J. Phys. Chem. 1991, 95, 10351-10359
10351
Isomerizations Controlled by Ultrashort Infrared Laser Pulses: Model Simulations for the Inversion of Ligands (H) in the Double-Well Potential of an Organometallic Compound, [(C,H,)(CO),FePH2] J. E. Combariza, B. Just, J. Manz, and C.K. Paramonov* Institut fur Physikalische Chemie. Universitdt Wiirzburg, Marcusstrasse 9- 1 1 , 0-8700Wiirzburg, Germany (Received: March 15, 1991; In Final Form: May 30, 1991) Model simulations for the inversion of ligands (H) in the double-well potential of [(C5H5)(C0)2FePH2]yield selective isomerizations controlled by a series of intense picosecond infrared (IR) laser pulses. Essentially, these pulses induce a correspondingseries of selective molecular transitions, from the vibrational ground state to more excited states of the reactant isomer, via a delocalized state above the potential barrier, to a highly excited state of the product isomer. Simple superposition of the individual laser pulses with analytical, e.g., Gaussian, shapes yield the effective overall pulse which may have a rather complex structure. Optimal laser parameters are tailored to maximum population of the product isomers. Repeated application of these overall pulses produces pure product isomers. This rather general strategy for selective isomerization is compared with inefficient alternative ones. The simulations involve various theoretical techniques, from quantum chemical ab initio calculations of the relevant double-well potential energy surface and electric dipole function, to calculations of vibrational states and dipole matrix elements, to evaluation of the laser-induced molecular dynamics by propagation of the algebraic version of the time-dependent Schrijdinger equation.
1. Introduction In this paper, we present a model simulation of an isomerization controlled by infrared (IR) laser pulses with analytical (e.g., sinZ or Gaussian) shapes in the picosecond (ps) time domain. Previous theoretical studies have already shown that such laser pulses may induce selective vibrational transitions between molecular eigenstates,lb or dissociation of molecular bonds7 Isomerization, e.g., inversion of ligands (H) in molecules with double-well potentials, is a novel class of chemical reactions which should be controlled by related techniques. The present approach to laser-assisted isomerization is not a trivial choice since there are several alternative strategies for selective laser control of molecular transitions or reactions; see the surveys in refs 8-19. In particular, Bergmann and coworkersZohave demonstrated the successful application of a sequence of rather weak nanosecond (ns) laser pulses for selective vibrational excitation of diatomic molecules. For the present purpose, i.e., isomerization of polyatomic molecules, we shall also employ a sequence of laser pulses; however, we prefer the picosecond time domain in order to compete with other ultrafast processes such as intramolecular vibrational energy redistribution (IVR). As a consequence, these picosecond laser pulses have to be rather intense, beyond the golden rule domain for single-photon absorption or emission processes; otherwise, according to a theorem of Brumer and Shapiro,21weak picosecond laser pulses cannot achieve any better selectivity than weak continuous wave (CW) laser^.^^-^' Stronger CW IR lasers would induce multiple photon transitions, but usually these are not state s e l e c t i ~ e . ~ ~Alter-~' natively, selective molecular transitions and reactions may also be achieved by means of strong (sub)picosecond IR laser pulses with highly structured, nonanalytical, optimized shape^.^^"^ However, we prefer analytical shapes, and other properties of lasers that may be prepared with available t e ~ h n o l o g y ; see ~ ~ -also ~ ~ refs 40-48. Still another strategy for selective laser control of isomerization reactions might employ photochemical processes on attractive potential energy surfaces of electronically excited states induced by laser pulses in the visible (vis) or ultraviolet (UV) frequency domains, e.g., via selective pump-and-dump seq u e n c e ~ . ~ ' See ~ ~ refs 52 and 53 for recent studies of isomerization processes. However, application of vis or UV laser pulses should be confined to isomerization of specific systems; e&, the laser excitation should not induce ultrafast competing processes such as photodissociation. In contrast, the present strategy should be *Author to whom correspondence should be addressed. Permanent address: lnstitute of Physics, BSSR Academy of Sciences, Minsk, BSSR, USSR.
0022-3654/91/2095-lO351$02.50/0
less restrictive since it employs IR picosecond laser pulses that induce isomerization on double-well potential energy surfaces of (1) Paramonov, G. K.; S a w a , V. A. Phys. Lett. A 1983, 97, 340. Paramonov, G. K.; Sawa, V. A. Opt. Commun. 1984, 52, 69. (2) Paramonov, G. K.; Sawa, V. A.; Samson, A. M. Infrared Phys. 1985, 25, 201. (3) Dolya, Z. E.; Nazarova, N. B.; Paramonov, G. K.; Sawa, V. A. Chem. Phvs. Lett. 1 M . 145. 499. -(4) Paramonov, G. K. Chem. Phys. Lett. 1990,169,573. Paramonov, G . K. Phys. Lett. A 1991, 152, 191. (5) Jakubetz, W.; Just, B.; Manz, J.; Schreier, H.-J. J. Phys. Chem. 1990, 94, 2294. (6) Breuer, H. P.; Dietz, K.; Holthaus, M. Z . Phys. D 1988, 8, 349. Breuer, H. P.; Dietz, K.; Holthaus, M. J . Phys. E. At. Mol. Opt. Phys. 1991, 24, 1343. (7) Manz, J.; Joseph, T. Mol. Phys. 1986, 58, 1149. (8) Ben-Shaul, A.; Haas, Y.;Kompa, K. L.; Levine, R. D. Losers and Chemical Change; Springer: Berlin, 198 1. (9) Bondybey, V. E. Annu. Reu. Phys. Chem. 1984, 35, 591. (10) Crim, F. F. Annu. Rev. Phys. Chem. 1984, 35, 647. (1 1) Reisler, H.; Wittig, C. Annu. Reu. Phys. Chem. 1986, 37, 307. (12) Lupo, D. W.; Quack, M. Chem. Rev. 1987,87, 181. (13) Levine, R. D.; Bernstein, R. B. Molecular Reaction Dynamics and Chemical Reactiuity; Oxford University Press: Oxford, UK, 1987. (14) Whitehead, J. C., Ed. Selectiuity in Chemical Reactions; Reidel: Dordrecht, 1988. Whitehead, J. C. J . Phys. B. At Mol. Opt. Phys. 1990, 23, 3433. (15) Bandrauk, A. D., Ed. Atomic and Molecular Processes with Short Intense Laser Pulses; Plenum Press: New York, 1988. (16) Letokhov, V. S. Appl. Phys. E 1988, 46, 237. (1 7) Manz, J. In Molecules in Physics, Chemistry, and Biology; Maruani, J., Ed.; Kluwer: Dordrecht, 1989; Vol. 3, p 365. (18) Wolfrum, J. J. Phys. Chem. 1986, 90, 375. (19) Hartke, B.; Manz, J.; Mathis, J. Chem. Phys. 1989, 139, 123. (20) Gaubatz, U.; Rudecki, P.; Becker, M.; Schiemann, S.; Kiilz, M.; Bergmann, K. Chem. Phys. Left. 1988,149,463. Gaubatz, U.; Rudecki, P.; Schiemann, S.;Bergmann, K. J. Chem. Phys. 1990, 92, 5363. (21) Shapiro, M.; Brumer, P. J . Chem. Phys. 1986,84, 540. Brumer, P.; Shapiro, M. Adu. Chem. I'hys. I 1988, 70, 365. Brumer, P.; Shapiro, M. Chem. Phys. 1989, 139, 22 1. (22) Frei, H.; Pimentel, G. C. J . Chem. Phys. 1983, 78, 3698. Frei, H.; Pimentel, G. C. Annu. Reu. Phys. Chem. 1985, 36, 491. (23) Schwebel, A.; Brestel, M.; Yogev, A. Chem. Phys. Lett. 1984, 107, 579. (24) Lin, W. A.; Ballentine, L. E. Phys. Reu. Lett. 1990, 65, 2927. (25) Asaro, C.; Brumer, P.; Shapiro, M. Phys. Reu. Lett. 1988, 60, 1634. (26) Tiller, A. R.; Clary, D. C. Chem. Phys. 1989, 139, 67. (27) Larsen, D. M.; Bloembergen, N . Opt. Commun. 1976, 17, 254. (28) Quack, M. Adu. Chem. Phys. 1982, 50, 395. (29) Lin, S. H.; Fujimura, Y.; Neusser, H. J.; Schlag, E. W. Multiphoton Spectroscopy of Molecules; Academic Press: Orlando, FL, 1983. (30) Bagratashvili, V. N.; Letokhov, V. S.;Makarov, A. A.; Ryaboy, E.
A. Multiple Photon Infrared Laser Photophysics and Photochemistry; Harwood: Chichester, U.K., 1984. (31) Jakubetz, W.; Manz, J.; Mohan, V. J . Chem. Phys. 1989,90,3686. (32) Shi, S.;Woody, A,; Rabitz, H. J. Chem. Phys. 1988,88, 6870. Shi, S.;Rabitz, H. Chem. Phys. 1989, 139, 185.
0 1991 American Chemical Society
"1352 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991 -.05 p X/ea,
" ' E,
-.06 .06
.03
.oo
Figure 1. Electric dipole function wLx(panel a, upper) and double-well
v
potential energy surface (panel b, lower) for the inversion of ligands ( H ) between isomers A and B of the model [CP(CO)@PHZI. Also indicated are the vibrational eigenenergies E, and wave functions 4" of levels u. T h e sequence of transitions u = 0 5 1I 17 25 16 for selective isomerization induced by corresponding laser pulses is indicated by arrows (see text).
-- - -
Combariza et al. states of the system. For illustration of our new strategy for IR picosecond laser pulse control of isomerizations, we present model simulations of selective inversion of ligands (H) in the double-well potential of an organometallic compound, [Cp(CO),FePH2] (Cp = cyclopentadienyl). Specifically, the laser pulses drive the hydrogen atoms of the phosphine group away from the carbonyl ligands and toward the cyclopentadienyl ligand, Le., from the most stable toward another, energetically less favorable isomer configuration of the metallophosphorus complex; see Figure 1. The choice of this system has been motivated for several reasons. First, the present organometallic complex has been suggested to us by one of our colleagues from inorganic chemistry, Professor W. M a l i ~ c has , ~a~candidate for our novel type of laser-assisted chemistry (compare with refs 7-36 and 55). Normally, the reagents such as [Cp(CO),FePH,] may exist with thermodynamical distribution of isomers, yielding corresponding distribution of products in sequel reactions. In this situation, laser-assisted preparation of specific isomers, or nonstatistical distribution of isomers, may serve as decisive initial step for specific synthesis of the desired products. Some related inorganic chemistry aspects of the present system and its laser-assisted =prereaction" isomerization will be discussed s e p a r a t e l ~see ; ~ ~also ref 54. Second, this system allows the adaptation of some general approximations that we have applied successfully in some related previous simulation of laser-induced molecular transitions, and in quantum chemical evaluation of electronic structure in transition-metal c o m p l e ~ e s . ~ ~In~ ~particular, * we use the BornOppenheimer separation of the nuclear and electronic degrees of freedom, together with the semiclassical dipole approximation for the molecule-laser interaction; i.e. the laser-assisted chemical reaction is simulated by solving the relevant time-dependent Schrginger equation
-+
a
i h -$ = H$ at
(1)
a single electronic state, typically the ground state, irrespective of any other necessary prerequisite of the electronically excited
where $ is the nuclear wave function and N is the corresponding Hamiltonian H = T I/- i i B ( t ) (2)
(33) Peirce, A. P.; Dahleh, M. A.; Rabitz, H. Phys. Reo. A 1988, 37,4950. (34) Dahleh. M.: Peirce. A. P.: Rabitz. H. Phvs. Reu. A 1980. 42. 1065. (35) Shi, S.; Rabitz, H. J . Chem. Phys. 1990,*92, 2927. Shi, S.; Rabitz, H . J , Chem. Phys. 1990, 92, 364. (36) Jakubetz, W.; Manz, J.; Schreier, H.-J. Chem. Phys. Lett. 1990, 165, 100. (37) Corkum. P. B. Om.Lett. 1983. 8. 514. Rolland. C.: Corkum. P. B. J . 6,a:Soc. .4m. B. 1988, 5, 641. Corkum, P. B.; Ho, P. P.: Alfano, R. R.; Manassah, J. T.Opt. Lett. 1985, 10, 625. (38) Kwok, H. S.; Yablonovitch, E.; Bloembergen, N. Phys. Reo. A 1981, 23, 3094. (39) Becker, P. G.; Fragnito, H . L.; Fork, R. L.; Beisser, F. A,; Shank, C. V. Appl. Phys. Lett. 1989, 54.41 I . Laenen, R.; Graener, H.; Laubereau, A. Opt. Commun. 1990, 77, 226. (40) Dulcic, A. Phys. Reu. A 1984, 30, 2462. (41) Warren, S.; Zewail, A. H. J . Chem. Phys. 1983, 78, 2298. (42) Diels, J.-C.; Stone, J. Phys. Reu. A 1985, 31, 2397. (43) Oreg. J.; Hioe, F. T.; Eberly, J. H . Phys. Reu. A 1984, 29, 690. (44) Peterson, G. L.; Cantrell, C . D. Phys. Reu. A 1985, 31, 807. (45) Diels, J.-C.; Besnainou, S . J . Chem. Phys. 1986, 85, 6347. (46) Hioe, F. T.; Eberly. J. H . Phys. Reo. A 1984, 29, 1164. (47) Warren, W. S. J . Chem. Phys. 1984, 81, 5437. (48) Fleming, G. R. Annu. Reu. Phys. Chem. 1986, 36, 81. Lin, C. P.; Bates, J.; Mayer, J. T.; Warren, W. S. J . Chem. Phys. 1987, 86, 3750. Lin, C. P.; Bates, J.; Mayer, J. T.; Warren, W. S. J . Chem. Phys. 1987, 87, 4241 (3). Warren, W. S.; Haner, M. In Atomic and Molecular Processes with Short Intense Laser Pulses; Bandrauk, A. D., Ed.; Plenum Press: New York, 1988; p 1. Weiner, A. M.; Heritage, J. P.; Kirschner, E. M. J . Opt. SOC.Am. B 1988, 5, 1563. Kaiser, W., Ed. Ultrashort Laser Pulses and Applications; Topics in Applied Physics, Vol. 60; Springer, Berlin, 1988. (49) Hamilton, C. E.; Kinsey, J. L.; Field, R. W. Annu. Reo. Phys. Chem. 1986. 37, 493. Schafer, F. P. Appl. Phys. B 1988, 46, 199. (50) Tannor, D. J.; Rice, S. A. J . Chem. Phys. 1985, 83, 5013. Tannor, D. J.; Kosloff, R.; Rice, S. A. J . Chem. Phys. 1986, 85, 5805: J . Chem. SOC. Faraday Trans. 2 19S6. 82, 2423. Kosloff, R.; Rice, S. A,; Gaspard, P.; Tersigni, S.; Tannor, D. Chem. Phys. 1989, 139, 201. ( 5 1 ) Abrash, S.; Repinec, S.; Hochstrasser, R. M . J . Chem. Phys. 1990, 93, 1041. Sension, R. J.; Repinec, S. T.; Hochstrasser, R. M. J . Chem. Phys. 1990, 93, 9185. Repinec, S. T.; Sension. R. J.; Hochstrasser, R. M . Ber. Bunsenges. Phys. Chem. 1991, 95, 248. (52) Gruner. D.; Brumer, P.; Shapiro, M . Preprint, 1991.
for the nuclear kinetic ( 0 and potential (V) energies 9f the molecule interacting with the electric fjeld of the laser ( 6 )via the electric dipole E . The laser field ( G ( t ) ) has to be designed such that $(t) evolves from a wavepacket which represents initially ( t = 0) the first (i) isomer, and finally, at the end of the laser pulse ( t = tp), the second isomer (f).
+
=
$1
$0,)= $f
(3)
In practice we shall assume polarized light interacting with a single component of the dipole operator, preferably that which varies most strongly along the reaction path, e.g., ii&(t) = k x G x ( t ) . (A constant dipole function would not yield any molecular transitions.) This assumption involves another implicit approximation, Le., (53) Field, R. W. Results presented at the ACS conference, Atlanta, 1991. (54) First indications for the reduction of inversion barriers by an organometallic fragment are given in: Buhro, W. E.; Zwick, B. D.; Georgiou, S.; Hutchinson, J . P.; Gladyz, J. A. J . Am. Chem. Soc. 1988, 110, 2427. Malisch, W.; Maisch, R.; Meyer, A.; Greissinger, D.; Cross, E.; Colquhoun, I. J.; McFarlane, W. Phosphorous Sulfur 1983, 299. Bouman, R. Doctoral Thesis, Universitat Wiirzburg, 1987. ( 5 5 ) Zinth, W. Naturwissenschaften 1988, 75, 173. Rasanen, M.; Kuntta, H.; Murto, J . Laser Chem. 1988, 9, 123. Butenhoff, T. J.; Chuck, R. S.; Limbach, H.-H.; Moore, C. B. J . Phys. Chem. 1990, 94, 7842. (56) Combariza, J . E.; Daniel, C.; Just, B.; Kades, E.; Kolba, E.; Manz, J.; Malisch, W.; Paramonov, G. K.; Warmuth, B. In Isotope Effects in Chemical Reactions and Photodissociation Processes; Kaye, J. A,, Ed.; ACS Symposium Series; American Chemical Society: Washington, in press. (57) Dunkerton, L. V.; Tyrrell, J.; Sasa, M.; Combariza, J. "The Chemistry of Carbonyl Sulfide"; Report 1986. DOE/FE/60339-T37. Available from Energy Res. Absfr. 1987, 12(5), Abstr. No. 9545. Tyrrell, J.; Combariza, J.; Dunkerton, L. V.; Pandey, A. Ab Initio Molecular Orbital Calculations Using Effectiue Core Potentia1 on Nickel Clusters; Report DOE/DC/91272-T3, 1987. Available from Energy Res. Abstr. 12(15). (58) Combariza, J. E.; Enemark, J . H.; Barfield, M.; Facelli, J. C. J . Am. Chem. SOC.1989, 1 1 1 , 7619. Combariza, J. E.; Barfield, M.; Enemark, J. H. J . Phys. Chem. 1991, 95, 5463.
Isomerizations Controlled by Laser Pulses decoupling of the overall molecular rotations, which appears to be justified in view of the rather large value of the moment of inertia of [ C P ( C O ) ~ F ~ P H , ]and , corresponding slow rotation period t,,, >> tp (e.g., trot = 5 ps >> t, = 1 ps for J = 1). The problem of solving eqs 1-3 for isomerizations appears to be similar to equivalent problems for state-selective transition^;'-^,^^-^^ however, the solution will require substantial extensions, beyond the simplistic adaptation of the techniques of refs 1-5. The relevant methods will be presented in section 2, together with a brief summary of the quantum chemical evaluation of the potential energy surface V and the dipole function ii in eq 2. Third, and beyond the rather general motivations summarized above, the structure of our model system (see Figure 1) suggests another, rather drastic simplification for prototype model simulation of laser-assisted isomerizations. By analogy with similar systems?9@ we shall assume that IVR from the phosphine group to other ligands is blocked, or hindered on the picosecond time scale by the heavy metal atom (so-called “heavy atom blocking”). Experimental work on organometallic compounds carried out by has suggested that the heavy metal atom acts Rowland et a1.61-62 as a barrier which hinders the exchange of intramolecular vibrational energy between ligands. See also refs 62-69. Our assumption is also supported by similar observations of sequential IVR in other systems such as HCCH70 and CHX3,7’in which initial deposition of vibrational energy in some C H vibrations (stretches or bends) may be conserved during ultrashort (picosecond or subpicosecond) time scales before intramolecular thermalization by sequential IVR processes. Likewise, we assume that vibrational energy may be stored in some vibrations of the PH2 ligand during, e.g., 1 ps (shorter periods would require the same strategy but with different laser parameters). Specifically, we shall model the isomerization as the inversion of the [FePH2] group from one isomer configuration to the other, assuming conservation of C, symmetry along the reaction path and decoupling of the remaining vibrotational degrees of freedom of the PH2 ligand. Certainly, equivalent simplifications of rather complex systems are legion in the literature, in particular in the textbooks, but of course, common practice is not a justification per se; Le., we are fully aware of the important effects of coupling of many degrees of freedom in real systems, which may be obscured in oversimplified one-dimensional model^.^^-^^ Therefore, from the outset the present model simulation should be considered as a simple illustration of a novel strategy for selective laser control of isomerizations, whereas the numerical results, e.g., the resulting optimal laser parameters, should be considered as no more than (59) Peng, X.; Jonas, J . J . Chem. Phys. 1990,93, 2192. Jonas, J.; Peng, X . Ber. Bunsenges. Phys. Chem. 1991, 95, 243. (60) Lederman, S. M.; Marcus, R. A. J . Chem. Phys. 1988, 88, 6312. (61) Rogers, P.; Montague, D. C.; Frank, J. P.; Tyler, S. C.; Rowland, F. S. Chem. Phys. Lett. 1982.89, 9. Rogers, P. J.; Selco, J. I.; Rowland, F. S. Chem. Phys. Lett. 1983, 97, 313. (62) Rowland, F. S. Faraday Discuss. Chem. SOC.1983, 75, 158. (63) Wrigley, S. P.; Oswald, D. A,; Rabinovitch, B. S. Chem. Phys. Lett. 1984, 104, 521. (64) Lopez, V.; Marcus, R. A. Chem. Phys. Lett. 1982, 93, 232. (65) Swamy, K. N.; Haser, W. L. J. Chem. Phys. 1985, 82, 123. (66) Lederman, S. M.; Lopez, V.; Voth, G. A.; Marcus, R. A. Chem. Phys. Lett. 1986, 124, 93. (67) Marshall, K. T.; Hutchinson, J. S. J. Phys. Chem. 1987, 91, 3219. (68) Lederman, S. M.; Lopez, V.; Fairen, V.; Voth, G. A,; Marcus, R. A. Chem. Phys. Lett. 1989, 139, 171. (69) Uzer, T.; Hynes, J. T. In Stochasticity and Intramolecular Redis-
tribution of Energy; Lefebvre, R . , Mukamel, S., Eds.; Reidel: Dordrecht, 1987; p 273. Uzer, T.; Hynes, J. T. Chem. Phys. 1989, 139, 163. (70) Holme, T. A,; Levine, R. D. J . Chem. Phys. 1988.89, 3379. Holme, T. A,; Levine, R. D. Chem. Phys. 1989, 131, 169. (7!) Marquardt, R.; Quack, M. J. Chem. Phys. Preprint and references therein, 1991. (72) Makri, N.; Miller, W. H. J . Chem. Phys. 1987.86, 1451. Miller, W. H.; Ruf, B. A.; Chang, Y.-T. J . Chem. Phys. 1988.89, 6298. (73) Okuyama, S.; Oxtoby, D. W. J . Chem. Phys. 1988,88,2405. Shida, N.; Barbara, P. F.; Almlof J . Chem. Phys. 1989, 91, 4061. (74) Sekiya, H.; Nagashima, Y.; Nishimura, Y. J . Chem. Phys. 1990, 92, 5761. Redington, R. L. J . Chem. Phys. 1990, 92, 6447. Bosch, E.; Moreno, M.; Lluch, J. M.; Bertran, J. J. Chem. Phys. 1990, 93, 5685. (75) Stiickli, A.; Meier, B. H.; Kreis, R.; Meyer, R.; Ernst, R. R. J . Chem. Phys. 1990,93, 1502. Meyer, R.; Ernst, R. R. J . Chem. Phys. 1990, 93, 5518.
The Journal of Physical Chemistry, Vol. 95, No. 25, 1991
10353
TABLE I: Selected Internuclear Distances (A) and Angles (deg) for the Complex [Cp(C0)2FePH2y Fe-P 2.30 Fe-CO 1.75
P-H
1.4328 1.7760 1.1500
Fe-Cp
c-c
1.34
c-0
HPH CFeC
95.0
PFe(C0) CpFeP
90.0
90.00
125.0
“Adapted from ref 54.
semiquantitative, subject to more accurate and self-consistent verification in more realistic, i.e., multidimensional models. The model and techniques, the results and the conclusions are presented in sections 2-4.
2. Methods 2.1. Ab Initio Calculations. The potential energy surface (PES) for the ground state of the complex [ C P ( C O ) ~ F ~ P H was ~ ] calculated using the a b initio program These calculations were carried out only at the SCF level due to the size of the system and the high number of electrons which make post-SCF calculations quite expensive. The corresponding energies and dipole moments were calculated as functions of the inversion angle ( u ) as seen in Figure 1. The basis sets used for all atoms were of double-{quality for the valence shells. For the iron atom Huzi n a g a ’ ~basis ~ ~ sets were used with the addition of a diffuse dfunction.78 The 4p orbitals were represented by two single ~rimitives.~’ All other atoms in the molecule were described using P ~ p l e ’ 4-3 s ~ 1G ~ basis sets. Selected internuclear distances and bond angles are shown in Table I. These geometrical parameters were taken from experimental information available for similar type of metallophosphiness0and the system is set so that the origin of the Cartesian coordinates is located at the center of mass. As seen in Figure 1, the profile for the PES shows two wells, supporting two isomers A and B, separated by an energy barrier of 83 kJ/mol. Despite the simplicity of the calculations, this energy barrier agrees (fortuitously) well with experimental data available for similar type of ferrophosphines.80 Also depicted in Figure 1 (top) is a profile of the x component of the dipole moment function plotted against the inversion angle (a). This component induces dominant laser transitions since it varies the most along the reaction path, unlike the z component which is almost constant and t h e y component which by symmetry reasons is always zero. 2.2. Laser-Assisted Reaction Dynamics. The time-dependent simulation of laser-assisted selective isomerizations of [Cp(C0)2FePH2],or similar systems with specific double-well potential V and electric dipole interactions E , poses a number of technical and strategic problems (assuming the simple model of section 1): (i) solution of the time-dependent Schrdinger equation (1) subject to the Hamiltonian H , depending on V and for the specific system, eq 2; (ii) specification of the initial ( t = 0) and final ( t = fp) wave functions $(O), and $(tp), eq 3; (iii) design of optimal laser pulses for the transition from $(O) to $(tp). The general solution of problem (i), as adapted from refs 1-5, will be summarized briefly below, followed by a more detailed presentation of our new solution of the related problems (ii) and (iii). Solution (i). For nondissociative isomerizations, the wave function # ( t ) may be expanded in terms of molecular eigenstates 4o with eigenenergies E,. In brief Dirac notation, ~
~
~~~~
(76) Original program assembled by the staff of the NRCC: M. Dupuis,
D. Spangler, and J. J. Wendoloski. National Resource for Computations in Chemistry Software Catalog, University of California: Berkeley, CA, 1980; Program QGOI. This version of GAMES is described in the Quantum Chemistry Program Exchange Newsletter: Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A., Jensen, J . H.; Koseki, S.; Gordon, M. S.; Nguyen, K. A.; Windus, T. L.; Elhert, S. T. QCPE Bull. 1990. IO, 52. (77) Huzinaga, S. Gaussian Basis Sets for Molecular Calculations; Elsevier: New York, 1984. (78) Hay, P. J. J. Chem. Phys. 1977, 66, 4377. (79) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971, 54,
-
774 . ..
(80) Angerer, W.; Sheldrick, W. S.;Malisch, W. Chem. Ber. 1985, 118, 1261. Malisch, W.; Angerer, W.; Cowley, A. H.; Norman, N. C. Chem. Commun. 1985, 1811. Malisch, W.; Weis, U. To be published.
10354 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991 I$i(t))
= CI4u)Cui(t)
Combariza et al. Bo-B10
40-------~11~
(4)
(CO-C10
U
with time-dependent coefficients Cui(t)and corresponding population probability for levels u Pui(t) = Icui(t)12
(5)
which depend on the initial (i) preparation, e.g., i = 0 for the initial ground state. For our model the wave functions $+,(a) = (al&) E (alu) versus inversion angle a are also shown in Figure 1, together with the energies E,,. They are obtained by solving the time-independent Schrijdinger equation Hmoh = Eu4u with molecular Hamiltonian Hmol = T V
(6)
I
A0
1
A 11
BO
1 J
B10 -
co
+
(7) for the double-well potential V evaluated in section 2.1, plus the kinetic energy T along the inversion coordinate a,
c10
Figure 2. Electric.dipole transition elements px,uvcoupling the levels u,u
Here I H H is the moment of inertia associated with the inversion of ligands (H). Essentially, the center of mass of the two hydrogen atoms with masses mHis turned around the phosphorus atom from isomer A to B at a distance p which is approximately constant, p = 0.968 A. Thus = 2mHp2 (9) As shown in Figure 1, the resulting wave functions are either localized in the potential well representing isomer A or in the well of isomer B, or they are delocalized, spreading over the common "C" domain for isomers A and B. It is, thus, convenient to consider the molecular states as A, B or C labeled either by overall molecular quantum numbers u, or by corresponding quantum numbers AuA,BuB,or Cut. For example, Figure 1 shows that the ground state of isomers A and B, i.e., q50 and 42,may be assigned as $AO and 4Bo,respectively. Likewise, the first delocalized state, with energy just below the potential barrier, is defined as 423= This definition of is made somewhat arbitrarily by inspection of the wave functions. A comprehensive list of corresponding quantum numbers for the molecular states of our model is presented in Table 11. Insertion of the expansion (4), followed by Dirac-bra operation of the molecular states (ut, converts the original time-dependent Schrijdinger equation (1) into its algebraic version IHH
ta.
a
i h - e i = %ei at
(10)
with vector ei of expansion coefficients Cui(t),and Hamiltonian matrix % with elements H u m = Eu6, - Z U u a t ) In the preferential case of x-polarized light, ZUU*&O
= PX,UU*~X(O
= Ut)
(1 1)
= AuA,BuB, CuCof isomers A, B and the group of highly excited states C (see Table 11). The absolute values of pxx,uv are indicated by the intensity of shaded squares which is proportional to the logarithm of (px,uvl.The largest and smallest intensities correspond to 1pX,,,,1= lo-' and 10-lo, respectively. Black diagonal elements and white off-diagonal elements (for values lpx.uvl< are not to scale.
carried out using atomic units. The numerical propagation should be converged with respect to the grid parameters used and with respect to the number of molecular eigenstates. Solution (ii). As initial state, let us assume that [Cp(C0)2FePH2] is prepared in its ground state I$(O))
= 10)
E
IAO)
with equivalent expansion coefficients C,(t=O) = 8,
The electric dipole transition elements px,ware illustrated in Figure 2. In practice, eqs 6-9 are evaluated by means of finite differences for spatial grid representations (Aa = ?r/720) of the wave functions &(a). The same grid representations are used for calculations of the electric dipole matrix elements (ulpxlu),eq 12, making use of the trapezoidal rule. Finally, the algebraic Schrijdinger equation (10) is propagated by means of the Rung-Kutta technique with time steps At = 1.292h/Eh. The routines are adapted from ref 81 and from the IMSL library.82 All numerical calculations are (81) Smith, G. D. Numerical Solution of Partial Differential Equations: Finite Difference Methods, 2nd ed.; Oxford University Press: Oxford, UK, 1978. (82) IMSL Library. Fortran Subroutinesfor Mathematics and Statistics; Version 9.0, 1985.
(1 3b)
Hence, for the purpose of isomerization from A to B, the ideal final state should be a superposition of molecular states representing the other isomer B, I$(tp)
) =
CBuB,AO(tp)
(14a)
UB
In principle, the general ansatz (14a) is rather flexible, allowing suitable specifications depending on the molecules and available laser fields. For [ C P ( C O ) ~ F ~ P Hor~similar ] systems we find it convenient to set I$(tp)) equal to a single, highly excited molecular eigenstate representing the B isomer (except for an irrelevant, arbitrary phase factor e'"), e.g. I$(tp))
= (B7)e'"
116)eia
(14b)
with equivalent expansion coefficients
CUO(~~) 6u16eia (12)
(134
(14c)
and with energy EI6= EB7 close to the barrier. In general, this selection of highly excited B states is motivated by two reasons: First, once these states are populated, in practice successive relaxation processes such as IVR, or collision-induced deactivations yield lower excited B states. Here one can let other competing processes such as IVR work in one's favor. Second, as justification a posteriori, our new strategy (iii) yields these highly excited B states more easily than lower ones. Solution (iii). The design of an optimal laser pulse for the transition from an initial state (13a) to a final state (14b), inducing the inversion process from isomers A to B, is of course the most difficult task. Our solution is based on a sequence of transitions between molecular eigenstates which is constructed and implemented according to the following set of rules (for illustrations see Figure 1; see also ref 83). (83) Paramonov, G. K.; Sawa, V. A. Chem. Phys. Lett. 1984,107,394.
The Journal of Physical Chemistry, Vol. 95, No. 25, 1991 10355
Isomerizations Controlled by Laser Pulses TABLE 11: Laser Pulse Induced Transitions in [Cp(CO),FePH2] * L 3 2 N“ 1 1 1 23 0 19+0 2360 ok+l Ok
-
+
10
nk uk Jcm-‘
C,,JEh 9;’ tpk/PS Ik/T W
618.58 0.1967 1 736.97
a0-I
cm-2
11 624.52 0.1918 1 718.61
11 629.28 0.2302 2.4 862.48 0.13 0.03 0.02 0.01 0.02
u
IU,d
Pu.q(tpk)e
0
0.46 0.18 0.02 0.04 0.02 0.01
0.18 0.1 1 0.01 0.02 0.03
5
A0 A1 BO A2 B1 A3
6 7 8 9 10 11
B2 A4 83 A5 84 A6
0.01 0.01 0.02 0.01 0.01 0.01
0.02 0.05 0.02 0.05
12 13 14 15 16
B5 A7 86 A8 87
0.02
1 2 3 4
0.01 0.01
A9 88 A10 B9 A1 1 B10
26 31
c8
37 38 39 240
C14 C15 C16 LC17
0.01 0.07* 0.07 0.01
...
...
1 343.94
5 5 56 4 5 1 2 5 ~ 1 7 1 6 ~ 2 5 ?-+2 1 1 1 1804.75 2121.46 1987.65 0.1129 0.0551 0.1713 1 1 1 422.99 206.44 641.80
0.01
0.04
0.04 0.01
0.05
0.99;
0.04 0.01 0.06 0.04
0.01
0.01 0.01 0.96*
0.01 0.02 0.01 0.01 0.01
0.02 0.03 0.03
0.97.
c2
c3
0.01
0.01
c1
3 1 7 6 11 1 1736.52 0.1117 1 418.50
0.97*
0.25* 0.03
0.01
J
2 ll+5 1 1890.29 0.0918
0.99
0.01 0.02; 0.01 0.02
co
c
J
1 5+0 1 1987.65 0.1713 1 641.80
0.03
0.01
0.13
17
18 19 20 21 22 23 24 25
c
C
J
0.26
0.56*
0.02
0.02 0.01 0.01 0.01
0.01 0.02 0.01 0.01
0.02 0.01
0.13 0.02
“Strategy employing N laser pulses (see text). N = 3: three-laser-pulsescheme. N = 2: two-laser-pulse scheme. N = 5: five-laser-pulse scheme (optimal strategy). bOptimal N = 5 strategy applied to the reaction starting from level BO to an unspecified target level. ‘ k : number of laser pulses ( = l , 2, ..., N). For inefficient strategies, e.g. N = 2 or 3, the results are presented exclusively for k = 1; vk+, v k : transitions from levels uk to target level o k + I . nk: approximate number of photons, eq 18. wk: carrier frequency of IR laser puke. Cxk: maximum field strength of x-polarized laser pulse. 1,: maximum intensity. tp: pulse duration. dlevel uI = uA. uB or uc of isomer I = A, B, or group of delocalized (“common”,C ) levels. ‘Population of levels at the end ( t = t p k ) of laser pulse, starting from level uk. For the optimal strategy ( N = 5), populations of target levels Vk+l are marked with an asterisk. Marginal populations (P < 0.01) are deleted.
-
Rule 1. The transitions are labeled k = 1,2, ...,N, and N should be as small as possible. Rule 2. The kth transition leads from a molecular eigenstate Iuk) to another Iok+,). The first transition starts out from the initial state, typically Iul) = (AO). The next transitions yield more excited isomers A with energies close to the potential barrier (A0 A3 A6 A9 in Figure 1). Then the next transition(s) yield(s) an excited delocalized state (A9 C2 in Figure l), and the final transition(s) lead(s) to the target state of isomer B (C2 8 7 in Figure l ) , as specified above (solution (ii)). In the present case, the entire sequence of transitions is thus
- -
-
-
A0
-
- - - - A3
A6
A9
C2
B7
(154
-- - - -
or in equivalent notation for overall molecular eigenstates. 0 5 11 17 25 16 (15b) The sequence ends at a highly B state, as anticipated above (solution (ii)). Any prolongation by additional transitions to less excited B states, say E7 B4, would be in conflict with rule 1. Rule 2 implies an energetic udetourn of the sequence of transitions, leading from the initial A state to the final B state via an even more excited C state. This is a tribute to the inherent nature
-
of isomerizations, leading from isomer A to B, with individual domains (wells) of the potential energy surface, and corresponding zero (or entirely negligible) overlap of the spatial domain of their mutual wave functions, IAuA), IBuB). As a consequence, most vanish-they cannot electric dipole matrix elements ( Bu&~~AuA) support laser-assisted transitions from A states to B states; see Figure 2. Therefore, laser-assisted isomerizations have to be mediated by transitions via delocalized states (Cu,) which spread over the spatial domains of IAuA) and I&), implying nonzero and A ) ( B V ~ ~ ~ , ~which C D , )serve as indirect elements ( C U C I ~ ~ I A U couplings of A and B states. In addition, this “energetic detour” increases the number N of transitions for isomerizations, in comparison with nonreactive excitation of individual molecules, as considered in refs 1-5 and 32-36. As a consequence, laserassisted isomerizations are inherently more difficult to achieve, and they call for more complex strategies, than nonreactive transitions; see also ref 84. Rule 3. The individual transitions k from Iuk) to I U ~ + ~ ) are achieved (for modifications see rule 4 below) by single IR laser pulses in the picosecond domain, with analytical shapes. The appropriate electric fields Z k ( t ) = Zk-[sin uk(t-tk)] OS^( t - t k ; t p k ) (16)
Combariza et al.
10356 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991
zk
have amplitudes = (6k,0,0)T in the case of x-polarized light, IR frequencies w k , delay times t k , pulse durations t p k , and normalized shapes, e.g.
Sk(T,tp) = exp[-4(ln 2)(27/tP -
(174
for Gaussian laser pulses or
Sk(7,tp)= sin2 ( m / t , )
( 17b)
for sin2 pulses. For a specific pulse duration tpkand delay time t , the parameters Gk and wk may be determined as in refs 1-5. In particular, the shape of the laser pulses (17a,b, etc.) is rather irrelevant,2 yielding similar optimal frequencies fdk close to zero-order frequencies wkoof nk-photon transitions between state 10,) and I U ~ + ~ ) , with eigenenergies Euk and
wk
wko =
IE”,,
- Eu,l/(nkh)
pulse duration should be sufficiently short ( t p5 etc.), and the overall efficiency, measured by Pfi(tp)should be as large as possible, close to or even larger than the reference value (22). Rule 5. For a selective isomerization from A to B, one should also verify that the effective laser pulses do not induce the reverse reaction from B to A, otherwise the success for the forward reaction would be annihilated by similar “successw for the back reaction. For this purpose one should test the effect of laser fields & k ( t ) on isomer B prepared in the ground state IBO). Rule 6. Finally, one should consider the entire distribution Pu,(tp)which is established at the end of the optimal laser pulses, as generated according to rules 1-4. In particular, the probabilities of observing isomers A, B, or the group C of ucommon”, highly excited delocalized states are PAJ(tP)= CPA”,,(t,)
(18)
(234
LA
For low-amplitude G k and maximum intensity
PBl(t,)
= Cp,,,(t,)
(23b)
“B
= C606k2
(19)
condition (18) should be satisfied preferably with low values of f l k , corresponding, e.g., to zero-order single or two photon transitions, rather than high-order multiple photon transitions. To some extent this latter condition would suggest a rather large number N of individual transitions; Le., rules 1 and 3 are somewhat antagonistic. In practice, one seeks a compromise; i.e., the energies EOkof successive levels Iuk) should satisfy condition (18) yielding an overall small number N of low-order nk-photon transitions, with frequencies wk of available lasers. The corresponding “compromise” sequence of transitions for our model, [Cp(C0)2FePH2],eq 15, is illustrated in Figure 1. In particular, all individual transitions have zero-order singlephoton transition frequencies. These laser frequencies are experimentally available, e.g., the second harmonic frequencies of C 0 2 lasers; see Table 11. Various other transitions, e.g., an alternative final transition to a B-state which is less excited than l B 7 ) ) , do not satisfy rules 1-3. IB7) (such as IC2) In ideal cases of isolated molecules, rules 1-3 would suggest a sequence of separate laser pulses for successive transitions k = 1, 2, 3, ..., N . The corresponding electric field is simply a superposition of the pulses for individual transitions (16)
-
3(t) = CZk(t) k
(20)
with delay time t k which separate the individual pulses. As a consequence, the overall pulse duration t , is rather long,
and the overall probability P4(tP)for population of the target state V, = I U ~ + ~ ) , starting from initial state li) = l u , ) , is essentially for all the individual the product of the probabilities Puk+,uk transitions, (see eq 4)
P/i(‘p)
~ ~ ~ + ~ u ~ ( ~ p N ) ~1..u~ ~P ~~ ~p ~ ((f ~p p 2( f)pNl~)-ulp ~
(22)
Pfiis smaller than any of the individual Put+,ut(except in the ideal case, P = l), and a large value of Pfi, i.e. high selectivity of the overall sequence of laser pulses, calls for a small number N (see rule l!) of highly efficient individual transitions, Puk+,uk 1 (see rule 3). A possible disadvantage of the combination of separated laser pulses (20) is, however, the rather long duration t,, see eq 21. In realistic cases, this overall pulse duration may exceed the time scale of competing processes, e.g., t, > TIVR such that IVR from “intermediate” molecular levels of the sequence (1 5) may destroy the overall selectivity of the ideal series of laser pulses (20), even if the individual pulse duration tpk is shorter than T I V R , etc. In order to reestablish a sufficient short duration of the overall sequence of laser pulses, we suggest the following. Rule 4. The individual pulses (16) should be “merged” with sufficiently short delay time t k and simultaneous retuning of the pulse parameters; see also refs 53 and 83. The resulting overall
PCI(t,)
= CPC“,,(t,)
(23c)
LC
In ideal cases of perfect selectivity, Le., exclusive population of the target state uN+,, eqs 23 yield p A ~ ( t p ) = PC~(tp)
= 0,
pB~(tp)
= puN+,t(tp) =
(24)
However, realistic cases deviate from (24), since all molecular levels will be populated with marginal probabilities. In practice, this nascent population will relax toward thermal distribution due to inter- and intramolecular energy relaxation processes, preferably by deactivation of highly excited states. As a consequence, it is fair to assume that most delocalized C states will end up as A or B states, on a time tA,B< >> picoseconds, where the nascent A and B states are essentially separated by the potential barrier (on a still longer time scale t t h >> tA,B+, the thermal equilibrium of A and B isomers will be reestablished, e.g., by tunneling or collision-induced barrier crossing). Let MAand APB be the increments of population probability of isomers A and B gained from nascent C states at time tA,BCC, U
A
APA
+ APB
N
APB
PC~(tp) N
0.5Pcl(tp)
(25a) (25b)
in the case of similar phase space of isomers A and B, as in the case for [Cp(C0)2FePH2],cf. Figure 1. Then the overall population probabilities of isomers A and B are
PA
J‘A,(tp)
+ MA, PB
PBl(tp)+ APB
(26)
at time t A , B d . For sufficiently low temperatures, most of the A states will be found in the ground state AO. One should now repeat the sequence of laser pulses: As a consequence, (most) part (i.e., PB)of the remaining isomer A will be transferred into isomer B, etc. After M shots of optimal series of laser pulses fired with delay time t, tA,B 0.97 for individual pulse durations tpk= 1 ps, with one exception, i.e., PaA9(tp) = 0.56. The transition from highly excited A states to delocalized C states turns out to be an (acceptable, see below) bottleneck, associated with relatively small
-
> E
. CD
15-’
1001
’
’
’
’
2
3
05-
=
u)
-100
; \\\,.
inn,
1
= 0.96.0.56*0.97.0.99.0.97 = 0.50
(28)
It is important that this selectivity (28) be achieved by means of a sequence of laser pulses which have realistic parameter^^'-^^ (see 0 1 2 Table 11). t t p s For appreciation of the success of our new strategy, let us Figure 3. Electric field C = Cx (panel b, middle) and resulting 0 u compare the results of rules 1-3 with alternative approaches. As transition probabilities Pa (panel c, bottom) versus time t. The electric discussed in section 2, there is no way for laser-induced isomerfield is a superposition of three Gaussian fields &xk(t) of successive laser ization from A to B states that would avoid the “detour” via highly pulses (k = 1, 2, 3) indicated by their envelopes Sk (panel a, top); see excited, delocalized C states. One of the simplest possibilities for eqs 16, 17a, and 20 and Table 11. They are tailored to successive excisuch a detour that comes into mind is a strategy for N = 2 laser tations u = 0 5 11 17 (or AuA = A0 A3 A6 A9) of pulses, for direct transitions from initial state IAO) to a delocalized vibrational levels u = AuA of isomers A of [Cp(C0)2FePH,]; see Figure C state JCuc),followed by a transition from ICu,) to a highly 1 and Table 11. Also indicated (panel c) are the sums Pk,, Pm, of excited B state, similar to the final transition IC2) IB7) in the complementary transition probabilities Pa(t) yielding levels u (#O, 5 , 11, 17) of isomers A,B or the “common” group C of highly excited delopreceding sequence (1 5), i.e., a “vibrational version” of the original calized levels, respectively. “electronic” pump-and-dump ~ c h e m e . To ~ ~explore , ~ ~ this possibility, we have tried to optimize an analytical IR ps laser p ~ l s e ’ ~ * ’ ~ with the carrier frequency w lis necessarily off-resonance; Le., it CO. The for the initial “pump” step, e.g., for the transition A0 cannot match all relevant energy gaps supported by strongly resulting optimal populations Pu,o(1 ps) are also shown in Table anharmonic double-well potentials. Moreover, a large set of 11. The result is entirely negative, Le., the maximum population significant electric dipole transition elements, (ulplu) (Figure 2), of the target state CO that is achieved after t p = 1 ps by means yield intense laser-induced couplings of many levels lu),lu), causing of 11-photon transitions, is only (.l. ps) = 0.02. Other broad distribution of populations. Similar obstacles may prohibit multiple-, single-, or double-photon transitions are even less efselective transitions by traditional C W multiphoton excitaficient. Scanning the pulse duration tpl in a wide range (500fs On the other hand, single- or few-photon transitions tion.12*28-30 to 4 ps) yield the maximum population of the target state PaA0(2.4 are blocked by exceedingly small dipole transition matrix elements ps) = 0.25, unfortunately though for a longer pulse duration t , (Figure 2). In conclusion, isomerization of molecules such as = 2.3 ps (Table 11). But even this “optimal” value is prohibitively [CP(CO)~F~PH cannot ~ ] be achieved with an all-too-small ( N small because the corresponding value of PA would exceed 0.75, I 3) number of laser pulses; they demand the present strategy calling for a large number M of laser shots to prepare pure isomers ( N = 5). B (see rule 6) eqs 23-27. Obviously, the vibrational version of Rule 4. The effects of merged laser pulses are demonstrated the “pumpand-dump” strategy is inefficient for selective inversion for two groups of transitions, inducing excitation of isomer A ( k of ligands (H) in [ C P ( C O ) ~ F ~ P H ~ ] . = 1, 2, 3) and isomerization ( k = 4, 5 ) in Figures 3 and 4, Still another strategy might employ N = 3 successive laser respectively. For simplicity, the delay time between any two pulses, e.g., first from the ground state to a highly excited state successive pulses has been set equal to tpk/2;Le., the sequel pulse of isomer A, followed by two laser pulses for selective transitions starts when the preceding one has its maximum intensity. In via a C state to the target B state. As a test of this strategy, we addition, we adapt all pulse parameters from Table I1 without present in Table I1 our best results for the first picosecond IR laser retuning. This model simulation should demonstrate that efficient pulse, taylored to the A0 A10 transition. Again, the maximum merging of laser pulses is possible. Optimization of rule 4, e.g., ps) = 0.07, is propopulation of the target state, PAIO,AO(tp=l by achieving even larger product selectivity within even more hibitively small. reduced overall pulse durations at the expense of considerable A detailed explanation of the failure of the two previous apretuning of laser parameters, is beyond the scope of this paper. proaches is beyond the scope of this paper. Suffice it here to say The efficiency of merged laser pulses is obvious from Figures that selective excitation of very high overtones by a single laser 3 and 4. This clear success is associated with some phenomena pulse is prohibited by two obstacles: On the one hand, for multiple which deserve special comments. zero-order photon transitions (eq 18) the energy hwl associated First, the effective laser fields are highly structured, similar to the laser fields obtained by laser pulse design with nonanalytical (84) Benmair, R. M. J.; Yogev, A. Chem. Phys. Lett. 1983,95, 72. shapes, as pioneered by Rabitz et a1.;32-35see also our comple(85) Combariza, J . E.; Gortler, S.; Just, B. In Selectioe Reacfions of mentary approach?6 On first glance, these laser fields may appear Metal-Actioafed Molecules; Werner, H., Griesbeck, A,, Eds.; Vieweg: Braunschweig, in press. as “impossible” or entirely unrealistic to the experimentalist. Yet,
-
-
-
-
-
-+
-
-
- - -
10358 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991 80r-
'
I
"
,
,
,
"
"
"
"
I
E >
. CD
r
,
,
,
,
,
,
,
,
,
-
-
Ln
,
-
the reverse process 8 7 C2. However, in practice most states lB7) will relax to less excited B states before any repetition of the pulse for the transition C2 87 (e.g., according to rule 6). Therefore, we may conclude safely that the series of laser pulses designed above will induce exclusively the forward reaction-quod erat demonstrandum. The robustness of product states lev,) against laser pulses for B is not all too surprising. After all, the forward reaction A the preparation of these laser pulses requires careful optimization of the laser parameters-deviation from a rather narrow range of optimum values destroys the selectivity; see the sensitivity analyses in refs 1-6. Likewise, there should exist some optimal laser pulses for the reverse reaction, again with very specific laser parameters. But it is entirely improbable that the optimum laser parameters for forward and backward reactions fall into the same, very narrow ranges. As a consequence, optimal laser pulses for the isomerization process A B will not induce the reverse process A. B Rule 6. The series of separated or merged laser pulses discussed above (see Table I1 and Figures 3 and 4) yields 0.50 population probability of the target state B7 of isomer B. The transition probability for isomerization from level A0 of isomer A to arbitrary = 0.55. An adlevels BvB of isomer B is slightly higher, PB,AO ditional fraction of isomer B, AB = 0.07 may be gained by relaxation of highly excited C states (see eqs 25 and 26), yielding an overall ratio of isomers
.
-801 801
Combariza et al.
,
-
P Q'
0.5
0.0
-
t I ps
Figure 4. Electric field &' = gX(panel b, middle) and resulting 17 u transition probabilities PVl7(panel c, bottom) versus time t . The electric field is a superposition of two Gaussian fields GXkof successive laser pulses (k = 4, 5 ) indicated by their envelopes Sk (panel a, top); see eqs 16, 17, and 20 and Table 11. They are tailored to selective isomerizations
by two successive transitions, starting from the highly excited vibrational level u = 17 N A u A = A9 of isomer A (as prepared by the sequence of laser pulses in Figure 3) via the highly excited, delocalized state u = 25 N CuC = C2 toward the highly excited level u = 16 N Bue = 8 7 of isomer B. Also indicated (panel c) are the sums Pb17,P'B17, P'c17 of complementary transition probabilities PUl7(t)yielding levels u ( f 17,25, 16) of isomers A, B or the "common" group C of states Cuc, respectively.
-
[B]:[A] = Ps:PA = 0.62:0.38
(29)
Further enhancement of isomer B may be achieved by M successive shots of laser pulses; e.g.
PB(M)= 1 - 0.38M > 0.95
for M 1 2
(30)
Thus, rather few repetitions of the present series of laser pulses yield highly purified B isomers of [Cp(CO),FePH,].
4. Conclusions The present model simulations in the double well potential of [CP(CO)~F~PH yield ~ ] selective isomerizations controlled by a series of intensive picosecond I R laser pulses with analytical, e.g. Gaussian, shapes. These pulses should be designed according to the set of rules 1-6 of section 3. Essentially, the pulses induce by construction, they are nothing else but a simple superposition a corresponding series of selective transitions, from the vibrational of a few (two or three) Gaussian laser pulses, which may be ground state to more excited states of the reactant isomer A, via prepared using available te~hnology.~'-~* a delocalized state belonging to the common C group of levels Second, the sequences of selective transitions v = 0 5 11 with energy close to or above the barrier, to a highly excited state 17 as well as 17 25 16, which have been determined for of the product isomer B. Simple "merging" of the individual separated laser pulses by the rules 1-3, appear to be also the pulses, i.e., superposition of laser pulses with the proper delay time dominant mechanism for the merged pulses; see the time evolution (and possibly with reoptimized parameters for the analytical for the corresponding transition probabilities Pm(t) for v = 0, 5, shapes), yields the effective overall pulse. In spite of this simple 11, 17,25, 16 shown in Figures 3 and 4. Turning the table, any construction, this overall pulse may have rather complex structures, 'bottleneck" prohibiting selective individual transitions vk 7vk+l similar to those obtained by nonanalytical design of laser pulses, may also act as an obstacle in merged laser pulses. In particular, as suggested by Rabitz et a1.31-35(see also ref 36). The relation C2 (or v = 17 the individual transitions between levels A9 of simple individual versus complex overall laser pulses will be 25) yield rather low population of the target state, P25,17(l ps) discussed elsewhere. The overall pulse is tailored to maximum = 0.56 (Table 11). As a consequence, merged pulses for transitions population (typically less than 100%) of the product target state. A9 C2 and C2 8 7 (or 17 25 and 25 16) also yield Repeated application of such overall laser pulses yields pure no more than 0.56 population of the target state 87. Hence, the product isomers, without any back-reactions to reactant isomers. overall efficiency of a series of merged laser pulses is determined The present strategy should be rather general, yielding selective by the "weakest member of the chain". It will be interesting to isomerizations in other molecules as well. However, the optimal investigate whether this limitation may be overcome by comchoice of the number and parameters of laser pulses will depend prehensive reoptimization of the parameters of merged laser pulses, on the specific system. For the present model compound, [Cpstarting from the reference values for separated laser pulses. (C0)2FePH2],N = 5 pulses with appropriate parameters were Rule 5. As a test for exclusive selectivity of the optimal laser found to be efficient, whereas in other cases, e.g., with lower pulses for the "forward" isomerization A B, we have carried barriers, N = 3 or even N = 2 pulses may be sufficient, in contrast out model simulations of the effect of these laser pulses on isomer with [ C P ( C O ) ~ F ~ P H Extrapolating ~]. the present results, there B. For example we list in Table I1 the transition probabilities should be only few "optimal" sequences of transitions satisfying Pu2(tpl) induced by the first laser field 6 , ( t )acting on isomer B all rules 1-3 for a specific molecular isomerization. prepared initially in the ground state, I$+(O)) = I$Bo) Obviously, the resulting value P2*(tpl)N 0.99 is entirely dominant; We anticipate a broad range of applications of the present strategy including also laser-induced selective isomerizations Le., the laser pulse for selective forward reactions A B leaves between more than two isomers, or preparation of specific isothe product isomer B unchanged. The only exception from this rule is the final pulse for the transition to isomer B, v N u ~ + ~ topomers for isotope separation in sequel reactions.56 Needless = C2 B7. By time reversal, the same pulse might also induce to add and to repeat the caveats in section 1, all model simulations
-
--
--
-
-
-
-
-
-
-
-
-
-
10359
J. Phys. Chem. 1991, 95, 10359-10369 have to be tested for self-consistency in more realistic modelsultimately by experimental verifications. In accord with previous and sequential IVR,70,71the models of heavy-at~m-blocking~~"~ next step in this direction should extend the present investigation from simple inversion to coupled inversion-rotation of the FePH2 group, possibly including the PH stretches. In any case, the present results point to series of IR picosecond laser pulses with analytical shapes as novel, promising tool for laser-assisted chemistry.
Acknowledgment. We extend thanks to Professor W. Malisch for stimulating discussions about his [ C P ( C O ) ~ F ~ P complex, H~] to Mrs. E. Kolba for presenting our results at the Kasha conference "Photoinduced Proton Transfer Dynamics", Tallahassee, FL, Jan
1991, and to Professors P. Brumer, M. Shapiro, and M. Quack for sending their papers prior to publication. G.K.P. thanks Mr. T.-M. Kruel for emergency computational support during some midnight sessions. J.M. thanks Professor X. Chapuisat for indepth correspondence on related aspects of the multidimensional dynamics in the system, and President M. Gorbachev for catalyzing this international cooperation. Generous financial support by the Fonds der chemischen Industrie and by the Deutsche Forschungsgemeinschaft (project DFG-SFB 347/C3) is also gratefully acknowledged. The computations were carried out on the Cray Y M P at HLRZ, Julich, VAX 6000-410 and S U N at the Rechenzentrum der Universitat Wurzburg, and our S U N and micro-VAX-I1 computers.
7-Azaindole in Alcohols: Solvation Dynamics and Proton Transfer Richard S. Moog* Department of Chemistry, Franklin & Marshall College, Lancaster, Pennsylvania 17604-3003
and Mark Maroncelli* Department of Chemistry, 152 Davey Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802 (Received: March 15, 1991; In Final Form: July 1 , 1991)
The photoinduced excited-state double proton-transfer reaction of 7-azaindole has been examined in a variety of alcohol solvents. The influence of temperature and solvent deuteration has been investigated. A time-dependent Stokes shift of the initially excited normal species is observed, and this species is found to be the kinetic precursor to the tautomeric form. A substantial overlap of the normal and tautomer emissions is found, indicating that the tautomer emission must be monitored at wavelengths of 550 nm or greater to avoid contamination from the normal emission. The observed proton-transfer times in alcohols at room temperature are well correlated with the solvation parameter ET(30), suggesting that the rate of proton transfer is related to the strength of solventsolute interactions. However, an unusual temperature-dependent isotope effect is also observed, in which the relative rates of proton transfer in normal and deuterated alcohols become closer as the temperature is lowered. These results are interpreted in terms of a two-step model for proton transfer, involving solvent rearrangement to an appropriate configuration for the reaction to occur, followed by rapid proton transfer.
I. Introduction The role of the solvent in the excited-state dynamics of 7azaindole (7AI) has been a subject of some interest and controversy since the discovery of its photoinduced double proton-transfer reaction over twenty years ago. In the seminal work on this reaction, Kasha and co-workers' proposed that dimers of 7AI in alkane solvents and 7AI-alcohol complexes in alcohol solutions can undergo a photoinduced excited-state double proton transfer to produce a tautomeric species. (See Scheme I.) In such solutions, two emission bands are generally observed, as illustrated by the spectrum in methanol solution shown in Figure 1. The more intense, higher energy emission is due to species which have not undergone proton transfer and has been labeled the normal emission (N), while the lower energy emission peaked around 500 nm has been attributed to the tautomeric species (T).1-3 The rate of proton transfer in 7AI dimers has been shown to occur on the picosecond time ~ c a l eover ~ , ~a wide range of temperatures, and the relative amount of tautomer emission is essentially in~~~~
SCHEME I
:
I
I
R
I
R
~~
( 1 ) Taylor, C. A,; El-Bayoumi, M. A,; Kasha, M. Proc. Nutl. Acud. Sci. U.S.A. 1969, 63, 253. (2) Ingham, K. C.; Abu-Elgheit, M.; El-Bayoumi, M. A. J . Am. Chem. SOC.1971, 93, 5023. (3) Collins, S . T. J . Phys. Chem. 1983, 87, 3202. (4) Hetherington 111, W. M.; Micheels, R. M.; Eisenthal, K. B. Chem. Phys. Lett. 1979, 66. 230. (5) Share, P. E.; Sarisky, M. J.; Pereira, M. A,; Repinec, S. T.; Hochstrasser, R. M. J . Lumin. 1991, 48/49, 204.
dependent of temperature below 150 K.2,6 However, in alcohols the production of tautomers through this excited-state reaction is slower than in the dimer and has a stronger temperature dependence. The activation energy of tautomerization, determined from the relative intensities of the normal and tautomer emissions, ( 6 ) Ingham, K. C.; El-Bayoumi, M. A. J. Am. Chem. SOC.1974,96, 1674.
0022-3654/91/2095-10359%02.50/0 0 1991 American Chemical Society
