SILYL FLUORIDE: LAMB-DIP SPECTRA and EQUILIBRIUM STRUCTURE Cristina PUZZARINI and Gabriele CAZZOLI Dipartimento di Chimica “G. Ciamician”, Università di

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


c

zobs

v10

++vvzaza--vvzaza

vvzz== 00

0 obs

czaobs /v10


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




Nuclear quadrupole coupling constantsNuclear quadrupole coupling constants






Spin-rotation interactionsSpin-rotation interactions






Spin-rotation interactionsSpin-rotation interactions

Spin-spin (direct)Spin-spin (direct) interactionsinteractions


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 correctionvibrational correctionss



- accurate method [- accurate method [CCSD(T)CCSD(T)]]

- cc basis set- cc basis set


- vibrational correctionvibrational correctionss




- cc basis set [- cc basis set [nnQQ]]






- cc basis set [- cc basis set [nnQQ]]

- CV correction- CV correctionss [ [additivityadditivity/CV bases/CV bases]]




- 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 correctionvibrational 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


THEORY:THEORY:


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


THEORY:THEORY:


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


J = 14 - 13, K = 9

EXP


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 structurepure 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)


THEORY:THEORY:

Cubic Force FieldCubic Force Field: : (ae)CCSD(T)/cc-pCVTZ(ae)CCSD(T)/cc-pCVTZ

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

Documents

SILYL FLUORIDE: LAMB-DIP SPECTRA and EQUILIBRIUM STRUCTURE Cristina PUZZARINI and Gabriele CAZZOLI Dipartimento di Chimica “G. Ciamician”, Università di