Two-dimensional Fourier transform electronic spectroscopy at a conical intersection Katherine A. Kitney-Hayes, Allison A. Ferro, Vivek Tiwari, and David M. Jonas Citation: The Journal of Chemical Physics 140, 124312 (2014); doi: 10.1063/1.4867996 View online: http://dx.doi.org/10.1063/1.4867996 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Investigating vibrational anharmonic couplings in cyanide-bridged transition metal mixed valence complexes using two-dimensional infrared spectroscopy J. Chem. Phys. 140, 084505 (2014); 10.1063/1.4866294 The methyl C–H blueshift in N , N -dimethylformamide-water mixtures probed by two-dimensional Fouriertransform infrared spectroscopy J. Chem. Phys. 124, 244502 (2006); 10.1063/1.2206177 A transferable electrostatic map for solvation effects on amide I vibrations and its application to linear and twodimensional spectroscopy J. Chem. Phys. 124, 044502 (2006); 10.1063/1.2148409 Two-dimensional cross-spectral correlation analysis and its application to time-resolved Fourier transform emission spectra of transient radicals J. Chem. Phys. 123, 184104 (2005); 10.1063/1.2074147 A pulse sequence for directly measuring the anharmonicities of coupled vibrations: Two-quantum twodimensional infrared spectroscopy J. Chem. Phys. 120, 8067 (2004); 10.1063/1.1649725
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 134.71.135.134 On: Sat, 22 Nov 2014 22:38:01
THE JOURNAL OF CHEMICAL PHYSICS 140, 124312 (2014)
Two-dimensional Fourier transform electronic spectroscopy at a conical intersection Katherine A. Kitney-Hayes, Allison A. Ferro,a) Vivek Tiwari, and David M. Jonasb) Department of Chemistry and Biochemistry, University of Colorado, 215 UCB, Boulder, Colorado 80309, USA
(Received 3 December 2013; accepted 26 February 2014; published online 28 March 2014) We report measurement and modeling of two-dimensional (2D) electronic spectra of a silicon naphthalocyanine (SiNc) in benzonitrile, a system for which the polarization anisotropy reveals passage through a square-symmetric Jahn-Teller conical intersection in ∼100 fs [D. A. Farrow, W. Qian, E. R. Smith, A. A. Ferro, and D. M. Jonas, J. Chem. Phys. 128, 144510 (2008)]. The measured 2D Fourier transform (FT) spectra indicate loss of electronic coherence on a similar timescale. The 2D spectra arising from femtosecond vibronic dynamics through the conical funnel are modeled by full non-adiabatic treatment of the coupled electronic and vibrational dynamics for a pair of un-damped Jahn-Teller active vibrations responsible for both electronic decoherence and population transfer. Additional damped Jahn-Teller active modes that can cause only decoherence or population transfer are treated with analytical response functions that can be incorporated into the numerical non-adiabatic calculation by exploiting symmetry assignment of degenerate vibronic eigenstates to one of two electronic states. Franck-Condon active totally symmetric modes are incorporated analytically. The calculations reveal that these conical intersection dynamics alone are incapable of destroying the coherence of the initially prepared wavepacket on the experimentally observed timescale and predict an unobserved recurrence in the photon echo slice at ∼200 fs. Agreement with the experimental twodimensional electronic spectra necessitates a role for totally symmetric vibrational dynamics in causing the echo slice to decay on a ∼100 fs timescale. This extended model also reproduces the ∼100 fs ultrafast electronic anisotropy decay in SiNc when an “asymmetric solvation mode” with a small stabilization energy of ∼2 cm−1 is included. Although calculations show that inhomogeneities in the energy gap between excited states can broaden the anti-diagonal 2D lineshape, the anti-diagonal width is dominated by totally symmetric vibrational motions in SiNc. For this shallow conical intersection, the non-adiabatic dynamics destroy electronic coherence more slowly than they destroy electronic alignment. © 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4867996] I. INTRODUCTION
The quantum description of molecules usually begins by solving the electronic Schrodinger equation for fixed nuclear coordinates, generating energy eigenvalues that are considered as adiabatic (or Born-Oppenheimer) electronic potential energy surfaces on which the rotation-vibration Schrodinger equation is solved.1 In the adiabatic approximation, electronic and vibrational motions are separable, and slow vibrational motion is confined to a single adiabatic potential energy surface corresponding to the electronic quantum state. When two adiabatic potential energy surfaces of polyatomic molecules intersect, the neighborhood around the intersection resembles the vertex of a right-circular double cone through which the two conical surfaces smoothly connect with each other.2 At these points of “conical intersection,” the electronic energy gap is zero. Conical intersections are required in degenerate electronic states by certain point group symmetries,3 but they
a) Present Address: Zeiss Inc., 5160 Hacienda Dr., Dublin, California 94568,
USA.
b) Author to whom correspondence should be addressed. Electronic mail:
[email protected]. Telephone: (303)492-3818.
0021-9606/2014/140(12)/124312/19
occur more generally by “accident.”4 Non-adiabatic movement of electrons between adiabatic electronic states becomes feasible near conical intersections5 and around near-misses between potential surfaces. A conical intersection or nearly missed intersection is called a “conical funnel”6 if changes in quantum state occur faster than vibrational relaxation. Such “sudden” changes in the electronic quantum state can result in fast reactions driven by the new electronic state. When these non-adiabatic changes lead to a rapid relaxation of photoexcited molecules to ground state products, the organic photochemistry concept of a “funnel” comes into play.7, 8 Conical intersections are now believed to be both common and responsible for some of the fastest chemical processes,9, 10 with lower dimensional hypersurfaces of intersecting conical intersections playing a role in some reactions.11–13 Conical intersections play an essential role in biological reactions such as the isomerization of retinal, the primary step in vision,14 intramolecular proton transfer reactions,11 and solar light harvesting reactions.15 A well-developed framework9, 13 for the coupled vibrational and electronic dynamics near a conical intersection has been used for many computational studies.8, 10, 12, 16 This framework shows that every conical intersection involves two crucial coordinates, one which
140, 124312-1
© Author(s) 2014
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 134.71.135.134 On: Sat, 22 Nov 2014 22:38:01
124312-2
Kitney-Hayes et al.
controls the energy gap, and one which controls the offdiagonal coupling – both gap and coupling must simultaneously be zero for potential surfaces to intersect. The present paper studies such dynamics for a shallow Jahn-Teller conical intersection (dynamic Jahn-Teller effect)17 in the doubly degenerate first excited electronic state of a 4-fold symmetric molecule. In 4-fold symmetric Jahn-Teller conical intersections, the vibrations which control the energy gap are of a different symmetry from those that control the coupling.3, 18–20 Thus, the intersection studied here has a lower symmetry than the prototypical Jahn-Teller conical intersections with 3-fold, 5-fold, or 6-fold symmetry, but a higher symmetry than the typical accidental conical intersection. Figure 14 of Ref. 19 shows a contour plot of the generic lower adiabatic surface for 4-fold symmetry, which has two equivalent minima separated by two equivalent saddle points, one on each side of the conical intersection. Conical intersections have been extensively studied experimentally.10, 21 The earliest time domain experiments concentrated mostly on vibrational motion through the conical intersection,22 although Stolow and co-workers probed rapid accompanying changes in the photoelectron spectrum quite early on.23 The pump-probe polarization anisotropy24–26 has electronic and vibrational contributions that can be used to probe valence electronic dynamics at a conical intersection.27, 28 Scrambling of electronic character due to non-adiabatic dynamics around a Jahn-Teller conical intersection in the silicon naphthalocyanine molecule studied here leads to a rapid
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 134.71.135.134 On: Sat, 22 Nov 2014 22:38:01
THE JOURNAL OF CHEMICAL PHYSICS 140, 124312 (2014)
Two-dimensional Fourier transform electronic spectroscopy at a conical intersection Katherine A. Kitney-Hayes, Allison A. Ferro,a) Vivek Tiwari, and David M. Jonasb) Department of Chemistry and Biochemistry, University of Colorado, 215 UCB, Boulder, Colorado 80309, USA
(Received 3 December 2013; accepted 26 February 2014; published online 28 March 2014) We report measurement and modeling of two-dimensional (2D) electronic spectra of a silicon naphthalocyanine (SiNc) in benzonitrile, a system for which the polarization anisotropy reveals passage through a square-symmetric Jahn-Teller conical intersection in ∼100 fs [D. A. Farrow, W. Qian, E. R. Smith, A. A. Ferro, and D. M. Jonas, J. Chem. Phys. 128, 144510 (2008)]. The measured 2D Fourier transform (FT) spectra indicate loss of electronic coherence on a similar timescale. The 2D spectra arising from femtosecond vibronic dynamics through the conical funnel are modeled by full non-adiabatic treatment of the coupled electronic and vibrational dynamics for a pair of un-damped Jahn-Teller active vibrations responsible for both electronic decoherence and population transfer. Additional damped Jahn-Teller active modes that can cause only decoherence or population transfer are treated with analytical response functions that can be incorporated into the numerical non-adiabatic calculation by exploiting symmetry assignment of degenerate vibronic eigenstates to one of two electronic states. Franck-Condon active totally symmetric modes are incorporated analytically. The calculations reveal that these conical intersection dynamics alone are incapable of destroying the coherence of the initially prepared wavepacket on the experimentally observed timescale and predict an unobserved recurrence in the photon echo slice at ∼200 fs. Agreement with the experimental twodimensional electronic spectra necessitates a role for totally symmetric vibrational dynamics in causing the echo slice to decay on a ∼100 fs timescale. This extended model also reproduces the ∼100 fs ultrafast electronic anisotropy decay in SiNc when an “asymmetric solvation mode” with a small stabilization energy of ∼2 cm−1 is included. Although calculations show that inhomogeneities in the energy gap between excited states can broaden the anti-diagonal 2D lineshape, the anti-diagonal width is dominated by totally symmetric vibrational motions in SiNc. For this shallow conical intersection, the non-adiabatic dynamics destroy electronic coherence more slowly than they destroy electronic alignment. © 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4867996] I. INTRODUCTION
The quantum description of molecules usually begins by solving the electronic Schrodinger equation for fixed nuclear coordinates, generating energy eigenvalues that are considered as adiabatic (or Born-Oppenheimer) electronic potential energy surfaces on which the rotation-vibration Schrodinger equation is solved.1 In the adiabatic approximation, electronic and vibrational motions are separable, and slow vibrational motion is confined to a single adiabatic potential energy surface corresponding to the electronic quantum state. When two adiabatic potential energy surfaces of polyatomic molecules intersect, the neighborhood around the intersection resembles the vertex of a right-circular double cone through which the two conical surfaces smoothly connect with each other.2 At these points of “conical intersection,” the electronic energy gap is zero. Conical intersections are required in degenerate electronic states by certain point group symmetries,3 but they
a) Present Address: Zeiss Inc., 5160 Hacienda Dr., Dublin, California 94568,
USA.
b) Author to whom correspondence should be addressed. Electronic mail:
[email protected]. Telephone: (303)492-3818.
0021-9606/2014/140(12)/124312/19
occur more generally by “accident.”4 Non-adiabatic movement of electrons between adiabatic electronic states becomes feasible near conical intersections5 and around near-misses between potential surfaces. A conical intersection or nearly missed intersection is called a “conical funnel”6 if changes in quantum state occur faster than vibrational relaxation. Such “sudden” changes in the electronic quantum state can result in fast reactions driven by the new electronic state. When these non-adiabatic changes lead to a rapid relaxation of photoexcited molecules to ground state products, the organic photochemistry concept of a “funnel” comes into play.7, 8 Conical intersections are now believed to be both common and responsible for some of the fastest chemical processes,9, 10 with lower dimensional hypersurfaces of intersecting conical intersections playing a role in some reactions.11–13 Conical intersections play an essential role in biological reactions such as the isomerization of retinal, the primary step in vision,14 intramolecular proton transfer reactions,11 and solar light harvesting reactions.15 A well-developed framework9, 13 for the coupled vibrational and electronic dynamics near a conical intersection has been used for many computational studies.8, 10, 12, 16 This framework shows that every conical intersection involves two crucial coordinates, one which
140, 124312-1
© Author(s) 2014
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 134.71.135.134 On: Sat, 22 Nov 2014 22:38:01
124312-2
Kitney-Hayes et al.
controls the energy gap, and one which controls the offdiagonal coupling – both gap and coupling must simultaneously be zero for potential surfaces to intersect. The present paper studies such dynamics for a shallow Jahn-Teller conical intersection (dynamic Jahn-Teller effect)17 in the doubly degenerate first excited electronic state of a 4-fold symmetric molecule. In 4-fold symmetric Jahn-Teller conical intersections, the vibrations which control the energy gap are of a different symmetry from those that control the coupling.3, 18–20 Thus, the intersection studied here has a lower symmetry than the prototypical Jahn-Teller conical intersections with 3-fold, 5-fold, or 6-fold symmetry, but a higher symmetry than the typical accidental conical intersection. Figure 14 of Ref. 19 shows a contour plot of the generic lower adiabatic surface for 4-fold symmetry, which has two equivalent minima separated by two equivalent saddle points, one on each side of the conical intersection. Conical intersections have been extensively studied experimentally.10, 21 The earliest time domain experiments concentrated mostly on vibrational motion through the conical intersection,22 although Stolow and co-workers probed rapid accompanying changes in the photoelectron spectrum quite early on.23 The pump-probe polarization anisotropy24–26 has electronic and vibrational contributions that can be used to probe valence electronic dynamics at a conical intersection.27, 28 Scrambling of electronic character due to non-adiabatic dynamics around a Jahn-Teller conical intersection in the silicon naphthalocyanine molecule studied here leads to a rapid
