Introduction Results Acknowledgement Electronic Structure of Rare Gas - Hydrogen Rydberg Molecules Erich W Schreiner and Geerd HF Diercksen Max-Planck-Institut für Astrophysik Garching, GERMANY November 13, 2007 Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Introduction Results Acknowledgement Outline Introduction 1 Atomic spectra Rydberg molecules Computational model outline Spectroscopic constants Results 2 Rare-gas hydrogen anions Rare-gas hydrogen molecules di-Helium hydrogen molecules Confined HeH structure and spectra Confined NeH structure and spectra Acknowledgement 3 Acknowledgement Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Outline Introduction 1 Atomic spectra Rydberg molecules Computational model outline Spectroscopic constants Results 2 Rare-gas hydrogen anions Rare-gas hydrogen molecules di-Helium hydrogen molecules Confined HeH structure and spectra Confined NeH structure and spectra Acknowledgement 3 Acknowledgement Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Hydrogen spectrum The Gymnasiallehrer J. J. Balmer from Basel, Switzerland, was the first to recognize that the spectrum of the hydrogen atom consists of series of spectral lines and that the frequencies of the lines can be calculated by the formula ν = ν 0 − R n 2 R : Rydberg constant . Reference: J. J. Balmer, Notiz über die Spektrallinien des Wasserstoffs, Verhandlungen der Naturforschenden Gesellschaft in Basel, 7 , 552 (1885) Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Hydrogen spectrum ✻ n=7 ▲ ▲ n=6 ❏▲ E ❏ ❍ n=5 ✟ n=4 n=3 n=2 n=1 l = 0 l = 3 l = 1 l = 2 Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Balmer Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Balmer Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Many-electron atom The Swedish physicist J. R. Rydberg (1854–1919) was the first to recognize that “the spectra of [many-electron] atoms can be understood much in the same way as the spectrum of the Hydrogen atom” and that the frequencies of the spectral lines can be computed by the formula: R ν = ν 0 − ( n − δ ) 2 R : Rydberg constant . Reference: J. R. Rydberg, On the structure of the line-spectra of the chemical elements, The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, 29 , 331 (1890) Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Many-electron atom The expectation value for the radius of a Rydberg state is given by the formula � r � = 3 n 2 − l ( l + 1 ) a 0 2 Z Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Many-electron spectrum n=7 n=200 60000 Bohr ▲ ✻ ✻ ▲ n=6 n=100 15000 Bohr ❏▲ ❏ n=5 ❍ 37.5 Bohr n=5 E ✟ � r � n=4 n=3 n=4 24.0 Bohr n=2 n=3 13.5 Bohr n=2 6.0 Bohr n=1 1.5 Bohr n=1 ⊕ proton l = 0 Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Rydberg Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Rydberg Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Rydberg Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Rydberg Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Outline Introduction 1 Atomic spectra Rydberg molecules Computational model outline Spectroscopic constants Results 2 Rare-gas hydrogen anions Rare-gas hydrogen molecules di-Helium hydrogen molecules Confined HeH structure and spectra Confined NeH structure and spectra Acknowledgement 3 Acknowledgement Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Characteristics Chemically un bound ground state Chemically bound excited states Large energy gap between ground and excited states Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Outline Introduction 1 Atomic spectra Rydberg molecules Computational model outline Spectroscopic constants Results 2 Rare-gas hydrogen anions Rare-gas hydrogen molecules di-Helium hydrogen molecules Confined HeH structure and spectra Confined NeH structure and spectra Acknowledgement 3 Acknowledgement Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Outline Schrödinger equation Configuration interaction (CI) method Confining potential Gaussian basis set Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Schrödinger equation [ H ( r )] Ψ( 1 , 2 , . . . , N ) = E Ψ( 1 , 2 , . . . , N ) N N M N � Z α � 2 ∇ 2 � − 1 � � � � � H ( r ) = + − + w ( r i ) i | r i − R α | i = 1 i = 1 α = 1 i = 1 N 1 � � � + | r i − r j | i > j Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Wavefunction approximation | Ψ � = | Φ � = Φ( x 1 x 2 · · · x N ) = ( N !) − 1 � χ i ( x 1 ) 2 � � χ j ( x 2 ) · · · χ k ( x N ) � � ψ · α χ = ψ · β � ψ i = c im ξ m m � � � C r a | Φ r C rs ab | Φ rs C rst abc | Φ rst | Ψ � = C 0 | Φ 0 � + a � + ab � + abc � + · · · ra a < b a < b < c r < s r < s < t Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Basis set conditions The basis functions have to describe/model at the Rydberg center: the electron distribution of the positive ion the electron distribution of Rydberg states the lectron distribution in the external potential, if present at the ligands: the electron distribution of the neutral system the electron polarisability the lectron distribution in the external potential, if present Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
Atomic spectra Introduction Rydberg molecules Results Computational model outline Acknowledgement Spectroscopic constants Outline Introduction 1 Atomic spectra Rydberg molecules Computational model outline Spectroscopic constants Results 2 Rare-gas hydrogen anions Rare-gas hydrogen molecules di-Helium hydrogen molecules Confined HeH structure and spectra Confined NeH structure and spectra Acknowledgement 3 Acknowledgement Erich W Schreiner and Geerd HF Diercksen Rydberg Molecules
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