摘要:

Vibronic structure in the luminescence spectra of tetragonal d2 and d8 complexes analyzed by wavepacket dynamics on two-dimensional potential surfaces 4 4 Myriam Triest, Steve Masson, John K. Grey and Christian Reber Département de chimie, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal QC, Canada H3C 3J7 Received 18th October 2000, Accepted 17th November 2000, Published 1st December 2000 The luminescence spectra of the tetragonal trans-ReO2(vinylimidazole)4+ complex and the square planar Pd(SCN)42– and Pt(SCN)42– complexes all show vibronic progressions in two predominant vibrational modes. In the first complex, the vibronic progressions involve high-frequency and low-frequency metal–ligand modes. In the square planar complexes, the two vibrational modes have similar frequencies.At the intermediate resolution, often observed experimentally, these compounds provide an example of the missing mode (or MIME) effect. Wavepacket dynamics on two-dimensional surfaces explain in a visual and intuitively appealing way the spectroscopic features. The distinct effects are caused by the different frequency ratios between the two modes of the two-dimensional models describing each complex. The emitting state structure determined from the spectra reveals similar changes along a bending normal coordinate for Pd(SCN)42– and Pt(SCN) 2–. 4h g) compounds. Often such spectra show resolved vibronic structure at low temperature, and usually only a few select vibrational modes from the observed progressions. We present the first low-temperature, single crystal experimental spectra of Pt(SCN) 2–.We present a new luminescence from Pt(SCN)42– with vibronic structure corresponding to an emitting-state distortion involving a bending mode. The comparison of this spectrum with the palladium analogue4 reveals quantitative differences in bonding for 4d and 5d metals. The six-coordinate tetragonal trans-ReO2(vinylimidazole)4+ complex5,6 is included in Fig. 1 and reveals progressions in two modes with very different frequencies. The time-dependent theory provides an intuitively appealing view of the vibrational dynamics associated with the electronic transition and we use animations to illustrate Fig. 1 Luminescence spectra of Pd(SCN)42– (red trace) at 10 K, Pt(SCN)42– (yellow trace) at 5 K and trans-ReO2(vinylimidazole)4+ (green trace) at 15 K.Introduction Transition metal complexes have a rich electronic structure and often ground and excited state molecular structures vary significantly, giving rise to interesting photochemistry.1 Materials incorporating transition metal chromophores are of current interest for their optical and magnetic properties.2 In both areas, key experimental information is provided by luminescence spectra.3 We present in the following paper a series of experimental spectra and animations in order to rationalize the vibronic structure and overall band shape of the spectra by examining wavepacket dynamics on the final state potential surface.These pictures are intuitively appealing and can be understood from classical mechanics, in contrast to the standard time-independent approach involving Franck– Condon factors. This analysis provides detailed insight into excited state properties and metal ligand bonding for the tetragonal title complexes. We have chosen these molecules for our comparative study because they represent the two limits for the tetragonal distortion of octahedral complexes: the trans-dioxo compound corresponds to a strongly compressed octahedron, the square planar complexes represent extreme cases of elongated octahedral coordination. The molecules are further related by the electron-hole analogy of their d2 and d8 electron configurations.Assuming idealized D point group symmetry, the orbital excitation for the lowest energy electronic transition occurs from a degenerate (e HOMO to a nondegenerate (b1g) LUMO orbital for the tetragonally elongated (square planar) compounds, in contrast to the tetragonally compressed complex, where it occurs from a nondegenerate (b2g) HOMO to a doubly degenerate (eg) LUMO orbital. The actual site symmetry of the complexes in the solids studied here is significantly lower than D4h, removing the degeneracies of the eg orbitals and leading to transitions between nondegenerate states, but the one electron picture remains qualitatively useful. We present time-dependent calculations of luminescence spectra observed for these tetragonal transition metal DOI: 10.1039/b008386k PhysChemComm, 2000, 12the dynamics and to derive and rationalize the vibronic structure observed in the experimental spectra.1,7 We have previously examined two coupled electronic states along a single normal coordinate using this approach.8 In the following we focus on a single electronic state (the ground state) defined by two normal coordinates.We start with a simple model: a two-dimensional potential whose frequencies along both normal coordinates are identical. We then present calculations for Pd(SCN)42– and Pt(SCN)42–, where the two vibrational frequencies differ by less than a factor of two and conclude with trans- ReO2(vinylimidazole)4+ where the difference between the frequencies is very large and where the experimental spectrum reveals evidence for mode coupling.Our goal is to compare the effect of the ratio between the two frequencies on the wavepacket dynamics and to explore how wavepacket dynamics is related to the different spectroscopic effects we observe for the title compounds.. Experimental section and spectroscopic results All compounds were prepared using published procedures and recrystallized several times before spectroscopic measurements.4,5,9 The compounds were analyzed by luminescence, Raman and infrared spectroscopy. Low-temperature luminescence spectra for trans- ReO2(vinylimidazole)4I and Pd(SCN)42– with several different counterions were measured using a He gas flow cryostat and the scanning instrumentation using a monochromator and IR-sensitive photomultiplier described before.10 The spectrum of (n-Bu4N)2Pt(SCN)4 was measured with a microspectrometer (Renishaw System 3000) equipped with a CCD camera for detection of the spectra.The experimental luminescence spectra are presented in Fig. 1. The spectra of the square planar complexes (red and yellow traces) show resolved vibronic structure involving two modes with frequencies lower than 300 cm–1. The spectrum of the platinum complex occurs at higher energy than the transition for the palladium analogue, a trend confirming published spectra of other complexes of these two metals.11 To the best of our knowledge, this luminescence has not been reported in the literature before.The rhenium(V) spectrum (green trace) is larger and involves a high-frequency mode, assigned as the symmetric rhenium-oxo mode observed at approximately 900 cm–1 for many trans-dioxo complexes of rhenium(V).12,13 The spectrum in Fig. 1 shows that each member of the highfrequency progression consists of a cluster of transitions in the low frequency mode. The intensity distribution within this cluster of bands is not identical along the progression. This is an experimental evidence for coupled coordinates,5,6,14,15 discussed and illustrated in the following discussion. V k 2 = + 1( ) 1 1Q2 2 kQ2 (1) 2 Discussion Potential energy surfaces The ground state potential energy surfaces of our target complexes are assumed to be harmonic with force constants determined by the experimental vibrational frequencies.We use two dimensionless coordinates Q1 and Q2 to define the ground-state potential surface: Fig. 2 Potentials and luminescence transitions for trans- ReO2(vinylimidazole)4+ (left) and Pd(SCN)42– (right). For the Re FRPSOH[WKHGLVSODFHPHQWV Q along the dimensionless axes Q885 cm–1 and Q175 cm–1 are 2.25 and –1.739, respectively, and the energy of the origin is E00 =14 700 cm–1 . For the palladium complex the GLVSODFHPHQWV Q along Q280 cm–1 and Q179 cm–1 are 3.49 and 1.93, respectively, and E00 is 14365 cm–1. 2– 4 k1 and k2 denote the vibrational frequencies of the two modes in wavenumber units. The relevant vibrational (Pt(SCN) 2– frequencies for Pd(SCN)4 ) are 280 cm–1 (300 cm–1) and 179 cm–1 (151 cm–1), respectively, corresponding to the totally symmetric metal–ligand stretching mode and an average S–M–S bending mode, determined from Raman spectra.4 In an idealized D4h symmetry these modes have a1g and b2g symmetry, respectively, but they are both totally symmetric in the low actual site symmetry of the complexes, allowing us to use non-degenerate emitting state potentials as illustrated in Fig.2. For trans- ReO2(vinylimidazole)4+ the frequencies are 885 cm–1 and 175 cm–1 corresponding to Re=O and Re-imidazole modes, respectively.5,6 The resulting potential surfaces and luminescence transitions are shown in Fig. 2. Wavepacket dynamics on the ground state potential energy surface Classical dynamics.We present and discuss the wavepacket dynamics on the ground state potential energy surfaces defined in the previous section. The luminescence transition corresponds to the lowest-energy emitting state eigenfunction being displaced vertically onto the ground state potential energy surface and then evolving with time.7 Its initial position in the Q1, Q2 coordinate system corresponds to the minimum of the emitting-state potential surface. If the ground state potential is harmonic we can use a classical analogy for the resulting dynamics: the twodimensional oscillator (with frequencies 1 and 2) whose motion is given by:16 Q t ( )= = Q t ( 0)cos( wt) (2) 1 1 1 Q t ( ( )= = Q t 0)cos( wt) (3) 2 2 2 These equations describe the well known Lissajous patterns and involve dynamics that is separable in the Q1 and Q2 dimensions.Time-dependent Schrödinger equation: quantum mechanical dynamics. In the time-dependent models the evolution of the eigenfunction of the excited state on theFig. 3 Contour view (left) and 3D representation (right) of the wavepacket dynamics on a two-dimensional potential surface with identical vibrational frequencies along the horizontal and vertical normal coordinates and no displacement in the direction of the horizontal coordinate. Click on the image or here for the MOV motion picture (2.037 Mb) ground state energy surface is calculated from the timedependent Schrödinger equation using the split-operator algorithm developed by Feit et al.17 We first illustrate a simplified situation not corresponding to a specific complex.We choose both vibrational frequencies to be identical, leading to the twodimensional potential energy surface with circular contours shown in Fig. 3. The excited state and ground state potentials have identical force constants. The starting position of our time-dependent wavefunction is at Q1 = 0, Q2 > 0. The result is a harmonic oscillation along the vertical axis, as observed by playing the animation in Fig. 3. The classic trajectory from eqn. (2) and (3) corresponds to a straight vertical line. It is important to note that the vibrational frequency of the horizontal Q1 coordinate has no influence on the dynamics. Electronic spectra (luminescence, absorption) show strong vibronic Q � 0.These modes are SURJUHVVLRQVRQO\LQPRGHVZLWK Fig. 4 Ground-state potential surface for Pd(SCN)42– with the wavepacket at time t = 0. The left-hand surface shows the evolution of the wavepacket with time, the right-hand surface shows the classical trajectory obtained with eqn. (2) and (3). Offsets at time t = 0 are 3.49 and 1.93 along Q280 and Q179, respectively. Click on the image or here for the MOV motion picture (9.939 Mb). .also most enhanced in resonance Raman excitation profiles. A one-dimensional potential well is sufficient to describe the situation illustrated in Fig. 3. 4 Our target complexes show spectra with vibronic structure involving two different modes and we therefore use two-dimensional potentials to show the wavepacket dynamics.In Fig. 4 we compare the classical trajectory to a numerical solution of the Schrödinger equation using the split-operator algorithm developed by Feit and Fleck. The potential energy surface is defined by the two vibrational frequencies for Pd(SCN) 2– and the initial position is obtained from fitting a calculated spectrum to the experiment. The following animation clearly shows the analogy between the motions of the classical trajectory and the maximum of the wavepacket. The Lissajous motion is obvious and it has an important influence on the vibronic structure observed in the spectrum, as discussed in the following.42–. Fig. 5 presents the corresponding animation for Pt(SCN) The vibrational frequencies used have a different ratio than for the palladium complex and the wavepacket motion is distinctly different.The comparison of Fig. 4 and 5 quantitatively illustrates the effect of the frequency ratio on the wavepacket dynamics. Fig. 6 shows the ground state potential energy surface for trans-ReO2(vinylimidazole)4+ in the same numerical Q1,2 range as for Fig. 4 and 5. The shape of the potential is much more elliptical than the potentials in Fig. 4 and 5, a consequence of the very different vibrational frequencies. The wavepacket oscillation along the high-frequency coordinate is much faster than it is along the low-frequency coordinate. The frequency ratio for Fig. 6 is approximately 5 : 1, not 3 : 2 or 2 : 1 as in Fig.4 and 5. These ratios lead to the different classical (Lissajous) trajectories as well as to different quantum mechanical wavepacket dynamics. More subtle differences can not be rationalized with the classical model. In Fig. 3, the vibrational frequencies of the emitting state potential were chosen to be identical to the ground state. This leads to a moving wavefunction that does not change shape: the outer perimeter of the moving function in Fig. 3 does not change with time and the wavepacket moves as a whole. In contrast, the vibrational Fig. 5 Ground-state potential surface for Pt(SCN)42– with the wavepacket at time t = 0. The left hand surface shows the evolution of the wavepacket with time, the right hand surface shows the classical trajectory obtained with eqn.(2) and (3). Offsets at t = 0 are 4.86 and 1.67 along Q300 and Q151, respectively. Click on the image or here for the MOV motion picture (3.664 Mb). Fig. 6 Ground-state potential surface for trans-ReO2(vinylimidazole)4+ with the wavepacket at time t = 0. The left hand surface shows the evolution of the wavepacket with time, the right hand surface shows the classical trajectory obtained with eqn. (2) and (3). Offsets at time t = 0 are 2.25 and –1.739 along Q885 and Q175, respectively. Click on the image or here for the MOV motion picture (12.280 Mb). ground state. As a consequence, the perimeter of the moving wavepacket in Fig. 6 changes with time and the dynamics no longer corresponds to a Lissajous motion of the wavepacket maximum.An important deviation from harmonic (Lissajous) dynamics occurs for potentials where the coordinates are coupled. Such effects lead to spectra as observed for the rhenium(V) dioxo complex in Fig. 1, where the shape of each cluster of bands forming the main progression varies along the progression. The potential energy surface in these cases can be defined by:14 V k 2 = + ( ) 1 1Q2 2 kQ2+k1 2Q1 n m Q2 (4) 12 where k12 is an adjustable phenomenological coupling term of the coordinates and both exponents n and m have to be different from zero. We have developed a physical model for d2 configured trans-dioxo complexes where the origin of the coupling is identified as the interaction between the ground state and several excited electronic states.5 Fig.7 compares the two potentials. The left hand panel shows the potential with coupled coordinates, corresponding to a non-Fig. 7 Ground-state potential surface for trans-ReO2(vinylimidazole)4+ with the wavepacket at time t = 0. The left-hand surface represents the coupled ground state and shows the evolution of the wavepacket with time. The right-hand surface shows the harmonic ground state and the moving wavepacket is the dference between the harmonic and coupled wavepacket. Click on the image or here for the MOV motion picture (7.145 Mb). zero coupling constant k12 in eqn. (4). The coupling leads to a surface described by non-elliptical contour lines. The wavepacket explores a cross section along the vertical high frequency coordinate with varying slope and curvature as it moves slowly along the horizontal low-frequency coordinate.The right-hand panel shows the harmonic potential from Fig. 6 for comparison and the difference between the wavepackets on the harmonic surface in Fig. 6 and the coupled surface in Fig. 7 are given throughout the animation, illustrating clearly that the dynamics on the coupled surface significantly deviate from Lissajous motions that can be separated along the two coordinates. Calculated luminescence spectra and autocorrelation functions The most important quantity linking the wavepacket dynamics in Fig. 2 to 4 to experimental luminescence spectra is the autocorrelation < | (t)>, i.e.the overlap of (t) with (t = 0).7 It can be Fourier transformed to the frequency domain according to eqn. (5), leading directly to the calculated luminescence spectrum. 2 2t t 00 3 i +¥ wt w w = I C e t j|j( ) lum( ) e h dt (5) -¥òì üiE ï ï - + G í ý ï ï î � In eqn. (5), is the frequency of the luminescence spectrum and is a phenomenological damping factor that determines the width of line in the spectrum. Both quantities are in wavenumber units. A variety of applications to any techniques of electronic spectroscopy have been described in the literature.1,18 We illustrate the concept with a one-dimensional model in Fig. 8, corresponding to the situation in Fig. 3. The animation shows the absolute value of the wavefunction as a function of time in the top panel.The function at t = 0 stays on as a reference to qualitatively estimate the value of the autocorrelation. It is obvious to understand the initial decrease of the autocorrelation and its recurrences after each vibrational period. Maxima occur after integer multiples of 120 fs, corresponding to the vibrational frequency of 280 cm–1. The damping factor causes the subsequent recurrences of the overlap to decrease in magnitude. The calculated spectrum obtained with eqn. (5) is shown in Fig. 9. In this case the increase of the damping factor leads to larger individual vibronic lines but the spacing of the vibronic progression stays constant for different values of . Fig. 8 Wavepacket dynamics on a one-dimensional potential surface (top panel) and the resulting autocorrelation function (bottom panel).Click on the image or here for the MOV motion picture (1.759 Mb). Fig. 9 Calculated luminescence spectra from the model in Fig. 3 and the corresponding one-dimensional model in Fig. 8 using values of 5 cm–1 (green trace), 30 cm–1 (red trace) and 60 cm–1 (yellow dotted trace). The influence of on the spectrum becomes important for two-dimensional potentials, as illustrated in Fig. 10 and 11. The source of this influence can be seen from the wavepacket dynamics. In the case of the palladium(II) complex in Fig. 4 the two frequencies lead to a classic Lissajous trace that "evenly maps out the plane" or explores the potential surface evenly. This causes the recurrence ofFig.10 Calculated spectra for the model in Fig. 4 using values of 5 cm–1 (green trace), 30 cm–1 (red trace) and 60 cm–1 (yellow dotted trace). Fig. 11 Calculated spectra for the model in Fig. 4 using values of 5 cm–1 (green trace), 30 cm–1 (red trace) and 60 cm–1 (yellow dotted trace). Fig. 12 Calculated spectra for the model in Fig. 6 using values of 5 cm–1 (green trace), 30 cm–1 (red trace) and 60 cm–1 (yellow dotted trace). the moving wavepacket to its starting position to be imperfect, leading to a "mismatch" which influences the spectrum: for a small damping factor the calculated spectrum shows peaks involving both frequencies and all combinations of them. For the highest value of the spectrum shows only a single vibronic progression with an interval of 215 cm–1 which does not exactly correspond to the frequencies of either normal mode used to define the potential.This is the missing mode effect (or MIME) observed in many incompletely resolved spectra involving two (or more) similar vibrational modes.19 The wavepacket motion for both the palladium and platinum complexes in Fig. 3 and 4 can be separated along the two normal coordinates. Two one-dimensional models of the type shown in Fig. 8 are therefore sufficient to calculate the spectrum. The autocorrelations for each orthogonal coordinate can be multiplied and the product autocorrelation is then used in eqn. (5) to calculate the spectrum. This one-dimensional approach is computationally more efficient than the full calculation on the two dimensional surfaces in Fig.4 and 5, which were presented in order to better visualize the wavepacket motion. The calculated spectra in Fig. 10 and 11 agree well with the experimental spectra of the square planar complexes in Fig. 1. It is interesting to comment on the differences between the platinum and palladium complexes based on the models used to analyze their spectra. The HOMO– /802H[FLWDWLRQ LQYROYHV D UHGXFWLRQ RI antibonding HOHFWURQ GHQVLW\ LQ WKH +202 DQG DQ LQFUHDVH RI antibonding electron density in the LUMO. The latter effect appears to be more important for the platinum complex, as the starting position of the wavepacket is at Q300 = 4.86, a larger value than for the palladium FRPSOH[ZKHUHZHGHWHUPLQH Q280 = 3.49.The emission origin of the platinum complex is higher in energy by 2600 cm–1 than for the palladium complex, another effect due (in part) to the stronger antibonding character of the LUMO orbital. The distortions involving the lower frequency S–M–S bending coordinates are 1.67 and 1.93 for the platinum and palladium complexes, respectively. These values indicate the distinct nature of distortions involving this bending mode. Square planar chloride complexes of the two metals show luminescence spectra involving a distortion along an asymmetric stretching coordinate (b1g in idealized D4h symmetry) that is VLJQLILFDQWO\ ODUJHU IRU SODWLQXP Q304 = 2.85) than for SDOODGLXP Q270 = 1.18).20,21 Our analysis of the spectra in Fig.1 reveals a first case of very similar excited state distortions for corresponding platinum and palladium complexes and reveals a fundamental difference between distortions along stretching and bending modes. In the case of the rhenium complex one of the frequencies is much larger than the other, causing the wavepacket to retrace a given curve. The low frequency induces a slow horizontal shift, as seen from the animation in Fig. 6, causing only a slight mismatch after one high frequency vibrational period. This has consequences on the autocorrelation function and the vibronic structure of the calculated spectrum. The calculated spectrum for the rhenium complex shows prominent peaks separated by the high vibrational frequency.Each of these peaks consists of clusters of lines separated by the low vibrational frequency. Its autocorrelation function shows recurrences at times very close to the vibrational period of the high-frequency mode, not a situation that leads to a pronounced MIME. The difference of the frequencies allows us to experimentally detect coupling of the two normal coordinates, an effect that requires the calculation of the wavepacket dynamics on the full two dimensional potential surface given in Fig. 7. This difference is illustrated in Fig. 13. The spectrum calculated from a harmonic potential (green trace) shows an identical intensity Fig. 13 Calculated spectra for the left hand model (coupled ground state) in Fig. 7 (red trace) and the right hand model (harmonic ground state, green trace).distribution within each cluster of peaks forming the main progression. It is in good agreement with the experimental spectrum in Fig.1, but does not account for the variation of the intensity distrition within each cluster of peaks. The red trace is calculated from the potential surface with coupled coordinates and clearly shows the non-replica clusters of peaks along the main progression observed in the experimental spectrum in Fig. 1, an experimental manifestation of coupling between normal coordinates. Fig. 14 Autocorrelation function for the models in Fig. 4 to 6 values of 5 cm–1 (green trace), 30 cm–1 (red trace) and 60 using cm–1 (yellow dotted trace).The wavepacket animations presented here provide an intuitive and quantitative link between the shape of ground state potential surfaces and the vibronic structure in luminescence spectra. The autocorrelation functions in Fig. 14 are the key intermediate quantities and show the influence of the resolution, expressed as the damping factor , on the observed spectra. The models visualized here address a number of effects observed in many spectra and can serve as qualitative starting points for the analysis of new electronic spectra. Acknowledgements We thank Florence Quist for synthesizing (n- Bu4N)2Pd(SCN)4 during her undergraduate research project. This work was made possible by grants from the Natural Sciences and Engineering Research Council (Canada). References 1 J.I. Zink and K.-S. Kim Shin, in Advanced Photochemistry, ed. D. H. Volman, G. S. Hammond and D. C. Neckers, John Wiley, New York, 1991, vol. 16, p. 119. 2 O. Kahn, Adv. Inorg. Chem., 1996, 43, 179. 3 T. Brunold and H. U. Güdel, in Inorganic Electronic Structure and Spectroscopy, ed. E. I. Solomon and A. B. P. Lever, John Wiley, New York, 1999, p. 259. 4 Y. Pelletier and C. Reber, Inorg. Chem., 2000, 39, 4535. 5 C. Savoie and C. Reber, J. Am. Chem. Soc., 2000, 122, 844. 6 C. Savoie and C. Reber, Coord. Chem. Rev., 1998, 171, 387. 7 E. J. Heller, Acc. Chem. Res., 1981, 14, 368. 8 M. Triest, G. Bussière, H. Bélisle and C. Reber, J. Chem. Ed., 2000, 77, 670, full article: http://jchemed.chem.wisc.edu/JCEWWW/Articles/inde x.html 9 J.-U. Rohde, B. von Malottki and W. Preetz, Z. Anorg. Allg. Chem., 2000, 626, 905. 10 M. J. Davis and C. Reber, Inorg. Chem., 1995, 34, 4585. 11 W. Tuszynski and G. Gliemann, Z. Naturforsch., A, 1979, 34a, 211. 12 J. R.Winkler and H. B. Gray, J. Am. Chem. Soc., 1983, 105, 1373. 13 J. R. Winkler and H. B. Gray, Inorg. Chem., 1985, 24, 346. 14 D. Wexler and J. I. Zink, J. Phys. Chem., 1993, 97, 4903. 15 C. Savoie, C. Reber, S. Bélanger and A. L. Beauchamp, Inorg. Chem., 1995, 34, 3851. 16 G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules, D. Van Nostrand, New York, 1945, p. 63. 17 M. D. Feit, J. A. Fleck, Jr. and A. Steiger, J. Comput. Phys., 1982, 47, 412. 18 A. B. Myers, Chem. Phys., 1994, 180, 215. 19 L. Tutt and J. I. Zink, J. Am. Chem. Soc., 1986, 108, 5830. 20 D. M. Preston, W. Güntner, A. Lechner, G. Gliemann and J. I. Zink, J. Am. Chem. Soc., 1988, 110, 5628. 21 Y. Pelletier, and C. Reber, Inorg. Chem., 1997, 36, 721. PhysChemComm © The Royal Society of Chemistry 2000

ISSN:1460-2733    

DOI:10.1039/b008386k

出版商:RSC    

年代:2000

数据来源: RSC