J . Phys. Chem. 1984, 88, 2423-2425
2423
Assignment of the Lower Electronic States of Potassium Tetrakis(p-diphosphonato)diplatinate ( I I ) Yuko Shimizu, Yuki Tanaka, and Tohru Azumi* Department of Chemistry, Faculty of Science, Tohoku University, Sendai 980, Japan (Received: August 29, 1983)
Assignment of the lower electronic states of K4[Pt2(P205H2),]has been made on the basis of calculations of the spin-orbit coupling. All the absorption bands observed below -43 000 cm-' have been assigned to 5d-6p transitions except a weak absorption band at -32 500 cm-', which has tentatively been assigned to a 5d-5d transition. Phosphorescenceis the emission from the lowest E, state which is mainly composed of the 'A2,, zero-order state. Approximately 50 cm-l below this level, there exists a nonemitting Al, state. Existence of this nonemitting state accounts for the significant temperature dependence of the phosphorescence lifetime. The fluorescence is the emission from the lowest A2,,state, which is mainly composed of the lA2,, zero-order state.
Introduction
Potassium tetrakis(p-diphosphonato)diplatinate(II), K4[Pt2(P205H2)4],is a novel diplatinum complex that has an intense luminescence in aqueous solution and in crystal even at room temperature.' The spectroscopic properties of the complex have been studied by Fordyce, Brummer, and Crosby2 and by Che, Butler, and Gray.3 According to these authors, the fluorescence (I,,, = 24800 cm-', 7 C 2 ns) and the phosphorescence = 19400 cm-I, 7 = 5.5 pus at 300 K) are the emissions from, re5d,z spectively, the lAzu and 3A2ustates created by the 6p, excitation. The strong absorption at, , ,? = 27200 cm-I (emax = 33500 M-' cm-l) and the weak absorption at I,,, = 22100 cm-' (emax = 120 M-l cm-I) are due to the transitions to the lA2,, and 3A2ustates, respectively. The phosphorescence lifetime is strongly temperature dependent: 5.5 ps at 300 K and 700 ps at 10 K. Fordyce et a1.2 have interpreted the temperature dependence in terms of the emissions from the two (one degenerate and one nondegenerate) Boltzmann populated triplet sublevels. The lifetimes of the upper and lower sublevels were determined as 1.58 and 880 ps, respectively, the zero-field splitting being -50 cm-'. Similar analysis has been performed recently by Markert, Clements, Corson, and Nagle4 with results almost identical with those of Fordyce et al? Existence of the two close-lying states has also been supported by direct spectroscopic measurements of Rice and Gray.5 The assignment of the lowest singlet and triplet states to the states produced by the 6p, 5d,z excitation seems reasonable in view of the analogy to platinum chain compounds.6 However, if we want to understand the spectroscopic and dynamic properties in a more quantitative manner, there are several points that need to be elucidated. These points are listed in the following: (1) What determines the zero-field splitting of 50 crn-'? Since the first-order spin-spin coupling should never lead to such a large splitting, the second-order spin-orbit coupling is considered most important. What are then the most important perturbing states? (2) Why is the sublevel of longer lifetime located at lower energy? Can this behavior be generalized to other dinuclear complexes, or should it rather be considered to be accidental? (3) What is the mechanism of lAzu 3A2uintersystem crossing? The direct spin-orbit coupling between the singlet and
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(1) Sperline, R. P.; Dickson, M. K.; Rouhdhill, D. M. J . Chem. Soc., Chem. Commun. 1977, 62. ( 2 ) Fordyce, W. A.; Brummer, J. G.; Crosby, G. A. J. Am. Chem. SOC. 1981,103, 7061. ( 3 ) Che, C. M.; Butler, L. G.; Gray, H. B. J . Am. Chem. SOC.1981,103,
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7196
(4) Markert, J. T.; Clements, D. P.; Corson, M. R.; Nagle, J. K. Chem. Phys. Lett., 1983, 97, 175. (5) Rice, S.F.; Gray, H. B. J. Am. Chem. SOC.1983, 105, 4571. ( 6 ) Krogmann, K. Angew. Chem., Int. Ed. Engl. 1969, 8, 35. (7) Filomena Dos Remedios Pinto, M. A,; Sadler, P. J.; Neidle, S.; Sanderson, M. R.; Subbiah, A.; Kuroda,, R. J. Chem. SOC.,Chem. Commun. 1980, 13.
triplet states of the same orbital configuration should vanish. Does the intersystem crossing then take place to a higher triplet state which is located below S1? Or is the direct Sl-to-Tl intersystem crossing due to vibronic spin-orbit coupling more important? (4) What are the absorption bands observed above 30000 cm-'? In view of the relatively large absorptivities, they are not likely to be due to the d-d transitions. Are they then due to d-p transitions, too, or something else? Having these questions in mind, we try in this paper to assign the lower electronic states of the complex and to understand the excited-state behavior in a more quantitative manner. As is discussed above, the excited-state behavior cannot satisfactorily be interpreted in terms of the single (5d,z, 6p,) configuration. We consequently consider all possible excited states arising from the promotion of an electron from one of all occupied 5d orbitals to a vacant 6pz orbital. We then diagonalize the energy matrices including the spin-orbit coupling. As is shown below, this simple picture accounts for the known experimental results quite satisfactorily. In addition to the theoretical analysis to be described below, we have made some spectroscopic measurements. Even though slight differences are noted, the results are qualitatively in agreement with previous We shall therefore not present our own experimental results in this paper. Analysis of the experimental results with special attention on the triplet sublevels will be presented elsewhere. The whole Pt2(P205H2)44ion belongs to the C4, point group.' However, the skeleton that is composed of Pt and P atoms belongs to the D4h point group. In this paper, as Fordyce et al.' have done, we shall assume Ddhsymmetry. Methods of Calculation and the Results
We assume that the molecular orbitals responsible for the lower electronic transitions are composed of atomic orbitals of the two platinum atoms only. That is, the effect of the diphosphonate bridges does not appear formally except that it produces the crystal field splitting of the parent atomic orbitals. We note that, of the two molecular orbitals composed of a pair of 6p, atomic orbitals of platinum, the bonding orbital is stabilized to a great extent by Pt-Pt interaction. This molecular orbital is undoubtedly the lowest vacant orbital in the ground state. The antibonding orbital is considered to lie at much higher energy, and therefore it does not appear to contribute to the lower electronic states. Of the eight occupied molecular orbitals composed of the four pairs of occupied atomic d orbitals, only the four molecular orbitals need be considered as long as the allowed transitions are considered. The relevant molecular orbitals and their symmetries are as follows: p; = 2-'I2(6pf - 6pz) d-,2 - 2-112 (5dt2 - 5d$) d-x z = 2-ll2(5d;, - 5d?J
0022-365418412088-2423$01.50/0 0 1984 American Chemical Societv I
,
(al,) (a2J (e,,)
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The Journal of Physical Chemistry, Vol. 88, No. 11, 1984 d;, = 2-1/2(5df, - 5 d 3
(e,)
d-XY = 2-1/2(5diy- 5diy)
(bl,)
where the superscripts 1 and 2 in the right-hand side refer to the individual atomic orbitals of Pt. The wave functions of the excited states are constructed in terms of the Slater determinants so that they form the irreducible representations of the D4L double group. Special attention has been focused on the wave functions of E, symmetry. Since there are four sets of doubly degenerate E, states, we need to diagonalize an eighth-order matrix unless wave functions are carefully determined. We have chosen the wave functions so that the eighth-order determinant is reduced to two equivalent fourth-order determinants. Table I summarizes the zero-order wave functions thus determined. They are specified by the double group representations together with the single group representations and spin multiplicities being indicated in parentheses. The zero-order states will sometimes be designated only by the single group representations. The single group representations are distinguished from the double group representations by the existence of a left superscript indicating the spin multiplicity. We assume that the eigenstates of the total Hamiltonian are obtained by diagonalizing these zero-order wave functions with respect to the spin-orbit coupling. In evaluating the spin-orbit coupling, we retain only the one-center terms. All the matrix elements are then expressed in terms of the atomic spin-orbit coupling parameter { for the Pt 5d orbital. The secular determinants obtained in this way are shown in Table 11. The energies of the zero-order states are unknown. Therefore, we solve the secular determinants for various diagonal energy terms. We then try to find out if there exists a parameter set which satisfactorily accounts for the experimental evidence. This approach has been shown to be powerful in interpreting the spectra of some mononuclear transition-metal complexes.* The spin-orbit coupling parameter {is 4060 cm-' for the free platinum atom.g It is generally believed'O that in the evaluation of molecular properties a smaller value of { should be adopted. In this paper, we adopt the value of 2600 cm-I that was suggested by Martin, Tucker, and Kassman." In the evaluation of transition dipole moments, the 5d atomic wave function proposed by Basch and Graylz has been used. The parameter set that reproduces the experimental data semiquantitatively has been determined uniquely. The calculated results are compared with experimentally observed absorption spectrum in Figure 1. The mixing coefficients are given in Table 111. The calculated results lead to the following conclusions. (1) The weak absorption band at 22 100 cm-' and the phosphorescence should be attributed to the lowest E, state. The transition between this state and the ground state is allowed due to the mixing of the lE, state. The squared mixing coefficient is as small as 0.007, and this small mixing accounts for the small absorptivity and the long phosphorescence lifetime. (2) Approximately 50 cm-' below the lowest E, state, there exists an A,, state. The transition to the ground state is forbidden in the D4{ point group; this accounts for the long lifetime of the lowest excited state and the temperature dependence of the phosphorescence lifetime. (3) The strong absorption band at 27200 cm-' and the fluorescence are attributed to the lowest A2, state. The squared mixing coefficient of the lAzuzero-order state is as large as 0.942. (4) The absorption band at around 36 000 cm-l is due to the second E, state, which is mainly composed of the 3Blu state. ( 5 ) The absorption band at around 41 000 cm-' is due to the third E, and the second A2, states. These two states may es(8) Piepho, S. B.; Schatz, P. N ; McCaffery, A. J. J . Am. Chem. SOC.1969, 91, 5994.
(9) McClure, D.S Solid State Phys 1959, 9, 399. (10) McGlynn, S. P.; Azumi, T.; Kinoshita, M. "Molecular Spectroscopy of the Triplet State"; Prentice-Hall: Englewood Cliffs, NJ, 1969; p 403. (1 1) Martin, D. S., Jr.; Tucker, M. A,; Kassman, A. J. Inorg. Chem. 1965, 4, 1682. (12) Basch, H.; Gray, H. B. Theor. Chim. Acta 1966, 4 , 367.
Shimizu et al. TABLE I: Excited-State Wave Functions Which Are the Bases of Irreducible Representations of the D,A' Double Group
representations single group group
double
wave functions
TABLE 11: Spin-Orbit Secular Determinants (Upper Triangles) Ai, symmetry
E(3E,) (3/2)1'2{ -E
I
-(3/2)'/2f E(3E,) -E
I
A2, symmetry
B s mmetry i"(yBlu) - E
E, symmetry E('E,) - E
WITHOUT WITH SPIN-ORBIT SPIN-ORBIT COUPLING COUPLING
E / IO2 M'crn'
5
IO
15
20
'"
45
Figure 1. Calculated and experimental energy-level scheme. The parameters for this calculation are as follows: E('A2J = 22610 cm-l, E('A2J = 28010 cm-I, E(3B,,) = 37110 cm-', E(3E,) = 40110 cm-I, E('E,) = 47610 cm-', { = 2600 cm-'. The left energy levels show the single group states in the absence of spin-orbit coupling. The right energy levels show the double group states when spin-orbit coupling is included. Each double group state is connected to the main contributing single group state. On the extreme right, the experimental absorption spectrum (curve) is compared with the calculated results (horizontal bars). The lengths of the bars are proportional to the calculated oscillator strengths. The intensity of the 27 200-cm-I band is reduced to 1/10 in both the experimental and calculated results.
The Journal of Physical Chemistry, Vol. 88, No. 11, 1984 2425
Lower Electronic States of K4[Pt2(P20~H2)4]
TABLE III: Comparison of the Observed and Calculated Energies for the Optical Absorption" double oscillator strength energy/cm-' group calcdb obsd calcd obsd representation 22 049 0.988 4.85 x 10-4 4.28 x 10-3 22100 22100 0.97 1 3.29 X 10-I 2.29 X 10-1 27224 27200 34 639 0.03 1 1.23 X 2.60 X lo-' 36560 36700 0.138 3.14 X 40 591 0.174 2.00 x 10-2 40672} 40900 0.240 3.02 X 40 897 42 582 -0.068i 48 191
}
-0.003 0.830 0.951 -0.266 0.558 -0.16 li
-0.130 0.240 -0.5581 0.287 0.938 0.985 -0.97 1 0.830i 0.147i
-0.088i -0.116i 0.176i
0.973
"For the following parameter set: E(3A2,)= 22610 cm-I, E('A2,) = 28010 cm-', E(3Bl,) = 37110 cm-I, E(3E,) = 40110 cm-I, E('E) = 47610 cm-I, { = 2600 cm-I. "Oscillator strengths have been calculated from the mixing coefficients of IA2, and 'E,states and their transition moments. sentially be regarded as the triplet sublevels of the 3E, state. Discussion
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All the observed absorption bands except the one at 32 500 cm-' 5d transitions. The unassigned band is probably due to a d-d transition. Even though the absorptivity might appear somewhat larger than that of typical d-d transitions, we consider this assignment rather reasonable since the transition may gain significant intensity through vibronic coupling with the nearby 'Azustate. As is seen in Table 111, 94.2% of the fluorescent state (the first Azustate) is composed of 'A2,, and 97.6% of the phosphorescent state (the first E, state) is composed of 3A2,. In this respect, the assignment of Fordyce et a1.2 that the fluorescence and phosphorescence are the emissions from, respectively, lAzuand 3A2u is quite reasonable. Further, the nonemitting lowest excited state is 97.0% 3A2u.Therefore, we may regard the two lowest excited states as the two triplet sublevels of 3Azu. We next discuss the energy ordering of the triplet sublevels. As is discussed above, the degenerate sublevel, Eu(3A2u), is stabilized via spin-orbit interaction with 'E, and 3E,. The nondegenerate sublevel, AlJ3EU),on the other hand, is stabilized via interaction with 3E,. In order to obtain a better insight, we estimate the stabilization energies by second-order perturbation theory. By using the matrix elements given in Table I1 we obtain the following expressions: (emax = 650 M-' cm-I) have been assigned to the 6p,
This quantity is negative as long as 3E, is located below IE,. We thus conclude that the degenerate sublevel ( x , y components) should necessarily be at higher energy than the nondegenerate ( z component) sublevel. This conclusion may be generalized to all dinuclear complexes of this electronic type in a tetragonal field. It is interesting to note that the recent results of Fordyce and Crosby13 on Rh(1)-Rh(1) dimers also agree with this conjecture; for all dinuclear complexes known as far, the degenerate sublevels are always above the nondegenerate sublevel. Finally, we shall comment on the mechanism of SI TI intersystem crossing. In a series of previous studies'e1g on organic molecules, the mechanism of intersystem crossing has been satisfactorily interpreted in terms of the perturbation treatment in the pure spin Born-Oppenheimer adiabatic basis. We shall therefore analyze the mechanism in this framework. As is discussed above, there is no direct intersystem crossing between IA, and 3A2u.Furthermore, as the results of the calculations show, between SIand TI there exists no triplet state to which intersystem crossing might take place. We therefore could conclude that the intersystem crossing takes place through a vibronic spin-orbit perturbation involving 3E,. This conclusion is, however, only tentative. For a complex of a heavy metal, Pt, one might argue that the mixed-spin Born-Oppenheimer adiabatic representation is more adequate than the pure-spin Born-Oppenheimer adiabatic representation. This subject will be discussed in more detail in the future after analyzing the triplet sublevel spectra.
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Acknowledgment. We thank Professor T. Nakajima, Professor Y. Sasaki, and Dr. F. Ueno of this Department for stimulating discussions. Registry No. K4[PtZ(P205H2)4], 8001 1-26-3.
The difference in the two stabilization energies is then expressed as
Fordyce, W. A.; Crosby, G . A. J. Am. Chem. SOC.1982, 104, 985. Kokai, F.; Azumi, T. J . Chem. Phys. 1981, 75, 1069. Kokai, F.; Azumi, T.J . Chem. Phys. 1982, 77, 2757. Yamauchi, S.;Azumi, T. J . Chem. Phys. 1977, 67, 7. Yamauchi, S.;Azumi, T. J . Chem. Phys. 1978,68, 4138. (18) Yamauchi, S.;Saigusa, H.; Azumi, T. J. Chem. Phys. 1981,74,5335. (19) Asano, K.; Aita, S.;Azumi, T. J . Phys. Chem. 1983,87, 3829. (13) (14) (15) (16) (17)
