions were red-shifted when the first 30 ML of GaAs capping layer were replaced by InxGa1–xAs layer. The PL peak of In0.2Ga0.8As-capped QDs reached 1.246 μm (1.335 μm) at 78 K (296 K). Energy differences between the excited and ground states became smaller with increasing In composition of the InxGa1–xAs capping layers because of increasingly lower InAs to InxGa1–xAs band edge discontinuity as a result of the chemical and strain relieving effects. In addition, PLE spectra clearly showed wetting layer and quantum well states caused by the InxGa1–xAs capping layer for GaAs- and InxGa1–xAs-capped QDs, respectively. Based on the current PL, PLE, and the calculated transition energies available in literature, the lowest electron state levels of ~60 meV and ~112 meV above the electron ground state and the lowest hole state levels of ~23 meV and ~55 meV above the hole ground state were extracted.

Performance of recent and high-performance approximate density functionals for time-dependent density functional theory calculations of valence and Rydberg electronic transition energies

We report a test of 30 density functionals, including several recent ones, for their predictions of 69 singlet-to-singlet excitation energies of 11 molecules. The reference values are experimental results collected by Caricato et al. for 30 valence excitations and 39 Rydberg excitations. All calculations employ time-dependent density functional theory in the adiabatic, linear-response approximation. As far as reasonable, all of the assignments are performed by essentially the same protocol as used by Caricato et al., and this allows us to merge our mean unsigned errors (MUEs) with the ones they calculated for both density functional and wave function methods. We find 21 of the 30 density functionals calculated here have smaller MUEs for the 30 valence states than what they obtained (0.47 eV) for the state-of-the-art EOM-CCSD wave function. In contrast, for all of density functionals the MUE for 39 Rydberg states is larger than that (0.11 eV) of EOM-CCSD. Merging the 30 density functionals calculated here with the 26 calculated by Caricato et al. makes a set of 56 density functionals. Averaging the unsigned errors over both the valence excitations and the Rydberg excitations, none of the 56 density functionals shows a lower mean unsigned error than that (0.27 eV) of EOM-CCSD. Nevertheless, two functionals are successful in having an overall mean unsigned error of 0.30 eV, and another nine are moderately successful in having overall mean unsigned errors in the range 0.32-0.36 eV. Successful or moderately successful density functionals include seven hybrid density functionals with 41% to 54% Hartree-Fock exchange, and four range-separated hybrid density functionals in which the percentage of Hartree-Fock exchange increases from 0% to 19% at small interelectronic separation to 65%-100% at long range.

Experimental and theoretical investigations on the tautomerism of 1-phenyl-2-thiobarbituric acid and its methylation reaction

In the present study, 1-phenyl-2-thiobarbituric acid (1) was synthesized and the tautomerism of this compound was investigated by FT-IR spectroscopy, X-ray analysis and 1H NMR study as well as quantum chemical calculations. It is found that compound 1 exists in triketo form in the solid state and in CDCl3 solution while tautomerization was observed in DMSO-d6, DMF-d7 and CD3OD solution. The geometry optimization of eight possible tautomers of 1-phenyl-2-thiobarbituric acid was performed in gas phase and in different solvents using COSMO method. The calculated results are in good accordance with experimental data. Additionally, the methylation reaction of 1-phenyl-2-thiobarbituric acid was investigated for the first time by combination of experimental and theoretical methods. The methylation product might be varied with three possible isomers because of the structural features of 1-phenyl-2-thiobarbituric acid. We identified the obtained methylation product by X-ray diffraction and FT-IR spectroscopy, and transition state search and energy calculation were conducted to elucidate experimental data, the results revealed that the theoretical calculations are consistent with experimental data.

Ab Initio Molecular Orbital Study on the Excited States of [2.2]-, [3.3]-, and Siloxane-Bridged Paracyclophanes

Paracyclophanes are simple idealized model molecules for the study of interacting π-stacking systems. In this study, the excited states of [2.2]paracyclophane ([2.2]PCP), [3.3]paracyclophane ([3.3]PCP), and siloxane-bridged paracyclophane (SiPCP) are systematically investigated using the multiconfiguration quasi-degenerated perturbation theory (MCQDPT) method. The excited states of the alkyl- and silyl-substituted benzene monomers and benzene dimer, which can be regarded as the building blocks of paracyclophanes, are also examined at the same level of theory for more detailed understanding. The accuracy of the time-dependent density functional theory (TD-DFT) method required for excited state geometry optimization of the paracyclophanes is confirmed from calculations of the benzene dimer. The equilibrium distances between the benzene rings of the paracyclophanes in the first excited states are shorter than those in the ground state, and the benzene rings at the excited state optimized geometries are in an almost eclipsed parallel configuration, which indicates excimer formation. The calculated transition energies and oscillator strengths are generally in good agreement with the corresponding experimental results. A clear correlation between the excited state properties and the molecular structures is systematically demonstrated based on the calculation results for the substituted benzene monomers and benzene dimer. The transition energies of SiPCP are close to the corresponding absorption and fluorescence energies of the experimentally studied phenylene-silica hybrids, which indicates that the electronic properties of organic-silica hybrids, which is a new class of material with potential in photofunctional applications, can be approximated by simple siloxane-bridged cyclophane derivatives.

Phenyl substituted Mg porphyrazines: The effect of annulation of a chalcogen-containing heterocycle on the spectral-luminescent properties

We have performed complex experimental and theoretical investigations of the spectral-luminescent properties and electronic structure of new phthalocyanine analogs, Mg octaphenylporphyrazine and its derivatives with an annulated thiadiazole or selenadiazole ring instead of two phenyl groups. Fluorescence characteristics have been determined at 293 and 77 K: emission, excitation, and fluorescence polarization spectra; fluorescence quantum yield φF, and lifetime τF. Annulation of a five-membered chalcogen-containing heterocycle leads to splitting of the long-wavelength absorption band Q(0-0) and to the bathochromic shift of its longest wavelength component Qx(0-0), which increase upon passage from S to Se. At the same time, the fluorescence quantum yield φF and lifetime τF decrease, which is related to the intramolecular heavy-atom effect. The geometric structure of the ground state of the Mg porphyrazine molecules has been determined based on the density functional theory (DFT), and excited electronic states have been calculated with modified parametrization of the INDO/S method, INDO/Sm. Semiquantitatively, the calculated level positions of the lowest Q states and spectral shifts of Mg octaphenylporphyrazine and S-derivative agree with experimental data. For the range of the Soret band, calculated transition energies and their intensity distributions substantially depend on the dihedral angle γ between a phenyl ring and porphyrazine macrocycle. We show that, based on calculations at the angle γ = 60°, bands in the observed absorption spectra can be assigned with an accuracy of ∼2000 cm−1.

Absorption and Emission Spectra of Solvated Molecules with the EOM-CCSD-PCM Method.

The accurate calculation of transition energies and properties of isolated molecules is not enough for realistic simulations of their absorption and emission spectra in solution. In fact, the solvent influences the solute geometry, electronic structure, and response to external fields, and a proper description of the solvent effect is fundamental. However, the computational cost of including explicit solvent molecules around the solute becomes rather onerous when an accurate method such as the equation of motion coupled cluster singles and doubles (EOM-CCSD) is employed. The polarizable continuum model of solvation (PCM) may provide an efficient alternative to explicit models, since the sampling of solvent configurations is implicit and the solute-solvent mutual polarization is naturally accounted for. In this contribution, the absorption and emission spectra of molecules in solution are modeled through the EOM-CCSD-PCM method. The equilibrium solvation regime is employed for the geometry optimization of the solute molecule in the ground and excited states, while the nonequilibrium solvation regime is employed for vertical transitions. The theory, implementation, and prototypical applications of the method are presented. The numerical tests involve solvents that are particularly challenging for PCM: low-polar and protic polar solvents. Nonetheless, the experimental trends are well reproduced, and the overall agreement with the measured data is remarkable.

The first detailed experimental investigation of the KMM + KMN Auger electron spectrum of Cu emitted in the EC decay of radioactive 65Zn in a solid state matrix

The KMM + KMN Auger spectrum of Cu emitted in the electron capture decay of radioactive 65Zn in a solid state matrix was investigated for the first time at the instrumental energy resolution of 14 eV. Energies and relative intensities of twelve resolved spectrum components were determined and compared with theoretical predictions. A reasonable agreement of the semi-empirical calculations of transition energies by Larkins with experiment was observed. A comparison of theoretical and the measured transition rates indicates the important role of a coupling scheme applied. A more detailed analysis was hampered by absence of theoretical intensities for the individual intermediate coupling spectrum components. A slight indication of the influence of the source backing material on the absolute energies was found for the L3M4, 5M4, 5 and L2M4, 5M4, 5 Auger lines.

Mechanistic DFT studies – helicate-type complexes with different alcylic spacers

Metal-controlled self-assembly of complexes is of high interest in the field of Supramolecular Chemistry [1,2]. In the current study, we synthesized binuclear complexes with different spacers and study the influence of chain length on their relative energy. The considered complexes prefer the zigzag conformation. Thus a bridge with an odd number of methylene units forms a meso-Helicate (ΔΛ or ΛΔ) and one with an even number leads to a Helicate (ΔΔ or ΛΛ) (figure ​(figure1)1) [3,4]. Figure 1 Geometrically optimized complexes with Ti(IV); left: energies of the complexes with different alcylic spacers; right: ΔΔ and ΛΔ form of the complex with a propylene spacer. Comparison of the calculated transition energies for the non-dissociative interconversions of the diastereomeres with experimental results provides inside into the isomerization process. Moreover, insertion of different cations (templates) into the cavities of the binuclear complexes and corresponding calculations allow prediction of their influence on the isomerization. Enlargement of the studied system results in binuclear complexes with imino-bridged ligands. The obtained computational results provide a possible explanation for the experimentally observed high diastereoselectivity. As the DFT functionals like B3LYP do not describe long-range interactions properly, we chose the coulomb-attenuating method CAM-B3LYP [5] which corrects the exchange interaction at long range. The complexes with Ti(IV) in their helical or meso form have been geometrically optimized at the CAM-B3LYP level of theory with the TZVP basis set and MDF10 as ECP for Ti(IV) as implemented in the program package Gaussian09 [6].

Excited states and absorption spectra of β-diketonate complexes of boron difluoride with aromatic substituents

In the approximation of the time-dependent electron density functional theory, we have studied using the quantum-chemical method the nature of excited states of boron difluoride acetylacetonate F2BAA and its substituted derivatives that contain aromatic groups with one or two benzene cycles in the β-position. Optimization of the geometry of complexes show coplanar positions of cycles for all compounds, except for that with the substituent C6H3(CH3)2. Based on the calculated transition energies and oscillator strengths, we have simulated the absorption spectra in the prevacuum range. The calculated absorption spectra have been compared with the experimental spectra in the gas phase or in solutions. We show that, in the absorption spectra of complexes that contain substituents with one benzene cycle, the first three bands are caused by the transition of π electrons of the substituent to the LUMO of the chelate cycle. In complexes with two cycles in the substituent, the number of these transitions increases to five. As the π system becomes more extended, a bathochromic shift of the first absorption band and an increase in the transition probability are observed.

Determining Relative f and d Orbital Contributions to M–Cl Covalency in MCl62– (M = Ti, Zr, Hf, U) and UOCl5– Using Cl K-Edge X-ray Absorption Spectroscopy and Time-Dependent Density Functional Theory

Chlorine K-edge X-ray absorption spectroscopy (XAS) and ground-state and time-dependent hybrid density functional theory (DFT) were used to probe the electronic structures of O(h)-MCl(6)(2-) (M = Ti, Zr, Hf, U) and C(4v)-UOCl(5)(-), and to determine the relative contributions of valence 3d, 4d, 5d, 6d, and 5f orbitals in M-Cl bonding. Spectral interpretations were guided by time-dependent DFT calculated transition energies and oscillator strengths, which agree well with the experimental XAS spectra. The data provide new spectroscopic evidence for the involvement of both 5f and 6d orbitals in actinide-ligand bonding in UCl(6)(2-). For the MCl(6)(2-), where transitions into d orbitals of t(2g) symmetry are spectroscopically resolved for all four complexes, the experimentally determined Cl 3p character per M-Cl bond increases from 8.3(4)% (TiCl(6)(2-)) to 10.3(5)% (ZrCl(6)(2-)), 12(1)% (HfCl(6)(2-)), and 18(1)% (UCl(6)(2-)). Chlorine K-edge XAS spectra of UOCl(5)(-) provide additional insights into the transition assignments by lowering the symmetry to C(4v), where five pre-edge transitions into both 5f and 6d orbitals are observed. For UCl(6)(2-), the XAS data suggest that orbital mixing associated with the U 5f orbitals is considerably lower than that of the U 6d orbitals. For both UCl(6)(2-) and UOCl(5)(-), the ground-state DFT calculations predict a larger 5f contribution to bonding than is determined experimentally. These findings are discussed in the context of conventional theories of covalent bonding for d- and f-block metal complexes.

Electronic states of cyclophanes with small bridges

Electronic absorption and magnetic circular dichroism were recorded for five cyclophanes with ethano bridges: [2.2]paracyclophane, (1,2,4)[2.2.2]cyclophane, (1,2,4;1,2,5)[2.2.2]cyclophane, (1,2,3,4,5,6)(1,2,3,4,5,6)cyclophane, and trans-[2.2]metacyclophane. Spectral and structural analyses were based on geometry optimization and calculations of transition energies, carried out using density functional theory methods. The assignments have been proposed for several electronic transitions observed in the region below 52,000 cm(-1). The observation of transitions which should be forbidden in the high D(2h) symmetry [2.2]paracyclophane suggests a twisted ground state structure of D(2) symmetry, although the former structure with large amplitude vibrations at room temperature cannot be excluded. The PBE0 functional turned out to appropriately reproduce the inter-ring distances and electronic transition energies.

The effect of zinc ion on the absorption and emission spectra of glutathione derivative: Predication by ab initio and DFT methods

Relying on the reaction of o-phthalaldehyde (OPA) with glutathione (GSH) to form a highly fluorescence derivative GSH–OPA has been widely used to measure reduced glutathione. In order to better understand spectra property of the GSH–OPA and the effect of zinc ion on it, the ground and the lowest singlet excited state properties, the electronic absorption and emission spectra are predicted by ab initio and DFT methods. The absorption spectra are simulated using time dependent DFT method (TD-DFT) whereas the emission spectra are approximated by optimizing the lowest singlet excited state by HF/CI-Singles and then subsequently using this geometry for the TD-DFT calculations. The solvent effects on transition energies have been described within the conductor-like polarizable continuum model (CPCM). The calculated transition energies (absorption and emission) are in agreement with available experimental information.

Cyclotron resonance and intersubband transitions in symmetric InSb/AlInSb quantum wells with a perpendicular magnetic field

Electronic states in symmetric InSb/AlInSb quantum wells are studied theoretically. An eight-band k·p calculation is performed for quantum wells with different barrier heights and well widths in the presence of a magnetic field applied perpendicularly to the quantum well. Influences due to strain and self-consistent Hartree potential are taken into account. By calculating transition energies and corresponding optical transition matrix elements, one can identify the calculated transitions as spin resolved cyclotron resonances, spin conserved, and spin flipped intersubband transitions. It is found that even with an in-plane optical polarization, the spin flipped intersubband transitions cannot be ignored completely. Using well-accepted bulk band parameters and experimentally known quantum well structure parameters, calculated transition energies are compared to experimental data of a recent magneto absorption measurement. A reasonably good agreement is found for the overall magnetic field dependence. The influence of a tilted magnetic field is also briefly discussed.

The effect of metal cations on the nature of the first electronic transition of liquid water as studied by attenuated total reflection far-ultraviolet spectroscopy

The first electronic transition (Ã←X̃) of liquid water was studied from the perspective of the hydration of cations by analyzing the attenuated total reflection far-ultraviolet (ATR-FUV) spectra of the Group I, II, and XIII metal nitrate electrolyte solutions. The Ã←X̃ transition energies of 1 M electrolyte solutions are higher (Li(+): 8.024 eV and Cs(+): 8.013 eV) than that of pure water (8.010 eV) and linearly correlate with the Gibbs energies of hydration of the cations. The increases in the Ã←X̃ transition energies are mostly attributable to the hydrogen bond formation energies of water molecules in the ground state induced by the presence of the cations. The deviation from the linear relation was observed for the high charge density cations, H(+), Li(+), and Be(2+), which reflects that the electronic energies in the excited states are also perturbed. Quantum chemical calculations show that the Ã←X̃ transition energies of the water-cation complexes depend on the hydration structures of the cations. The calculated Ã←X̃ transition energies of the water molecules hydrating high charge density cations spread more widely than those of the low charge density cations. The calculated transition energy spreads of the water-cation complexes directly correlate with the widths of the Ã←X̃ transition bands measured by ATR-FUV spectroscopy.