silyl fluoride: lamb-dip spectra and equilibrium structure cristina puzzarini and gabriele cazzoli...
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SILYL FLUORIDE: SILYL FLUORIDE: LAMB-DIP SPECTRA and LAMB-DIP SPECTRA and
EQUILIBRIUM STRUCTUREEQUILIBRIUM STRUCTURE
CCristinaristina PUZZARIN PUZZARINII and Gabriele CAZZOLI and Gabriele CAZZOLIDipartimento di Chimica “G. Ciamician”Dipartimento di Chimica “G. Ciamician”, , Università di Università di
BolognaBologna
Jürgen GAUSSJürgen GAUSSInstitut für Physikalische Chemie, University of MainzInstitut für Physikalische Chemie, University of Mainz
ColumbColumbus — us — JuneJune 2626, 200, 20099
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1) 1) Hyperfine StructureHyperfine Structure:: - - Instrument Instrument && Technique Technique - - Theory Theory && Computations Computations
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1) 1) Hyperfine StructureHyperfine Structure:: - - Instrument Instrument && Technique Technique - Theory - Theory && Computations Computations
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MILLIMETER-WAVE EXPERIMENTAL SET-UPMILLIMETER-WAVE EXPERIMENTAL SET-UP BLOCK DIAGRAM OF THE 50-800 GHz BLOCK DIAGRAM OF THE 50-800 GHz SPECTROMETERSPECTROMETER
SYNTH10 kHz-1 GHzMULT fS
nfS
MIXMULT
SYNCRref: 20 MHz
RF OSCILL3.7- 7.6 GHz
fRF
20 MHz
90 MHz|fG - mfRF |
GUNN P. SUPPLY and
SYNCRref: 73 MHz
|fRF - nfS|
HP8642ASYNTH
MIX
corr
fG
fGMULTIPLIER
InSbDETECTOR
PREAMPL
LOCK - IN
10 MHzfreq. standard
1.666 kHz
ref
GUNNDIODES THERMOSTAT
or liquid N2 system
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Measurements: Measurements: Lamb-dip techniqueLamb-dip technique
Corner cube mirror
Cell
InSb detector
Polarizer
Frequency modulated
source
Scheme of the radiation pathScheme of the radiation path
Using Using free-space cellfree-space cell
G. Cazzoli & L. Dore, J. Mol. Spectrosc. 143, 231 (1990).
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1) Partial saturation1) Partial saturation2) Only Doppler profile2) Only Doppler profile3) Rad: back and forward3) Rad: back and forward
Measurements: Measurements: Lamb-dip techniqueLamb-dip technique
c
zobs
v10
++vvzaza--vvzaza
vvzz== 00
0 obs
czaobs /v10
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Measurements: Measurements: Lamb-dip techniqueLamb-dip technique
109782.0 109782.1 109782.2 109782.3 109782.4
Frequency (MHz)
C18O: J = 1-0
Doppler profile
Dip profile
28 kHz
539120 539125 539130 539135 539140
FREQUENCY (MHz)
539120 539125 539130 539135 539140
CHCH22BrFBrF
DopplerDoppler
Lamb-dipLamb-dip
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1) 1) Hyperfine StructureHyperfine Structure:: - Instrument - Instrument && Technique Technique - - Theory Theory && Computations Computations
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Parameters of Rotational Parameters of Rotational SpectroscopySpectroscopy
Rotational HamiltonianRotational Hamiltonian
Rotational constantsRotational constants
Effective Hamiltonian: determination of HEffective Hamiltonian: determination of HRotRot via quantum chemistry via quantum chemistry
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Parameters of Rotational Parameters of Rotational SpectroscopySpectroscopy
Rotational HamiltonianRotational Hamiltonian
Rotational constantsRotational constants
Nuclear quadrupole coupling constantsNuclear quadrupole coupling constants
Effective Hamiltonian: determination of HEffective Hamiltonian: determination of HRotRot via quantum chemistry via quantum chemistry
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Parameters of Rotational Parameters of Rotational SpectroscopySpectroscopy
Rotational HamiltonianRotational Hamiltonian
Rotational constantsRotational constants
Nuclear quadrupole coupling constantsNuclear quadrupole coupling constants
Spin-rotation interactionsSpin-rotation interactions
Effective Hamiltonian: determination of HEffective Hamiltonian: determination of HRotRot via quantum chemistry via quantum chemistry
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Parameters of Rotational Parameters of Rotational SpectroscopySpectroscopy
Rotational HamiltonianRotational Hamiltonian
Rotational constantsRotational constants
Nuclear quadrupole coupling constantsNuclear quadrupole coupling constants
Spin-rotation interactionsSpin-rotation interactions
Spin-spin (direct)Spin-spin (direct) interactionsinteractions
Effective Hamiltonian: determination of HEffective Hamiltonian: determination of HRotRot via quantum chemistry via quantum chemistry
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Quantum-Chemical CalculationQuantum-Chemical Calculation of Spectroscopic Parameters of Spectroscopic Parameters
• Spin-rotation interactionSpin-rotation interaction
second-order property: requires second derivatives of energysecond-order property: requires second derivatives of energy
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requires equilibrium geometry: no „electronic property“requires equilibrium geometry: no „electronic property“
addditional contribution due to: addditional contribution due to:
indirect spin-spin couplingindirect spin-spin coupling (usually negligible) (usually negligible)
Quantum-Chemical CalculationQuantum-Chemical Calculation of Spectroscopic Parameters of Spectroscopic Parameters
• Spin-spin couplingSpin-spin couplingDIPOLAR SPIN-SPIN COUPLING TENSOR
vibrational correctionsvibrational corrections (anharmonic force field) (anharmonic force field)
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Beyond the Rigid-Rotator Beyond the Rigid-Rotator ApproximationApproximation
COUPLING of ROTATIONAL and VIBRATIONAL COUPLING of ROTATIONAL and VIBRATIONAL MOTIONMOTION
Vibrational corrections to properties:Vibrational corrections to properties:
r sr
sr
Qsr
KL
r
Qr
KLKLeq
KL QQQQ
QQ ,
...DD
DD0
2
02
1
PERTURBATION THEORYPERTURBATION THEORY starting from starting from the rigid-rotator harmonic oscillator approximationthe rigid-rotator harmonic oscillator approximation
Vibrational corrections require: Vibrational corrections require: anharmonic force field anharmonic force field
calculationscalculations
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Accurate hyperfine parametersAccurate hyperfine parameters
>>>> Main requirements>>>> Main requirements::
- accurate method- accurate method
- cc basis set- cc basis set
- CV correction- CV correctionss
- vibrational correction- vibrational correctionss
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Accurate hyperfine parametersAccurate hyperfine parameters
>>>> Main requirements>>>> Main requirements::
- accurate method [- accurate method [CCSD(T)CCSD(T)]]
- cc basis set- cc basis set
- CV correction- CV correctionss
- vibrational correctionvibrational correctionss
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Accurate hyperfine parametersAccurate hyperfine parameters
>>>> Main requirements>>>> Main requirements::
- accurate method [- accurate method [CCSD(T)CCSD(T)]]
- cc basis set [- cc basis set [nnQQ]]
- CV correction- CV correctionss
- vibrational correctionvibrational correctionss
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Accurate hyperfine parametersAccurate hyperfine parameters
>>>> Main requirements>>>> Main requirements::
- accurate method [- accurate method [CCSD(T)CCSD(T)]]
- cc basis set [- cc basis set [nnQQ]]
- CV correction- CV correctionss [ [additivityadditivity/CV bases/CV bases]]
- vibrational correctionvibrational correctionss
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Accurate hyperfine parametersAccurate hyperfine parameters
>>>> Main requirements>>>> Main requirements::
- accurate method [CCSD(T)]- accurate method [CCSD(T)]
- cc basis set [n- cc basis set [nQ]Q]
- CV correction- CV correctionss [additivity [additivity/CV bases/CV bases]]
- vibrational correction- vibrational correctionss [ [ff:ff: --correlcorrelatedated methmethodod-basis: n-basis: nTT]]
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1) 1) Hyperfine StructureHyperfine Structure:: - Instrument - Instrument && Technique Technique - Theory - Theory && Computations Computations
RESULTS
RESULTS
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(values in kHz)(values in kHz) TheoryTheory
FF CCNN (C (Cxxxx=C=Cyyyy)) 2.712.71
CCKK (C(Czzzz)) 44.9444.94
HH CCxxxx 0.640.64
CCyyyy -1.19-1.19
CCzzzz -6.64-6.64
CCxzxz 0.600.60
CCzxzx 3.033.03
H-FH-F -3D-3D11 (1.5 D (1.5 Dzzzz)) -11.36-11.36
-0.5D-0.5D22 (((D(Dxxxx-D-Dyyyy)/4)/4)) -1.75-1.75
H-HH-H 1.5D1.5D33 (1.5 D(1.5 Dzzzz)) 12.4612.46
2828SiHSiH33FF
CCFOURFOUR: : http://www.http://www.cfourcfour.de.de
THEORY:THEORY:
EquilibriumEquilibrium: (ae)CCSD(T)/aug-cc-pCVQZ: (ae)CCSD(T)/aug-cc-pCVQZVib. CorrectionsVib. Corrections: (ae)CCSD(T)/cc-pCVTZ: (ae)CCSD(T)/cc-pCVTZ
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429150.50 429150.55 429150.60
J = 15 - 14, K = 13
only FF + H
EXP
FREQUENCY (MHz)
2828SiHSiH33FF
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429150.50 429150.55 429150.60
J = 15 - 14, K = 13
only FF + H
EXP
FREQUENCY (MHz)
2828SiHSiH33FF
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(values in kHz)(values in kHz) TheoryTheory ExperimenExperimentt
FF CCNN (C (Cxxxx=C=Cyyyy)) 2.712.71 2.712.71fixedfixed
CCKK (C(Czzzz)) 44.9444.94 4545..74(35)74(35)
HH CCxxxx 0.640.64
CCyyyy -1.19-1.19
CCzzzz -6.64-6.64
CCxzxz 0.600.60
CCzxzx 3.033.03
H-FH-F -3D-3D11 (1.5 D (1.5 Dzzzz)) -11.36-11.36
-0.5D-0.5D22 (((D(Dxxxx-D-Dyyyy)/4)/4)) -1.75-1.75
H-HH-H 1.5D1.5D33 (1.5 D(1.5 Dzzzz)) 12.4612.46
2828SiHSiH33FF
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(Values in kHz)(Values in kHz) TheoryTheoryFF CCNN (C (Cxxxx=C=Cyyyy)) 2.692.69
CCKK (C (Czzzz)) 44.9344.93
SiSi CCNN (C (Cxxxx=C=Cyyyy)) -8.89-8.89
CCKK (C (Czzzz)) -41.89-41.89
HH CCxxxx 0.630.63
CCyyyy -1.18-1.18
CCzzzz -6.64-6.64
CCxzxz 0.590.59
CCzxzx 3.033.03
F-SiF-Si 1.5D1.5D33 (1.5 D (1.5 Dzzzz)) 16.4516.45
F-HF-H -3D-3D11 (1.5 D (1.5 Dzzzz)) -7.46-7.46
-0.5D-0.5D22 ((D ((Dxxxx-D-Dyyyy)/4))/4) 4.844.84
Si-HSi-H -3D-3D11 (1.5 D (1.5 Dzzzz)) -11.30-11.30
-0.5D-0.5D22 ((D ((Dxxxx-D-Dyyyy)/4))/4) -1.73-1.73
H-HH-H 1.5D1.5D33 (1.5 D (1.5 Dzzzz)) 12.4212.42
2929SiHSiH33F F
CCFOURFOUR: : http://www.http://www.cfourcfour.de.de
THEORY:THEORY:
EquilibriumEquilibrium: (ae)CCSD(T)/aug-cc-pCVQZ: (ae)CCSD(T)/aug-cc-pCVQZVib. CorrectionsVib. Corrections: (ae)CCSD(T)/cc-pCVTZ: (ae)CCSD(T)/cc-pCVTZ
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425220.35 425220.40 425220.45 425220.50
J = 15 - 14, K =13
F + 29Si + H
F + 29Si
only F
FREQUENCY (MHz)
2929SiHSiH33FF
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425220.35 425220.40 425220.45 425220.50
J = 15 - 14, K =13
F + 29Si + H
F + 29Si
only F
EXP
FREQUENCY (MHz)
2929SiHSiH33FF
recorded in natural abundancerecorded in natural abundance
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(values in kHz)(values in kHz) TheoryTheory
FF CCNN (C (Cxxxx=C=Cyyyy)) 2.232.23
CCKK (C(Czzzz)) 45.4645.46
3030SiHSiH33FF
CCFOURFOUR: : http://www.http://www.cfourcfour.de.de
THEORY:THEORY:
EquilibriumEquilibrium: (ae)CCSD(T)/aug-cc-pCVQZ: (ae)CCSD(T)/aug-cc-pCVQZVib. CorrectionsVib. Corrections: (ae)CCSD(T)/cc-pCVTZ: (ae)CCSD(T)/cc-pCVTZ
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393942.75 393942.80
hfs due to F (mod=30 kHz)
J = 14 - 13, K = 9hfs due to F (mod=15 kHz)
FREQUENCY (MHz)
3030SiHSiH33FF
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393942.75 393942.80
hfs due to F (mod=30 kHz)
J = 14 - 13, K = 9
EXP
hfs due to F (mod=15 kHz)
FREQUENCY (MHz)
3030SiHSiH33FF
recorded in natural abundancerecorded in natural abundance
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2) 2) Equilibrium StructureEquilibrium Structure:: - - semi-exp structuresemi-exp structure - - pure ab initio structurepure ab initio structure
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2) 2) Equilibrium StructureEquilibrium Structure:: - - semi-exp structuresemi-exp structure - pure ab initio structure- pure ab initio structure
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Empirical equilibrium structureEmpirical equilibrium structure
r
Bre BB
2
10
from from EXPERIMENTEXPERIMENT(various isotopic species)(various isotopic species)From From THEORYTHEORY
(cubic force field)(cubic force field)
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1) 1) 2828SiHSiH33F: AF: A00 && B B00
2) 2) 2828SiDSiD33F: AF: A00 && B B00
3) 3) 2929SiHSiH33F: BF: B00
4) 4) 2929SiDSiD33F: BF: B00
5) 5) 3030SiHSiH33F: BF: B00
6) 6) 3030SiDSiD33F: BF: B00
7) 7) 2828SiHDSiHD22F: AF: A00,, BB00 && C C0 0
8) 8) 2828SiHSiH22DF: ADF: A00,, BB00 && C C00
BB0 0 from from EXPERIMENTEXPERIMENT (various (various isotopic species)isotopic species)
- harmonic ff: analytic 2nd deriv. of - harmonic ff: analytic 2nd deriv. of EE
- anharmonic part: numerical differ.- anharmonic part: numerical differ.
Vibrational Corrections fVibrational Corrections from rom THEORYTHEORY (cubic force field(cubic force field: : (all)CCSD(T)/CVTZ(all)CCSD(T)/CVTZ))
Actual FIT:Actual FIT:moments of inertiamoments of inertia
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Computation of Cubic and Quartic Force Computation of Cubic and Quartic Force FieldsFields
• cubic force fields:cubic force fields:
single numerical differentiation along qr
• quartic force fields:quartic force fields:
double numerical differentiation along qr
Schneider Schneider && Thiel, Thiel, Chem. Phys. LettChem. Phys. Lett. . 157157, 367 (1989), 367 (1989)Stanton et al., Stanton et al., J. Chem. PhysJ. Chem. Phys. . 108108, 7190 (1998), 7190 (1998)
CCFOURFOUR: : http://www.http://www.cfourcfour.de.de
THEORY:THEORY:
Cubic Force FieldCubic Force Field: : (ae)CCSD(T)/cc-pCVTZ(ae)CCSD(T)/cc-pCVTZ
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2) 2) Equilibrium StructureEquilibrium Structure:: - semi-exp structure- semi-exp structure - - pure ab initio structurepure ab initio structure
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Best estimated equilibrium structureBest estimated equilibrium structure
- geometry optimization- geometry optimization::
(bases: cc-pVn Z, n =Q,5,6; cc-pCV5Z)
- - full-T correctionsfull-T corrections::
(basis: cc-pVTZ)
- - pert-Q correctionspert-Q corrections::
(basis: cc-pVDZ)
- on the whole- on the whole::
dx
coreEd
dx
TCCSDEd
dx
SCFHFdE
dx
dEtot )()(()(
))(()()( TCCSDrCCSDTrTfullr
))(()()()( QrTfullrErbestr tote
)())(())(( CCSDTrQCCSDTrQr
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2) 2) Equilibrium StructureEquilibrium Structure:: - semi-exp structure- semi-exp structure - pure ab initio structure- pure ab initio structure
RESULTS
RESULTS
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(dist: Å / ang: º)(dist: Å / ang: º) F-SiF-Si Si-HSi-H HSiFHSiF
CCSD(T)/VQZCCSD(T)/VQZ 1.60071.6007 1.47551.4755 108.34108.34
CCSD(T)/V5ZCCSD(T)/V5Z 1.59701.5970 1.47451.4745 108.34108.34
CCSD(T)/V6ZCCSD(T)/V6Z 1.59631.5963 1.47441.4744 108.33108.33
CBSCBS 1.59611.5961 1.47441.4744 108.31108.31
CBS+CVCBS+CV 1.59091.5909 1.46991.4699 108.31108.31
CBS+CV+full-TCBS+CV+full-T 1.59111.5911 1.47011.4701 108.31108.31
CBS+CV+full-T+CBS+CV+full-T+(Q)(Q)
1.59151.5915 1.47021.4702 108.32108.32
Pure ab initio equilibrium structure:Pure ab initio equilibrium structure:basis set convergence and higher excitations basis set convergence and higher excitations
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EQUILIBRIUM STRUCTURE:EQUILIBRIUM STRUCTURE:pure ab initio structurepure ab initio structure
vs vs semi-experimental geometrysemi-experimental geometry
(dist: Å / ang: º)(dist: Å / ang: º) F-SiF-Si Si-HSi-H HSiFHSiF
CBS+CV+full-T+CBS+CV+full-T+(Q)(Q)
1.59151.5915 1.47021.4702 108.32108.32
Semi-Semi-experimentalexperimental
[uncertainties: 3[uncertainties: 3]]
1.5906(1)1.5906(1) 1.4698(2)1.4698(2) 108.29(2108.29(2))
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THANK YOUTHANK YOU for your attention!! for your attention!!