SILYL FLUORIDE: LAMB-DIP SPECTRA and EQUILIBRIUM STRUCTURE Cristina PUZZARINI and Gabriele CAZZOLI...

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

1) 1) Hyperfine StructureHyperfine Structure:: - - Instrument Instrument && Technique Technique - - Theory Theory && Computations Computations

1) 1) Hyperfine StructureHyperfine Structure:: - - Instrument Instrument && Technique Technique - Theory - Theory && Computations Computations

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

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).

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

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

1) 1) Hyperfine StructureHyperfine Structure:: - Instrument - Instrument && Technique Technique - - Theory Theory && Computations Computations

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

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

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

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

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

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)

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

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

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

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

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

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]]

1) 1) Hyperfine StructureHyperfine Structure:: - Instrument - Instrument && Technique Technique - Theory - Theory && Computations Computations

RESULTS

RESULTS

(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

429150.50 429150.55 429150.60

J = 15 - 14, K = 13

only FF + H

EXP

FREQUENCY (MHz)

2828SiHSiH33FF

429150.50 429150.55 429150.60

J = 15 - 14, K = 13

only FF + H

EXP

FREQUENCY (MHz)

2828SiHSiH33FF

(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

(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

425220.35 425220.40 425220.45 425220.50

J = 15 - 14, K =13

F + 29Si + H

F + 29Si

only F

FREQUENCY (MHz)

2929SiHSiH33FF

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

(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

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

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

2) 2) Equilibrium StructureEquilibrium Structure:: - - semi-exp structuresemi-exp structure - - pure ab initio structurepure ab initio structure

2) 2) Equilibrium StructureEquilibrium Structure:: - - semi-exp structuresemi-exp structure - pure ab initio structure- pure ab initio structure

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)

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

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

2) 2) Equilibrium StructureEquilibrium Structure:: - semi-exp structure- semi-exp structure - - pure ab initio structurepure ab initio structure

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

2) 2) Equilibrium StructureEquilibrium Structure:: - semi-exp structure- semi-exp structure - pure ab initio structure- pure ab initio structure

RESULTS

RESULTS

(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

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))

THANK YOUTHANK YOU for your attention!! for your attention!!