Top Curr Chem (2016) 368: 273–346
DOI: 10.1007/128_2014_618
# Springer International Publishing Switzerland 2014
Published online: 12 April 2015
Nonlinear Spectroscopy of Core and Valence
Excitations Using Short X-Ray Pulses:
Simulation Challenges
Yu Zhang, Weijie Hua, Kochise Bennett, and Shaul Mukamel
Abstract Measuring the nonlinear response of electrons and nuclei to attosecond
broadband X-ray radiation has become possible by newly developed free electron
lasers and high harmonic generation light sources. The design and interpretation of
these novel experiments poses considerable computational challenges. In this
chapter we survey the basic description of nonlinear X-ray spectroscopy signals
and the electronic structure protocols which may be used for their simulation.
Keywords Core excitation Á DFT Á Double excitation Á Double-quantumcoherence Á MCSCF Á Nonlinear spectroscopy Á Real-time TDDFT Á Stimulated
X-ray Raman spectroscopy Á TDDFT Á X-ray
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
2 Nonlinear X-Ray Spectroscopies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
2.1 Time-Resolved Four-Wave Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
2.2 Double-Quantum-Coherence Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
2.3 Stimulated X-Ray Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
2.4 Correlation Function Expressions for SXRS Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
2.5 Discussion of Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
3 Quantum Chemistry Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
3.1 ΔSCF-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
3.2 TDDFT Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
3.3 MCSCF Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
3.4 Other Core Hole State Simulation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
Y. Zhang, W. Hua, K. Bennett, and S. Mukamel (*)
Department of Chemistry, University of California, Irvine, CA 92697, USA
e-mail: smukamel@uci.edu
DOI: 10.1007/128_2014_618
# Springer International Publishing Switzerland 2014
Published online: 12 April 2015
Nonlinear Spectroscopy of Core and Valence
Excitations Using Short X-Ray Pulses:
Simulation Challenges
Yu Zhang, Weijie Hua, Kochise Bennett, and Shaul Mukamel
Abstract Measuring the nonlinear response of electrons and nuclei to attosecond
broadband X-ray radiation has become possible by newly developed free electron
lasers and high harmonic generation light sources. The design and interpretation of
these novel experiments poses considerable computational challenges. In this
chapter we survey the basic description of nonlinear X-ray spectroscopy signals
and the electronic structure protocols which may be used for their simulation.
Keywords Core excitation Á DFT Á Double excitation Á Double-quantumcoherence Á MCSCF Á Nonlinear spectroscopy Á Real-time TDDFT Á Stimulated
X-ray Raman spectroscopy Á TDDFT Á X-ray
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
2 Nonlinear X-Ray Spectroscopies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
2.1 Time-Resolved Four-Wave Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
2.2 Double-Quantum-Coherence Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
2.3 Stimulated X-Ray Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
2.4 Correlation Function Expressions for SXRS Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
2.5 Discussion of Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
3 Quantum Chemistry Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
3.1 ΔSCF-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
3.2 TDDFT Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
3.3 MCSCF Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
3.4 Other Core Hole State Simulation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
Y. Zhang, W. Hua, K. Bennett, and S. Mukamel (*)
Department of Chemistry, University of California, Irvine, CA 92697, USA
e-mail: smukamel@uci.edu