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TitleAdvances in Multi-Photon Processes and Spectroscopy: (Volume 21)
LanguageEnglish
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Total Pages257
Table of Contents
                            CONTENTS
Preface
1. Vibrational and Electronic Wavepackets Driven by Strong Field Multiphoton Ionization
	1.1 Introduction
	1.2 Theoretical Concepts
		1.2.1 The time-independent Schrödinger equation and its implications on dynamics
		1.2.2 Spin-orbit coupling and diabatic vs. adiabatic states
		1.2.3 Nuclear time-dependent Schrödinger equation
			1.2.3.1 Second-order differentiator
			1.2.3.2 Split-operator method
		1.2.4 Stark shifts
		1.2.5 Multi- vs. single-photon transitions
		1.2.6 Laser-dressed states
		1.2.7 Photon locking
		1.2.8 Hole burning
		1.2.9 Strong-field ionization
	1.3 Computational and experimental details
	1.4 Vibrational Wavepackets Created by Multiphoton Ionization
		1.4.1 Phase-dependent dissociation
			1.4.1.1 Photon locking
			1.4.1.2 Hole burning
		1.4.2 Ionization to different ionic states
			1.4.2.1 Preparing electronic wavepackets via SFI
			1.4.2.2 VMI measurements to identify dissociation pathways following SFI
	1.5 Conclusion and Outlook
	References
2. Orientation-Selective Molecular Tunneling Ionization by Phase-Controlled Laser Fields
	1 Introduction
	2 Photoionization Induced by Intense Laser Fields
		2.1 MPI in standard perturbation theory
		2.2 Keldysh theory: From MPI to TI
		2.3 Characteristics of TI
		2.4 Molecular TI
	3 Directionally Asymmetric TI Induced by Phase-controlled Laser Fields
		3.1 Phase-controlled laser fields
		3.2 Directionally asymmetric TI (atoms)
		3.3 Directionally asymmetric TI (molecules)
	4 Experimental
	5 Results and Discussion
		5.1 Diatomic molecule: CO
			5.1.1 Photofragment detection
			5.1.2 Photoelectron detection
		5.2 Other molecules
			5.2.1 Nonpolar molecule with asymmetric structure: Br(CH2)2 Cl
			5.2.2 Large molecule: C6H13I
			5.2.3 Systematically changing molecular system: CH3X(X=F,Cl,Br, I)
			5.2.4 OCS molecule investigated by nanosecond ω + 2ω laser fields
	6 Summary
	Acknowledgments
	References
3. Reaction and Ionization of Polyatomic Molecules Induced by Intense Laser Pulses
	1.1 Introduction
	1.2 Ionization Rate of Molecules in Intense Laser Fields
		1.2.1 Theoretical approaches for ionization rates of molecules in intense laser fields
		1.2.2 Experimental measurements of ionization rates of molecules and comparations with theory
	1.3 Fragmentation of Molecules in Intense Laser Fields
		1.3.1 Ionization-dissociation of molecules in intense laser fields and statistical theoretical description
		1.3.2 Effects of cation absorption on molecular dissociation
	1.4 Dissociative Ionization and Coulombic Explosion of Molecules in Intense Laser Fields
		1.4.1 Dissociative ionization of formic acid molecules
		1.4.2 Coulombic explosion of CH3I
	1.5 Summary and Perspectives
	Acknowledgments
	References
4. Ultrafast Internal Conversion of Pyrazine Via Conical Intersection
	1.1 Introduction
	1.2 Pyrazine: Ultrafast S2(1B2u, ππ*) — S1(1B3u, nπ*) Internal Conversion Via Conical Intersection
	1.3 Sub-20 fs Deep UV Laser for TRPEI of Pyrazine
	1.4 Time-Resolved Photoelectron Imaging
		1.4.1 TRPEI of Ultrafast S2–S1 internal conversion in pyrazine
		1.4.2 Analysis of PAD
	1.5 Conical Intersections in Cation and Rydberg States of Pyrazine
	1.6 Toward Sub-30 fs TRPEI in VUV Region
	1.7 Summary
	Acknowledgments
	References
5. Quantum Dynamics in Dissipative Molecular Systems
	1 Introduction
	2 HEOM versus Path Integral Formalism: Background
		2.1 Generic form and terminology of HEOM
		2.2 Statistical mechanics description of bath influence
		2.3 Feynman–Vernon influence functional formalism
		2.4 General comments
	3 Memory-Frequency Decomposition of Bath Correlation Functions
		3.1 PSD of Bose function
		3.2 Brownian oscillators decomposition of bath spectral density function
	4 Optimized HEOM Theory With Accuracy Control
		4.1 Construction of HEOM via path integral formalism
		4.2 Accuracy control on white-noise residue ansatz
		4.3 Efficient HEOM propagator: Numerical filtering and indexing algorithm
	5 HEOM in Quantum Mechanics for Open Systems
		5.1 The HEOM space and the Schrödinger picture
		5.2 HEOM in the Heisenberg picture
		5.3 Mixed Heisenberg–Schrödinger block-matrix dynamics in nonlinear optical response functions
	6 Two-Dimensional Spectroscopy: Model Calculations
	7 Concluding Remarks
	Acknowledgments
	References
6. First-Principles Calculations for Laser Induced Electron Dynamics in Solids
	1 Introduction
	2 Formalism
		2.1 A time-dependent Kohn-Sham equation in periodic systems
		2.2 Polarization field
		2.3 Derivation from a Lagrangian
		2.4 Computational method
	3 Real-Time Calculation for Dielectric Function
		3.1 Linear response calculation in transverse geometry
		3.2 Linear response calculation in longitudinal geometry
		3.3 Example: Dielectric function of bulk Si
	4 Coherent Phonon Generation
		4.1 Physical description
		4.2 TDDFT calculation for Si
	5 Optical Breakdown
		5.1 Incident, external, and internal electric fields
		5.2 Intense laser pulse on diamond
	6 Coupled Dynamics of Electrons and Electromagnetic Fields
		6.1 Maxwell + TDDFT multiscale simulation
		6.2 Example: Laser pulse irradiation on Si surface
	7 Summary
	References
                        
Document Text Contents
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Reaction and Ionization of Polyatomic Molecules 115

Therefore, by using similar treatment of Keldysh and KFR theories and
under the assumption that the ionization only takes place from the HOMO,
the photoionization rate constant can be formulated,25,31 given as

k( �F) = 2πS2
Ne∑

j,j′=1
cjc


j′


d3p

(2π)3
χ̂j(�p)χ̂∗j′(�p)

×
(

p2

2me
+ I0

)2 ∣∣∣∣∣JN
(

e �F · �p
meω

2
,
Up



)∣∣∣∣∣
2

× cos (�p · (�Rj − �Rj′))
∞∑

N=−∞
δ

(
I0 + Up +

p2

2me
− Nω

)

=

N

2πS2
Ne∑

j,j′=1
cjc


j′


d3p

(2π)3
χ̂j(�p)χ̂∗j′(�p)

×
(

p2

2me
+ I0

)2 ∣∣∣∣∣JN
(

e �F · �p
meω

2
,
Up



)∣∣∣∣∣
2

× cos(�p · (�Rj − �Rj′))δ
(

I0 + Up +
p2

2me
− Nω

)

=

N

k(N) (1.18)

with JN is the generalized Bessel function, cj the coefficients of the linear
combination of atomic orbitals-molecular orbital, S =


2 for the closed

shell parent molecule or molecular cation, and S = 1 for the open shell. The
g-KFR theory has been widely used to diatomic and polyatomic molecules.

On the other hand, Ammosov, Delone and Krainov32 developed the
PPT theory22 for treating arbitrary states of hydrogen atoms in intense
electromagnetic fields to the ionization rates for arbitrary atoms

w =
(

3e

π

)3/2
Z2

3n∗3
2l + 1

2n∗ − 1
[

4eZ3

(2n∗ − 1) n∗3F
]2n∗−3/2

exp

[−2Z3
3n∗3F

]
,

(1.19)

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116 Advances in Multi-Photon Processes and Spectroscopy

with e = 0.71828 . . . , n∗ and l∗ the effective quantum numbers. In this
atomic ADK theory, the major improvement is to modify the radial wave
function of the outermost electron in the asymptotic region where tunneling
occurs and therefore the theory is an extension of the PPT only for hydrogen
atoms to more complex atomic system. However, for a molecular system,
the calculation for ionization rates is even complicated since multi-centre
problem has to be treated. Based on the similar consideration on the
asymptotic feature of electronic wave functions and symmetric feature,16

Tong et al. expressed the molecular electronic wave functions in the
asymptotic region in terms of summations of spherical harmonics in a one-
center expansion,16

ψ
m
(�r) =


l

ClFl(r)Ylm(r̂),

with a normalized coefficient Cl for insuring the wave function in the
asymptotic region can be expressed as

Fl(r → ∞) ≈ rZc/κ−1e−κr,
with Zc the effective Coulomb charge, κ =


2Ip, and Ip the ionization

potential for the given valence orbital. They realized the ADK theory
calculation for the ionization rates of diatomic molecules with an arbitrary
Euler angle �R with respect to the low frequency ac field direction (non-
aligned) is

w(F, R) =
(

3F

πκ3

)1/2∑
m′

B2(m′)
2|m′||m′|!

1

κ2Zc/κ−1

(
2κ3

F

)2Zc/κ−|m′|−1
e
−2κ3/3F

(1.20)

where, if Dl
m′,m(

�R) is the rotation matrix, one has

B(m

) =


l

ClD
l
m′,m(

�R)Q(lm′),

Q(lm) = (−1)m


(2l + 1)(l + |m|)!
2(l − |m|)! .

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First-principles Calculations 243

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