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Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Calculation Methods
  5. Results
  6. Discussion and Future Work
  7. Acknowledgement
  8. References
  9. Supporting Information

The ground state configuration of the gas phase cationic dyes pinacyanol chloride and rhodamine B are optimized with HF/6–311 + G(2d,2p) method and basis set. B3PW91/6–311 + G(2df,2p) functional and basis set is used to calculate the Mulliken atom charge distribution, total molecular energy, the dipole moment, the vertical ionization potential, the adiabatic electron affinity and the lowest excited triplet state, the last three as an energy difference between separately calculated open shell and ground states. The triplet and extra electron states are optimized to find the relaxation energy. In the ground state optimization of both dyes the chloride anion migrates to a position near the center of the chromophore. For rhodamine B the benzoidal group turns perpendicular to the chromophore plane. For both dyes, the LUMO is mostly of π character associated with the aromatic part of the molecule containing the chromophore. The highest occupied MOs consist of three almost degenerate eigenvectors involving the chloride anion coordinated with σ electrons in the molecular framework. The fourth highest MO is of π character. For both molecules in the gas phase ionization process the chloride anion loses the significant fraction of electric charge. In electron capture, the excess charge goes mainly on the dye cation.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Calculation Methods
  5. Results
  6. Discussion and Future Work
  7. Acknowledgement
  8. References
  9. Supporting Information

Due to their absorption in the lower energy of the visible spectrum, cationic dyes have numerous applications in solid state physics, photochemistry and photobiology. For more than half a century these materials were important sensitizers of photographic film [1]. Today they are still in the forefront of a broad variety of scientific investigations [2].

This work is focused on two exemplar cationic dye molecules, the cyanine dye 1,1′-diethyl-2,2′carbocyanine chloride, or pinacyanol chloride (PCl) and the xanthene-based dye, rhodamine B (RB). Both these substances have a variety of current applications including situations where the dye has been adsorbed on a substrate in a photocell or tagged to a larger biological macromolecule.

In the case of PCl, Khouri and Buss [3] show that interaction of the tagged dye with a biomolecule can shift the UV- and circular dichroism into the visible region allowing the biopolymers to be spectroscopically studied at a more accessible wavelength range. These authors suggest that PCl monomers can form an algal alginate bound chiral dimer on the macromolecule and they stress that the behavior of the dye in the gas phase can be significantly different from the situation when it is adsorbed on a substrate or tagged to a macromolecule.

Gas phase rhodamine B derivatives have been studied by Sagoo and Jockusch [4] and Chingin et al. [5] They use electrospray ionization to generate RB ion derivatives in the gas phase. Dye ions are selected in a mass-spectrometer and held in a quadrupole ion trap to examine gas phase fluorescence properties. These authors stress that understanding the photophysics of these dyes systems depends in part on having information on the isolated dye molecule in the gas phase independent of environmental influence.

Along difference lines, Seno et al. [6] investigate the photoionization spectra of RB at aqueous solution surfaces using synchrotron radiation and compare the photoionization threshold for RB of 5.6 eV to an earlier experimental value of 6.7 eV obtained in 1981. This large difference between the gas phase and adsorbed IP of rhodamine B is also found for pinacyanol chloride.

In a recent article [7], we reported that the properties of the isolated PCl molecule are significantly different from the properties both in the adsorbed state and in the dimer as well. The calculations predicted that the IP of the isolated gas phase PCl molecule was ca 6.3 eV, which is 1.3 eV above the experimental IP of <5 eV for the dye when it is adsorbed on a dielectric substrate. Earlier experimental work by Nelson [8], and Selsby and Nelson [9] clearly demonstrate that the affect of the dielectric substrate on the measured IP of the dye is <0.3 eV. This raises the important question of whether or not an optically excited singly adsorbed dye monomer has sufficient energy to sensitize the substrate by the well-accepted electron transfer process (see [1, 2, 7]). Reference [7] did find that the calculated IP of the isolated dimer does reduce to ca 5 eV as compared to the monomer. Thus, an excited adsorbed dimer could energetically sensitize a substrate.

Furthermore, in reference [7], it was found that the three highest occupied MOs of the isolated PCl molecule are not MOs with π character, but are MOs associated with the chloride anion and not the organic cation. Considerations, dating back over the past 60 years have assumed that the experimental optical first singlet excitation maximum of the cationic dye in solution (2.05 eV), or adsorbed on a substrate (1.98 eV; [10]), is an electron π–π* transition between the HOMO and LUMO of the dye. Reference [7] indicates that for the ground state of the salt, the observed π–π* singlet transition must correspond to an excitation from the fourth highest occupied MO to the LUMO.

One question, which appears central to the investigation of cationic dyes is determining the role that the anion plays in the photophysics involved. The answer must begin with a careful study of the isolated salt. In this study, the gas phase states of neutral RB and PCl are calculated with particular attention paid to the understanding the role the chloride anion plays in determining the properties of the isolated molecule.

Calculation Methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Calculation Methods
  5. Results
  6. Discussion and Future Work
  7. Acknowledgement
  8. References
  9. Supporting Information

The calculations in this work use GAUSSIAN 09 software [11]. One of the most accurate methods for the total energy calculation of small molecules is B3LYP/6–311 + G(2df,2p; [12]). First, the optimized atomic configuration for a molecule is obtained by HF/3–21G(d). Then a single point calculation with B3LYP is performed to obtain the molecular properties.

In calculating the IP as an energy difference, we have found that the density functional theory (DFT) B3PW91 functional produces better results when compared with B3LYP. This has also been reported by others [13, 14]. Testing several of these methods on a variety of small to large molecules with well known IP and dipole moment suggests that the best overall results for the molecules in our study would come from B3PW91/6–311 + G(2df,2p)//HF/6–311 + G(2d,2p). Herein, the latter HF basis is used for the optimization and the DFT B3PW91 for final calculation of the molecular properties of the closed and open shell states. The initial molecular geometry can begin with any molecular drawing program.

In this study, an optimization procedure replaces the use of idealized coordinates for the bond lengths of the cation atoms and the arbitrarily chosen positions of the halide anion adopted in reference [7]. A Hartree–Fock (HF) procedure is used to optimize the ground state structure and to determine the location of the anion in the gas phase of both molecules. Then a fixed point DFT calculation is used to determine the Mulliken atom excess charge distribution, the dipole moment and vertical ionization potential, the latter as an energy difference of the ground and ionized states. The adiabatic electron affinity is also computed as an energy difference of the ground and a reoptimized doublet state in which the structure of the negative dye molecule is allowed to relax. We conclude with a calculation of the lowest excited triplet state, obtaining the vertical value and then allowing the triplet state structure to optimize to find the relaxation energy and resulting charge densities.

In reference [7], we discuss the differences between using a “restricted” and “un-restricted” wave function for the calculation of an open shell electronic system. We showed, using DFT, HF and CNDOS-Δζ, that calculations of the IP, EA and the changes in the local charged densities obtained from either type of open shell wave function were all quite similar for these large organic molecules. We found that the IP with the restricted wave function would be less than <0.2 eV when the un-restricted wave function is used for PCl. Results similar to this for the EA are reported by Decent [15] in a detailed theoretical study of anthracene. She calculated expectation values of the S2 operator, which indicated that use of the unrestricted wave function does not produce significant error for the electron affinity and the results compare well with the experimental values. In fact, we have been able to calculate that the combined procedure used in this work, employing HF optimization followed by DFT energy difference calculations, (B3PW91/6–311 + G(2df,2p)//HF/6–311 + G(2d,2p), yields IPs and EAs in excellent agreement with experimental values for many molecules we have tested.

The DFT atomic orbital coefficients of the molecular eigenvectors are used to identify the character of the frontier molecular orbitals of the both dyes. It is highest occupied (HOMOs) and lowest unoccupied (LUMOs) molecular orbitals which are involved in ionization, electron capture and excitation and future study must reveal how these gas phase MOs are modified when the dye molecule interacts with the environment.

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Calculation Methods
  5. Results
  6. Discussion and Future Work
  7. Acknowledgement
  8. References
  9. Supporting Information

Overall, we find a great deal of similarity between gas phase molecular properties of the salts of the cyanine and xanthene-based dye. Even though there are obvious structural differences in PCl and RB, both gas phase salts are shown to have a ground energy level structure where the HOMO is not a π type molecular orbital.

The pinacyanol chloride molecule

For optimization of PCl, the initial atomic coordinates were determined from idealized bond lengths and angles. The color scheme in Fig. 1 is gray for hydrogen, green for carbon, purple for nitrogen and yellow for chlorine. The dipole moment vector, P, is superimposed on the figure as a white arrow. In the starting configuration for the optimization process, the chromophore carbon and nitrogen atoms were aligned on the x-axis of Fig. 1 and the chloride anion was initially positioned out of the x–y plane of the chromophore near the nitrogen atom, N52. As seen from the optimized positions in Fig. 1, the chloride anion, Cl53, has migrated from its very un-symmetric starting position to a symmetric central lower position nearly on the y-axis.

image

Figure 1. Opimized ground state structure of pinacyanol chloride (C25H25N2Cl). The color scheme is gray for hydrogen, green for carbon, purple for nitrogen and yellow for chlorine. The dipole moment vector, P, is superimposed on the figure as a white arrow. Note that the chloride anion, Cl53, has migrated from a starting position behind N52 to almost the symmetric center of the chromophore on the y-axis.

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Many initial positions for the Cl anion were examined. We had expected to find a number of local minima, but in each case starting positions below the x–y plane resulted in migration of the chloride anion to that of Fig. 1. The task was simplified by the use of the CNDOS-Δζ semi-empirical calculation developed in [7]. However, when the Cl was placed near the positive y-axis above the chromophore we finally found a second local minima again symmetrically located almost on the y-axis and as close to the chromophore as Coulomb repulsion allows. The energy of this local minimum was 0.2 eV higher than the structure of Fig. 1. Thus, the optimization routine seems to generate the most symmetrically possible structure which, neglecting the ethyl groups, is close to C2v symmetry. The molecule remains essentially planar with only a slight bending of the chromophore atoms from their starting positions on the x-axis to negative y-values for atoms on the chromophore ends.

Figure 1 illustrates the final optimized atom locations for the ground state of PCl. The optimized Cartesian coordinates for this structure is given in Table S1 (Supporting information).

Table 1 gives the eigenvalues and the significant atomic orbital coefficients for the selected MOs obtained from B3WP91 for the ground state of PCl. The normalization condition for the atomic orbital (AO) coefficients, c, is ∑μν ciμc Sμν = δij, where Sμν is the overlap integral between AOs φμ and φν. Thus, some│c│ can be >1.0. However, of the 1185 AO in the basis set, only a few coefficients that are significantly different than zero define the MO. To characterize a particular MOj we examined all the AO coefficients selecting AOs whose coefficient has a value greater than some minimum absolute value for the MO under consideration, e.g. │c│ ≥ 0.10, as given in Table 1.

Table 1. DFT B3PW91 frontier molecular orbitals for pinacyanol CL 206 electrons in 103 occupied MOs. MO: φi = Σrn cri ψr with n = 1185 AOs. HOMO = 103, LUMO = 104. The numerical values of the AO, the cri coefficients, determine the character type of the molecular orbital
Eigenvalues in eV
−7.314 occ−5.404 occ−4.773 occ−4.735 occ−4.664 occ−2.868 unoc
Significant atomic orbital coefficients, (cri), for molecular orbitalsa
MO (99)aMO(100)MO (101)MO (102)MO(103) HMO (104) L
  1. a

    17 cri ≥ 0.10 means 17 out of 1185 AO coefficients for MO(99) have absolute value >0.10.

17 cri ≥ 0.0912 cri ≥ 0.1034 cri ≥ 0.1335 cri ≥ 0.2031 cri ≥ 0.1524 cri ≥ 0.10
1168 cri ≤ 0.091173 cri ≤ 0.101151 cri ≤ 0.131150 cri ≤ 0.201154 cri ≤ .151161 cri ≤ 0.10
C29 3pz −0.117C35 2pz 0.124H7 3s 0.136C26 5S −0.379C26 5s −0.319C27 3pz −0.130
C29 4pz −0.100C35 3pz 0.189H8 3s −0.136C26 5px 0.321C26 5py −0.116C27 4pz −0.159
C30 3pz −0.127C35 4pz 0.185C26 5s 0.500C26 5py 0.382C28 5px −0.150C27 5pz −0.123
C30 4pz 0.113C37 2pz −0.124C27 5s −0.421C27 5px 0.327C29 5s −0.279C34 2pz 0.109
C32 3pz −0.130C37 3pz −0.189C28 5px 0.237C28 5px 0.381C32 5s −0.209C34 3pz 0.169
C32 4pz −0.025C37 4pz −0.185C31 5s −0.804C28 5py −0.226C32 5px −0.137C34 4pz 0.199
C36 3pz 0.103C47 5s −0.173C31 5px −0.178C30 5s −0.273C33 5s 0.369C34 5s −0.136
C36 4pz 0.090C48 5s 0.173C32 5px −0.588C31 5s 0.217C34 5s 0.348C36 2pz −0.111
C40 3pz 0.130N51 3pz −0.144C33 5s 0.784C32 5s −0.214C34 5px −0.226C36 3pz −0.171
C40 4pz 0.113N51 4pz −0.147C33 5px −0.301C33 5py −0.261C38 5s 0.346C36 4pz −0.184
C42 3pz −0.123N52 3pz −0.144C34 5s 0.245C34 5s 0.440C38 5py −0.224C36 5pz −0.121
C42 4pz −0.111N52 4pz −0.147C34 5py −0.455C34 5py 0.573C39 5s 0.369C38 2pz 0.109
C43 3pz −0.117 C35 5py 0.277C35 5s 0.248C40 5s −0.209C38 3pz 0.169
N51 3pz −0.116 C36 5px −0.182C35 5py −0.209C40 5px 0. 136C38 4pz 0.199
N51 4pz −0.107 C37 5py −0.276C36 5s 0.259C43 5s −0.281C38 5s −0.136
N52 3pz −0.116 C38 5s −0.242C37 5s 0.248C44 5px 0.150C45 3pz −0.130
N52 4pz −0.107 C38 5py 0.453C37 5py −0.209C46 5s −0.318C45 4pz −0.159
  C39 5s −0.784C38 5s 0.440C47 5s 0.519C45 5pz −0.123
  C39 5px −0.302C38 5py 0.572C47 5pz 0.130C47 5s 0.188
  C40 5px −0.590C39 5px 0.324C48 5s 0.519C48 5s 0.188
  C41 5s 0.808C39 5py−0.261C48 5pz 0.130N51 3pz −0.140
  C41 5px −0.179C40 5s −0.214C49 5s −0.267N51 4pz −0.159
  C44 5px 0.238C41 5s 0.217C50 5s −0.268N52 3pz −0.140
  C45 5s 0.422C42 5s −0.273N51 5s −0.153N52 4pz −0.159
  C46 5s 0.501C44 5px −0.381N52 5s −0.153 
  C47 5s 0.859C44 5py −0.226  
  C48 5s 0.858C45 5px −0.327  
  C48 5px −0.183C46 5s −0.379  
  C49 5s −0.309C46 5px −0.321  
(all CL 53 <0.005)(all CL 53 <0.005)C50 5s 0.308C46 5py 0.381CL53 8pz −0.210(all CL 53 <0.005)
  CL53 8px−0.214CL53 8py 0.209CL53 10pz −0.238 
  CL53 10px 0.244CL53 10py −0.236CL53 11py −0.126 
  CL53 11px 0.517CL53 11py −0.511CL53 11pz −0.514 
  CL53 12px 0.435CL53 11pz −0.127CL53 12py −0.104 
   CL53 12py −0.391CL53 12pz −0.398 

The semi-empirical calculation, CNDOS-Δζ, in reference [7] predicted that the highest occupied MOs of PCl were three, almost degenerate eignevectors, each of which had only one non-zero AO coefficient of ca 0.999 corresponding to a 3pz, 3py and 3px AOs on the chloride anion, respectively. B3WP91/6–311 + G(2df,2p) gives a more realistic picture in which the three highest occupied molecular orbitals show the chloride anion interacting with the ethyl groups and some of the sigma bonding AOs of the cation. Electrons in three highest occupied MOs are definitely not the π electrons of the cation. However, Table 1 indicates that the LUMO, MO104 and the fourth MO100 and fifth MO99 are, in fact, of π character associated with the π type AOs on the cation.

B3WP91/6–311 + G(2df,2p) computes the components of the dipole moment of PCl, using the optimized ground state structure, as:

  • display math(1)

The dipole moment vector, P, is superimposed on Fig. 1 as a white arrow, and, by convention, is directed from negative to positive charge so that it points into the origin of the x, y and z coordinate system.

Performing the fixed point DFT B3WP91 calculation of the ionized doublet state of PCl, using the ground state coordinates, the vertical IP is found to be:

  • display math(2)

which can be compared with 6.2 eV obtained in reference [7]. Herein, Rg is the optimized ground state coordinates.

The vertical electron affinity is found to be 1.74 eV as compared to the 1.86 eV found for the d-methyl PCl in reference [7]. Within four optimizations of the doublet state structure the total energy of this negative ion converged to three decimal placed yielding an adiabatic electron affinity as follows:

  • display math(3)

This implies a rearrangemnt energy of 0.33 eV when the dye molecule has captured an extra electron. Ropt is the optimized structure of the extra electron state. The vertical and optimized charge distributions of the negative dye molecule show no outstanding differences.

The lowest excited triplet excitation, ΔET, is calculated as an energy difference between the system with single α spin electrons in the LUMO and HOMO, MOs 104 and 103, respectively, and the ground state energy. The triplet vertical and relaxed energies are given below:

  • display math(4)
  • display math(5)

where ET(Ropt) has been optimized to the lowest energy structure losing 0.32 eV in the relaxation process.

Table 2 gives the Mulliken excess atom charge for the ground, the positive ion, the negative ion and the lowest excited triplet states. In the sp2 configuration, where nitrogen forms three planar bonds, each nitrogen atom contributes π electrons to the aromatic system and, along with 21 aromatic carbon atoms, the PCl cation has a system of 24 π electrons. It is typical to find the structure of PCl drawn with a plus charge placed on one of the nitrogen atoms (e.g. see reference [16]). Table 2 clearly indicates that DFT predicts a symmetric configuration to be the one of lowest total energy with positive charge of ca +0.5e shared equally on the two nitrogen atoms.

Table 2. DFT B3PW91 Mulliken excess atom charge densities for ground, ionized, extra electron and triplet states of pinacyanol chloride
AtomGround*+Ion−IonTriplet§AtomGround+Ion−IonTriplet
  1. * The ground state geometry is optimized. † The positive ion is calculated with the ground state geometry.‡  The negative ion's geometry has been separately optimized.§  The triplet state geometry has been separately optimized. The atom numbering refers to Figs. 1 and 2. Bold face numerical entries indicate sites of the larger charge changes from the ground state value. The numbers in this table are reflected in the blue (−) to red (+) color scheme of Fig. 2.

H1 ring0.1410.1480.1270.137C26 ring−0.668−0.661−0.643−0.631
H2 ring0.1210.1370.1020.119C27 ring−0.351−0.305−0.501−0.415
H3 ring0.1240.1370.1060.123C28 ring0.4790.4800.3660.360
H4 ring0.1310.1480.1120.131C29 ring0.2190.2460.2380.297
H5 ring0.1350.1500.1170.134C30 ring−0.567−0532−0.596−0569
H6 ring0.1510.1580.1360.147C31 ring−0.676−0.645−0.711−0.686
H7 ring0.1540.1470.1520.162C32 ring−0.026−0.020−0.002−0.012
H8 ring0.1540.1470.1520.162C33 ring0.3230.3220.2010.126
H9 ring0.1510.1580.1360.147C34 ring−0.0040.0160.0980.093
H10 ring0.1350.1500.1170.134C35 ring0.0800.1040.1710.284
H11 ring0.1310.1480.1120.131C36 ring−0.287−0.272−0.468−0.484
H12 ring0.1130.1370.1060.123C37 ring0.080−0.1040.1710.283
H13 ring0.1240.1370.1020.118C38 ring−0.004−0.1060.0980.093
H14 ring0.1210.1480.1280.137C39 ring0.3230.3210.2010.126
H15 ring0.1410.1460.1030.117C40 ring−0.026−0.020−0.0020.012
H16 ethyl0.1300.1140.0760.092C41 ring−0.676−0.645−0.711−0.686
H17 ethyl0.0950.1320.1420.149C42 ring−0.567−0.532−0.596−0.569
H18 ethyl0.1480.1320.1420.149C43 ring0.2190.2460.2380.298
H19 ethyl0.0950.1140.0760.092C44 ring0.4790.4800.3660.360
H20 ethyl0.1160.1180.1100.109C45 ring−0.351−0.305−0.501−0.415
H21 ethyl0.0890.1060.0770.095C46 ring−0.678−0.661−0.643−0.630
H22 ethyl0.1260.1330.1140.123C47 ethyl−0.072−0.089−0.045−0.070
H23 ethyl0.1260.1330.1140.123C48 ethyl−0.072−0.089−0.045−0.070
H24 ethyl0.0890.1060.0770.095C49 ethyl−0.308−0.287−0.339−0.332
H25 ethyl0.1160.1180.1100.108C50 ethyl−0.308−0.287−0.339−0.332
N51 0.5120.5460.4720.519
N52 0.5120.5460.4720.519
Cl53 −0.765−0.475−0.798−0.650

The Mulliken excess charge distribution of the optimized ground state, the vertical positive ion doublet state, the optimized negative ion doublet state, and the lowest excited triplet state are shown in Fig. 2a–d, respectively. The color scheme indicates excess atom charge density, which ranges from negative in blue to neutral in gray to positive in red. Figure 2 visually summarizes the results of Table 2.

image

Figure 2. (a–d) Comparison for Mulliken excess atom charge densities for the ground, ±ionized and lowest triplet states of PCl. The blue–gray–red color ranges from negative to positive excess charge.

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Comparison of Fig. 2a and b and Table 2 clearly shows that in the ground state the chloride anion retains −0.77e of its excess charge and loses −0.29e upon ionization. Furthermore, there is no significant loss of negative charge from any other atom in the cation upon ionization. This is consistent with the suggestion of reference [7] that the ionization of the PCl salt is dominated by change in the charge of the dye counter ion. On the other hand, addition of an electron to the dye salt does symmetrically affect the aromatic carbons C28 and C44, C33 and C39, central carbon C39, with the largest change occurring on C27 and C45.

For both the negative ion and triplet states the optimized structure has bent symmetrically downward in the y direction. This becomes apparent when the pictures are overlaid using the computer.

The triplet state shows a redistribution of charge along the chromophore atom chain between the nitrogen atoms, N52 and N51. For the salt, the triplet state energy of 1.1 eV falls well below the conduction band of typical a substrate such as AgBr.

The rhodamine B molecule

The optimization of the ground state structure of RB was begun with the benzoidal central ring lying in the x–y plane and the chloride anion near atom N60. Initial atomic coordinates were determined by idealized bond lengths and angles. From this starting position it was possible for the chloride anion to migrate toward the carboxyl group and attempt to form the zwitterionic or even the laconic form of RB. This did not happen in the ground state calculation. The central ring of the benzoidal group turned almost perpendicular to the chromophore and the chloride anion had migrated to a symmetric position near the y-axis on the opposite side of the molecule to the carboxyl group. The color scheme in Fig. 3 is as follows: gray—hydrogen; green—carbon; purple—nitrogen; blue—oxygen and yellow—chlorine. In Fig. 3, the x–y plane has been rotated slightly around the z-axis so that benzoic group can be seen. Figure 3 illustrates the final optimized structure ground state of RB. The anion Cl65 is behind carbon atoms 43, 43 and 45. The optimized Cartesian coordinates are given in Table S2.

image

Figure 3. Optimized rhodamine B structure (C28H31N2O3Cl) with x–y coordinates slightly rotated to distinguish atom numbering. The color scheme is: gray, hydrogen; green, carbon; purple, nitrogen; blue, oxygen; and yellow, chlorine. The chloride anion, CL65, has migrated from a starting point near N61 to a symmetric position behind carbons 39, 44 and 43 on the negative y-axis. The chromophore is bounded by N60 and N61 at the ends. H31 belongs to the COOH group. The benzyl ring lies in the y–z plane, having rotated 900 from a starting position in the x–y plane of the xanthene rings. P is the dipole moment vector.

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The general character of the MOs produced by B3WP91 can be seen in Table 3, which lists the AOs with significant non-zero coefficients for these MOs. The atom numbering is shown in Figure 3. Three, nearly degenerate MOs, nos. 125, 126 and the HOMO, no. 127, have a strong component on the chloride anion and almost no mixing with the π electron system on the cation. The fourth and fifth highest occupied MOs, nos. 124 and 123, respectively, show strong π electron character and have no significant component on the chloride anion or the benzoidal group. The LUMO, no. 128, has π character, having components on the xanthene part of the cation and on the benzoidal group as well.

Table 3. Rhodamine B (C28H31N2O3Cl) basis set B3PW91/6–311 + G(2df,2p) 254 electrons in 127 occupied MOs. MO: φi = Σrn cri ψr with n = 1443 AOs HOMO = 127 LUMO = 128. The numerical values of the AO, the cri coefficients, determine the character type of the molecular orbital
Eigenvalues in eV
−7.314 occ−5.789 occ−4.287 occ−4.265 occ−4.217 occ−2.701 unoc
Significant atom orbital coefficients (cri) for molecular orbitalsa
MO (123)MO(124)MO (125)MO (126)MO(127) HMO (128) L
  1. a

    17 cri ≥ 0.10 means 17 of 1185 AO coefficients for MO(99) have absolute value >0.10.

27 cri > 0.1022 cri > 0.1047 cri > 0.1045 cri > 0.1232 cri > 0.1523 cri > 0.10
1416 cri ≤ 0.1014121 cri ≤ 0.101396 cri ≤ 0.101398 cri ≤ 0.121411 cri ≤ 0.151420 cri ≤ 0.10
C32 5s 0.131C33 3pz 0.148C32 5s 0.292C32 5s 0.391C32 5px −0.406C32 3pz 0.251
5py −0.1464pz 0.1305py −1.0905py 0.345C33 5s −0.4794pz 0.264
C33 5s 0.1345pz 0.1115pz 0.2775pz −0.9705py −0.1615s −0.218
C34 5s −0.108C35 3pz −0.105C33 5s 0.457C33 5s 0.457C34 5s 0.1565py −0.224
C35 5s −0.1184pz −0.1005px −0.2465px −0.4115px −0.2585pz −0.406
C37 2pz 0.125C36 5s −0.161C34 5s −0.4765py 0.218C35 5s 0.217C33 5s −0.122
3pz 0.192C37 3pz −0.107C35 5s −0.5935pz 0.3455py −0.2925pz −0.139
4pz 0.1704pz −0.1005py 0.211C34 5s −0.379C36 5px 0.447C34 4pz −0.139
5px −0.101C40 3pz 0.107C36 5s −0.303C35 5s −0.4745px −0.190C38 4pz −0.118
C40 2pz 0.1254pz 0.1005px −0.276C36 5s −0.303C37 5px −0.153C39 4pz −0.118
3pz 0.192C41 5s 0.1625py 0.3995px −0.320C38 5px −0.852C43 4pz −0.139
4pz 0.170C42 3pz 0.105C37 5s 0.1755py 0.2035py −0.104C44 5s −0.122
5px 0.1024pz 0.1005px −0.524C37 5s 0.160C39 5px 0.8505pz −0.139
C42 5s −0.118C44 3pz −0.148C38 5s 0.1275px −0.2725py 0.104C47 5s −0.230
C43 5s −0.1074pz −0.1305px −0.205C38 5s 0.385C40 5px −0.153C48 5s −0.231
C44 5s 0.1335px 0.1115py −0.494C39 5s 0.385C41 5px 0.447C53 5s 0.215
C49 5s −0.141N60 2pz 0.126C39 5s 0.128C40 5s 0.1595py 0.190C54 5s −0.211
C50 5s −0.1413pz 0.1905px 0.2055px 0.272C42 5s −0.217C55 5s 0.691
N60 2pz −0.1034pz 0.190C40 5s 0.175C41 5s −0.1855py 0.292C56 5py −0.258
3pz −0.154N61 2pz −0.1265px 0.5245px 0.320C43 5s −0.157C57 5s −0.371
4pz −0.1543pz −0.190C41 5s −0.3015py 0.2035px −0.2575py −0.213
N61 2pz −0.1034pz −0.1905px 0.277C42 5s −0.474C44 5s −0.4785pz −0.356
3pz −0.1545py 0.400C43 5s −0.3795py −0.161C58 5pz 0.233
4pz −0.154C42 5s −0.593C44 5s 0.449C45 5s 0.118
O62 2pz −0.1155py 0.2135px 0.441C46 5s −0.119
3pz −0.171C43 5s −0.4765py−0.218C49 5s −0.146
4pz −0.160C44 5s 0.4555pz 0.345C50 5s 0.146
5px 0.245C53 5py 0.449C57 5px 0.138
C53 5s 0.8905pz 0.294
5py−0.347C54 5pz 0.273
5pz −0.269C55 5py−0.516
C54 5pz −0.214C56 5py−0.939
C55 5s −0.1435pz −0.332
5py 0.198C57 5s 0.136
C56 5pz −0.2275pz −0.127
C57 5s −0.689C58 5s 0.512
5pz −0.2195p 0.997
C58 5s −0.3225pz 0.341
5py −0.814C59 5s 0.520
C59 5s −0.276
O62 5s 0.154
(all Cl53 < 0.01)(all Cl53 < 0.01)Cl65 8py 0.193Cl65 8pz −0.194Cl65 8px 0.216(all Cl53 < 0.01)
10py −0.21910py −0.120Cl65 10px −0.246
10pz −0.10710pz −0.221Cl65 11px −0.527
11py −0.47111py −0.228Cl65 12px −0.416
11pz −0.22911pz −0.472
12py −0.38112py −0.173
12pz −0.17612pz −0.349

The components of the calculated dipole moment of RB are as follows:

  • display math(6)

The direction of the vector P is shown as a blue arrow in Fig. 3 and, by convention, is directed from negative to positive charge so that it points into the origin of the x, y and z coordinate system.

A fixed point B3PW91 calculation of the ionized doublet state is performed using the ground state coordinates. The vertical IP of RB is found to be as follows:

  • display math(7)

This can be compared with an experimental value of 6.70 ± 0.05 eV, which was made in 1981 [17]. A search of the literature does not reveal any other IP gas phase measurements.

The Mulliken charge distribution of the optimized ground state, the vertical +ion doublet state, the optimized negative ion doublet state, and the optimized lowest excited triplet state are given in Table 4.

Table 4. DFT B3PW91 Mulliken net atom charge densities ground, ±ionized states and lowest triplet sates of rhodamine B
AtomGround*+Ion−IonTriplet§AtomGround+Ion−IonTriplet
  1. * The ground state geometry is optimized. † The positive ion is calculated with the ground state geometry. ‡ The negative ion's geometry has been separately optimized. § The triplet state geometry has been separately optimized. The atom numbering refers to Figs. 3 and 4. Bold face numerical entries indicate sites of the larger charge changes from the ground state value. The numbers in this table are reflected in the blue (−) to red (+) color scheme of Figs. 4 and 5.

H1 ring0.1400.1580.1650.146C34 ring−0.645−0.611 −0.417 −0.654
H2 ring0.1360.1530.1360.131C35 ring−0.216 −0.161 −0.126 −0.180
H3 ring0.1300.1450.1170.130C36 ring−0.405 −0.374 −0.468 −0.297
H4 ring0.1310.1450.1230.127C37 ring−0.097−0.077 −0.225 −0.165
H5 ring0.1330.1530.1220.130C38 ring0.8260.684 0.498 0.430
H6 ring0.1400.1580.1500.150C39 ring0.8250.683 0.402 0.176
H7 ethyl0.0950.1100.0800.089C40 ring−0.098−0.078−0.127−0.084
H8 ethyl0.1130.1130.1130.118C41 ring−0.404 −0.373 −0.513 −0.290
H9 ethyl0.0930.1020.0770.089C42 ring−0.215 −0.160 −0.223 −0.272
H10 ethyl0.0950.1100.0780.092C43 ring−0.645−0.610 −0.756 −0.732
H11 ethyl0.0930.1020.0820.091C44 ring−0.058−0.085 0.234 0.299
H12 ethyl0.1130.1130.1250.113C45 ethyl−0.270−0.252−0.285−0.287
H13 ethyl0.0870.1000.0680.080C46 ethyl−0.270−0.252−0.307−0.274
H14 ethyl0.1150.1180.1270.104C47 ethyl−0.241−0.237−0.231−0.215
H15 ethyl0.1150.1180.0990.110C48 ethyl−0.241−0.238−0.214−0.216
H16 ethyl0.0870.1000.0700.082C49 ethyl−0.254−0.248−0.231−0.235
H17 ethyl0.0880.1030.0640.081C50 ethyl−0.254−0.248−0.240−0.227
H18 ethyl0.1220.1180.0940.106C51 ethyl−0.259−0.249−0.286−0.276
H19 ethyl0.1220.1150.0990.112C52 ethyl−0.259−0.248−0.283−0.267
H20 ethyl0.0880.1020.0700.083C53 benzyl−0.168−0.128−0.042−0.132
H21 ethyl0.0920.1030.0830.089C54 benzyl−0.335−0.320 −0.504 −0.324
H22 ethyl0.0940.1080.0740.088C55 benzyl−0.436−0.427 −0.348 −0.458
H23 ethyl0.1120.1110.1180.113C56 benzyl−0.402−0.460 −0.235 −0.295
H24 ethyl0.1120.1110.1180.114C47 benzyl0.5360.536 0.360 0.319
H25 ethyl0.0940.1080.0780.090C58 benzyl−0.538−0.489 0.364 0.270
H26 ethyl0.0920.1030.0820.090C59 COOH0.8360.819 0.001 0.077
H27 benzyl0.1490.1600.1250.138 N 60 0.5170.5380.4590.458
H28 benzyl0.1310.1440.1180.127 N 61 0.5170.5380.4460.510
H29 benzyl0.1420.1470.1860.132O62−0.187−0.168−0.198−0.206
H30 benzyl0.1900.1700.1960.182O63 COOH−0.454−0.427−0.419−0.396
H31 COOH0.3710.384 0.271 0.290 O64 COOH−0.371−0.384−0.270−0.282
C32 ring0.8300.8660.8321.116CL65 anion −0.921 −0.376 −0.930 −0.586
C33 ring−0.058−0.084−0.2320.072

Figure 4a and b show the optimized ground and vertical positive ion doublet states, respectively. The color scheme indicates excess negative charge in blue to neutral in gray and to excess positive charge in red. Figure 4 visually summarizes the results of Table 4.

image

Figure 4. Mulliken excess atom charge distribution for RB with the blue–gray–red color ranges from negative to positive excess charge, respectively. (a) Ground state, (b) vertical positive ionized doublet state. The loss of charge upon ionization is clearly shown by the change in the blue of Cl65, which has lost 0.55e of negative charge. (c) Relaxed negative ion doublet state and (d) lowest excited triplet state.

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In the ground state the Cl65 anion has retained 0.92e of its negative charge. As with PCl, some negative charge from the anion has distributed itself on the further parts of the cation. The overall result is similar to that obtained for PCl.

Table 4 shows that the chloride anion, Cl65, loses 0.56e of negative charge upon ionization. This is consistent with results found for PCl although the initial charge on the Cl is larger for RB. Thus, the principal electron loss upon ionization comes from the chloride anion.

The relaxed EA of RB is determined by optimizing the extra electron state and finding the energy difference:

  • display math(8)

This is necessarily greater than the vertical EA of 1.55 eV, indicating a rearrangement energy of 0.69 eV after gaining the extra electron. The lowest excited triplet excitation of RB, ΔET, is calculated as an energy difference between the system with single α spin electrons in the LUMO and HOMO, MOs 128 and 127, respectively, and the ground state energy. The vertical and relaxed values are given below:

  • display math(9)
  • display math(10)

where ET (Ropt) has been optimized to its lowest energy structure having relaxed by 0.40 eV. The excess Mulliken atom charges for ET (Ropt) are given in Table 4 along with the ground state charge densities for comparison. The optimized negative ion doublet state and the lowest excited triplet state Mulliken excess charge densities are shown in Fig. 4c and d, respectively. We note that for RB carboxyl carbon, C59, has become ca 0.8e more positive for both the negative ion and triplet state as shown in Table 4.

Discussion and Future Work

  1. Top of page
  2. Abstract
  3. Introduction
  4. Calculation Methods
  5. Results
  6. Discussion and Future Work
  7. Acknowledgement
  8. References
  9. Supporting Information

In this study, we have provided a theoretical quantum picture of the isolated salts of PCl and RB. The molecular orbital structure of both PCl and RB indicates that the three highest occupied MOs are not associated with the π electron system of the cation. These MOs clearly involve AOs on the Chloride anion interacting with σ AOs on the cation. On the other hand, the LUMO of both dyes has significant components from the π AOs of the cation and none from the AOs on the anion. Due to the small overlap, the transition moment from any of the three HOMOs to the LUMO is not likely. Thus, the lowest excited singlet state should correspond to a transition from fourth highest π type MO to the LUMO for both PCl and RB isolated salt molecules. We are investigating this carefully in a separate study.

The calculated ionization energy of 6.35 eV for PCl raises some question about monomer sensitization of a substrate by this dye. When the dye has been absorbed by evaporation from extremely low concentrations onto a substrate surface of Pyrex glass or Ag Br, photoionization into the vacuum of the residue dye yields a vertical IP of less than 5 eV [7]. We are attempting to find by direct calculation what local surface molecular interaction can induce such a large change in the ground state energy level of the dye.

We have found that the IP of PCl is relatively insensitive to the position of the halide anion. A second local energy minimum for the Cl anion exists at a central position near the positive y-axis (see Fig. 1) above the chromophore. It gives an IP of 6.4 eV as compared with 6.3 eV found in for the lower Cl position. We have investigated cis and trans forms of PCl with the ethyl groups on opposite sides of the molecular plane and with a twisting of the quinoline groups about the central chain. These configurations are found not to significantly alter the IP of the isolated molecule. We have found that the IP for di-ethyl PCl differs little from the IP of the di-methyl carbocyanine reported in reference [7]. However, it has been observed experimentally that when adsorbed on a substrate, sensitization of the di-ethyl PCl is found to be far greater than that of the di-methyl [2]. This is counter-intuitive since the latter should be able to get closer to the substrate. As the dye has been dissolved in ethanol, methanol or water we have considered the possibility of the reaction:

  • display math(11)

We have studied the cation-OH molecule using the semi-empirical CNDOS-Δζ of [7]. The frontier MOs of the dye hydroxide do dramatically change so that the IP lowers to ca 5.2 eV and the HOMO–LUMO is a π–π* transition. This is currently under study using the ab initio methods of this article. However, we note that there is no experimental evidence in the literature to indicate that the dye hydroxide forms.

Along other lines, our previous study [7] does show that a simple J-aggregated dimer of PCl has an IP of ca 5.2 eV and that this lowering of the IP can be understood in terms of the cation–anion arrangement of the dimer. We are currently studying the dimer formation of both PCl and RB.

Acknowledgement

  1. Top of page
  2. Abstract
  3. Introduction
  4. Calculation Methods
  5. Results
  6. Discussion and Future Work
  7. Acknowledgement
  8. References
  9. Supporting Information

The authors would like to thank Dr. Yasuyki Ishikawa, who is a coauthor with us on our related work [7] and who made very helpful suggestions on this project.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Calculation Methods
  5. Results
  6. Discussion and Future Work
  7. Acknowledgement
  8. References
  9. Supporting Information
  • 1
    Tani, T. (1995) Chapter 5. Spectral Sensitization in Photographic Sensitization Theory and Mechanism (Edited by M. Lapp, J.-I. Nishizawa, B. B. Snavely, H. Stark, A. C. Tam and T. Wilson), pp. 1164. Oxford University Press New York, Oxford.
  • 2
    Eachus, R. S., A. P. Marchetti and A. A. Muenter (1999) The photophysics of silver halide imaging materials. Annu. Rev. Phys. Chem. 50, 117144.
  • 3
    Khouri, S. J. and V. Buss (2011) Interaction of cationic cyanine dye with algal alginates: Evidence for a polymer bound dimer. J. Biophys. Chem. 2(4), 380385.
  • 4
    Sagoo, S. K. and R. A. Jockusch (2011) The fluorescence properties of cationic rhodamine B in the gas phase. J. Photochem. Photobiol. A: Chem. 220, 173178.
  • 5
    Chingin, K., R. M. Balabin, K. Barylyuk, H. Chen, V. Frankevich and R. Zenobi (2010) Rhodamines in the gas phase: Cations, neutrals, anions, and adducts with metal cations. Phys. Chem. Chem. Phys. 12, 1171011714.
  • 6
    Seno, K., T. Ishioka, A. Harata and Y. Hatano (2001) Photoionization of rhodamine byes adsorbed at the aqueous solution surfaces investigated by synchrotron radiation. Anal. Sci. 17(Suppl.), i1177i1179.
  • 7
    Delgado, J. C., Y. Ishikawa and R. G. Selsby (2009) The calculated ionization potential and electron affinity of cyanine cationic dyes. Photochem. Photobiol. 85(6), 12861298.
  • 8
    Nelson, R. C. (1967) Ionization energy of adsorbed dye molecules. J. Mol. Spectros. 23, 213218.
  • 9
    Selsby, R. G. and R. C. Nelson (1970) The ionization energy of cationic cyanine dyes. J. Mol. Spectrosc. 33, 118.
  • 10
    Nelson, R. C. and P. Yianoulis (1974) A statistical model for the energies of spectral sensitization. J. Photogr. Sci., 22, 1722.
  • 11
    Frisch, M. J., G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery Jr, T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez and J. A. Pople. (2009) Gaussian 09, Revision C.02, Gaussian, Inc., Wallingford, CT.
  • 12
    Foresman, J. B. and A. Frisch (1996) Exploring Chemistry with Electronic Structure Methods, pp. 143150. Gaussian Inc., Pittsburgh, PA.
  • 13
    Salavati-Niasari, M., S. N. Mirsattari, M. Monajjemi and M. Hamadanian (2010) Density functional B3LYP and B3PW91 studies of the properties of four cyclic organodiboranes with tetramethylene fragments. J. Struct. Chem. 51, 437443.
  • 14
    Batham, J. and P. Derosa (2008) Comparative study of the performance of DFT B3PW91 for the prediction of electronic properties of molecules. Am. Phys. Soc. APS March Meeting, abstract #Q13.009.
  • 15
    Dessent, C. E. H. (2000) A density functional theory study of the anthracene anion. Chem. Phys. Lett. 330, 180187.
  • 16
    Barazzouk, S., H. Lee, S. Hotchandani and P. V. Kamat (2000) Photosensitization aspects of pinacyanol H-aggregates. Charge injection from singlet and triplet excited states into SnO2 nanocrystallites. J. Phys. Chem. B 104, 36163623.
  • 17
    Timoshenko, M. M., I. V. Korkoshko, V. T. Kleimenov, N. E. Petrachenko, V. V. Chizhov, V. V. Tyl'lov and M. E. Akopyan (1981) Ionization potential for rhodamine dyes. Dokl. Phys. Chem. 260, 138.

Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Calculation Methods
  5. Results
  6. Discussion and Future Work
  7. Acknowledgement
  8. References
  9. Supporting Information
FilenameFormatSizeDescription
php1222-sup-0001-TableS1.docWord document74KTable S1. Pinacyanol chloride (C25H25N2Cl) ground state configuration Cartesian coordinates.
php1222-sup-0002-TableS2.docWord document83KTable S2. Rhodamine B (C28H31N2O3Cl) ground state configuration Cartesian coordinates.

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