QUANTUM PHOTOCHEMISTRY: DIRECT CALCULATION OF DIABATIC STATES AND SEMICLASSICAL DYNAMICS A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY SHIKHA NANGIA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DONALD G. TRUHLAR APRIL 2006 UMI Number: 3212073 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted.
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ProQuest Information and Learning Company 300 North Zeeb Road P. Box 1346 Ann Arbor, MI 48106-1346 UNIVERSITY OF MINNESOTA This is to certify that Ihave examined this copy a doctoral thesis by SHIKHA NANGIA and have found that it is complete and satisfactory in all respects, and that any and all revisions required by the final examining committee have been made. Truhlar Name of the Faculty Adviser 7 Signature of Faculty Adviser /⁄22⁄.£ as R006 Date GRADUATE SCHOOL Acknowledgments I, first and foremost, thank my adviser Don Truhlar for providing me with the excellent opportunity to work in his research group and learn from his immense knowledge in this field. I have always admired Don for his intellect, enthusiasm in science, determination, and dedication to his work.
I also thank my husband Arindam Chakraborty, who along with working on his doctoral work, always made sure to make himself available for long thoughtful discussions at times when I needed his opinion. I would like to express my gratitude to the members of my research group Amos Anderson, Adam Chamberlin, Arindam Chakraborty, Erin Dahlke, Ben Ellingson, Ahren Jasper, Hai Lin, Ben Lynch, Vanessa A. Lynch, Hisao Nakamura, Jingzhi Pu, Dan Theis, Jason Thompson, Oksana Tischenko, Chaoyuan Zhu, and Yuan Zhang. I thank would like to my parents J.
Nangia, and my sister Shivangi for their love, effort, support, and encouragement in fulfilling my academic milestones. Finally, I would like to thank my two month old daughter Somya for being immensely cooperative in helping me finish the thesis write-up and cheering me up with her beautiful smile. ii Abstract This thesis presents progress in six areas of quantum photochemistry: (1) a new algorithm for carrying out efficient semiclassical dynamical calculations using a trajectory surface hopping method for systems with weakly coupled electronic states, (ii) an improved treatment of electronic coherence and decoherence in electronically nonadiabatic molecular collisions, (iii) calculations of coupled diabatic potential energy surfaces by a multi-reference electronic structure method, (iv) comparison of adiabatic ground-state and excited-state adiabatic surfaces calculated by multi-reference electronic structure methods to those calculated by a single-reference method-of-moments and coupled cluster method, (v) fitting coupled diabatic potential energy surfaces for ammonia, and (vi) photodissociation dynamics for van der Waals complexes of Li---FH and Na---FH. Chapter 1 introduces the topic of semiclassical dynamics for electronically nonadiabatic processes and provides an overview of the calculation and fitting of coupled diabatic surfaces.
Chapter 2 describes, a new algorithm called the army ants algorithm for trajectory surface hopping. Chapter 3 presents an algorithm called coherent switching with decay of mixing, which is an improved treatment of electronic coherence in non- Born—Oppenheimer trajectories. Chapter 4 provides a comparison of the completely renormalized equation-of-motion coupled-cluster method with multi-reference quasi degenerate perturbation theory near a conical intersection and along a photodissociation coordinate in ammonia. Chapter 5 presents the calculation and fitting of diabatic potential energy surface of ammonia along with the mapping of a four-dimensional conical intersection seam.
Chapter 6 presents a study of the photodissociation dynamics of Li---FH and Na---FH van der Waals complexes. 11 TABLE OF CONTENTS Acknowledgme€rifS. - cà HH TH T0 T1 7g 1 ADSUtract 0h. Sàn ng gi nh nh nh như 1 1.
-ó- - 5 HH TH HH TH KH ne 1 1. Adiabatic representation of a molecular sysfem. The Born-Oppenheimer apprOXImAtiOT. - 5 ng HH ng tư6 1.- cọ TH TH TH THTT7 1.
Trajectory surface hoppITE. --- 5 4 HH TT TH HH HH8 1. Tully’s fewest-switches method. - Ác HH HH HH HH ng ngu ưa 10 Hư V0.
Coupled potential energy SUTÍAC©S.-- - HH HH Hưng Hà 15 1. Is it necessary to use multi-reference methods?. Calculation and fitting of diabatic states of AMMONIA. ARMY ANTS ALGORITHM FOR RARE EVENT SAMPLING OF DELOCALIZED NONADIABATIC TRANSITIONS BY TRAJECTORY SURFACE HOPPING AND THE ESTIMATION OF SAMPLING ERRORS BY THE BOOTSTRAP METHOD.
Sampling algorithms for TSHH.- 0Á HH HH HH HH ki29 2.- ---- ‹ cọ nọ ng 30 2. - --- cọ Hi nọ TY 31 2. Generalization to more than two electronic stafes. Army ants aÏgOTItHm.
-- -- cọ HH HH HH TH HH 1010130 33 2. The YRH model system. -- - LH HT nu nu TH HH 40 2. Final state anaÌÏS1S.- «St TT Họ TT ti1 tà41 2.
Bootstrap resampling: Method of error anaÏyS1S. Calculations and r€SUÏ(S. HH HH HH Họ k0 614 050 48 2. ác HH HT TH TH Tà HH HH nh CĐ T013 0 50 2.
- -‹ HH TH TH TH HH nh 51 Âu10. ccscescssesseseecesecececeesestsseceeesceeeeeseesceaceessesssesacsscseesssesesessseeaesseeseessesseveneess 56 Tables TT —. COHERENT SWITCHING WITH DECAY OF MIXING: AN IMPROVED TREATMENT OF ELECTRONIC COHERENCE FOR NON-BORN-OPPENHEIMER TRAJECTORTES. - QC ngu HH ni gu ngư 71 3.- nọ ng nọ nọ E418 605080 8.
Fundamental time-dependent equations .-- - Án HH ng như, 77 3. ECP-TSH method na. Self-consistent potential methodS. -- -- 5< HH HH ng nh Hiệp 82 3.
HH Hà HT HT Họ Hà Tà nh 84 3.- -- cà HH HH TH TH TH nh th 89 3. Decay-of-mixing time. sóc HT TH TH ng HH kh 90 3. Three-dimensional test cases and methodology.
Results and ISCUSSIOTI. SH TH HT TH TH TT HH 95 3. -- ch gọn gu nọ TT Hàn ng ng, 101 3.- ch TH TH TH TH HH Hà TH TH nh cư 104 [. 0 HH HH go TH HT TT H0 107 Tables ose.
CAN A SINGLE-REFERENCE APPROACH PROVIDE A BALANCED DESCRIPTION OF GROUND AND EXCITED STATES? A COMPARISON OF THE COMPLETELY RENORMALIZED EQUATION-OF- MOTION COUPLED-CLUSTER METHOD WITH MULTI- REFERENCE QUASI DEGENERATE PERTURBATION THEORY NEAR A CONICAL INTERSECTION AND vi ALONG A PHOTODISSOCIATION COORDINATE IN 90/00). - cọ HH HH TT Tu hi ngàn 117 PM.- Ác HH HH Hà TH Tà HH ngư 119 4. Calculations and r€SuÏ{S. Discussion and concluding rermaTÏkS.
ác ng ng gi th 123 4. HH HH gu HH TH TH HH ĐH 125 ;s{oc ¿cv E. DIRECT CALCULATION OF COUPLED DIABATIC POTENTIAL ENERGY SURFACES FOR AMMONIA AND MAPPING OF A FOUR-DIMENSIONAL CONICAL INTERSECTION SEAM. Ă Ác nh HH TH TH TH TT TH TH HH te 134 5.
Ab-initio electronic structure calculations. Summary of diabatization procedure and theOry. Computational proC€dUFC. --- - «HH HH HH HT ri 141 5.
Fit to the diabatic potential energy Surfaces. Go HH ngờ 145 5.2, II SUTÍAC€. LG Q TH HH KH 149 5. HH HH TT HH TH TH Hà ngành 151 l9 9o.
HH HH HT HH TT TT TT TH TH Hà re 161 Tables oo. PHOTOCHEMISTRY OF LIFH AND NAFH VAN DER WAALS COMPLEXES .---- -s ktcsh HYTHYTHT Tg H TT T g g TH T H H g gà HànH 195 6. Analytic potential energy SUTÍäC€S.- - Ác n9 HH HH ng ng 197 6. Photoabsorption spectrum of LIFHH.
--- Ác HH ng HH re200 6. Electronic transition dipole moment functions. Vibrational energies and wave funCtiOTS. Semiclassical trajectory calculations.
Results and diSCUSSIOT.- Gà HH HT HT TH Hà HH Hà Hà nhe 211 6. Photoabsorption spectra for LIFTH. - sa sec ssssvseseesre 211 6. Semiclassical trajectory photodissociation calculations.
--- -‹ s49 HH HH TH TH TH HH TH nh 222 Appendix A. HT HH HT gi TT HT. Ti TH TT TH he 224 Tables. General remarks The application of quantum mechanics to a molecular system usually starts with the Born—Oppenheimer approximation.
It leads to a great amount of simplification and is valid in most cases, so it is critical to many applications, but sometimes it breaks down. This thesis is concerned with those cases, namely the cases where the Born—Oppenheimer approximation is not valid. The key idea of the Born—Oppenheimer approximation is the separation of the motion of the electrons in a molecule or molecular collision from the motion of the nuclei.! The electrons are much lighter than the nuclei, and due to this mass difference the electrons may be treated for many purposes as if they are moving infinitely rapidly as compared to the nuclei. The consequence of this approximation is that the electronic wave function can be calculated for any specific nuclear geometry R as if the nuclei were Static, and the resulting electronic energy serves as an effective potential energy for the nuclear motion.
Since R acts as a parameter, electronic energies can be calculated for each specific nuclear geometry, and by doing this for various different R values the entire potential energy surface can be mapped out. Another way to represent the nuclear degrees of freedom is to describe them as "adiabatic" parameters,’ since they change slowly as compared to the electronic coordinates. The Born—Oppenheimer approximation states that by using such nuclear adiabatic parameters, collected in the nuclear coordinate vector R, the system can be well characterized using a single electronic energy state, defined at each fixed value of the nuclear parameter, with no contribution from the other electronic States. 2 Because of the small mass of the electrons the spacing between electronic states is usually very large compared to nuclear kinetic energies, leading to a rapid time scale for electronic motion.
In certain regions, the electronic spacing is slower, and the adiabatic parameter R changes quickly compared to the locally slow electronic time scale (which is specified below), and the electronic variables cannot fully follow the changes in the nuclear coordinates. Then the Born-Oppenheimer approximation breaks down. In such cases, the nuclear motion is no longer restricted to a single electronic state, but is influenced as well by the other electronic states. This is what is meant by electronically nonadiabatic systems, also called vibronically coupled systems.
Such systems can be described in terms of coupled potential energy surfaces. In order to understand the problem of coupled surfaces, it is important to specify more quantitatively what we mean by fast nuclear motion coupling the electronic states. The analysis of Born and Oppenheimer’ shows that the electronically adiabatic approximation becomes reliable when the nuclear kinetic energy is comparable to (or larger than) the spacing between the electronic states. As mentioned above, this often happens not because the nuclear kinetic energy gets large but because the electronic spacing is sometimes small (for example it may even be zero because two states become degenerate by symmetry or accidentally).
Electronically nonadiabatic systems can be classified as strongly or weakly coupled depending on the magnitude of coupling between the electronic states. An example of a strongly coupled system is the three-body Na + H; system,“Š and an example of a weakly coupled system is Br + Hạ, the details which are provided elsewhere.** Many photochemical processes,”'? molecular collisions, and chemical reactions involve electronically coupled systems. There has also been a great amount of experimental work, in which the dynamics of excited-state reactions have been studied.'''? Some of the reactions of direct relevance to the present proposed work are the decay process of the photochemically excited transition states of Li.FH and Na.FH van der Waals complexes.
