Transcript Interplay.ppt

QUANTUM-CHEMICAL
CALCULATIONS of SPECTROSCOPIC
PARAMETERS
for ROTATIONAL SPECTROSCOPY:
the NEED of the INTERPLAY
between EXPERIMENT and THEORY
Cristina PUZZARINI
Dip. di Chimica “G. Ciamician”, Università di Bologna
Int. Symposium on Molecular Spectroscopy
66th Meeting – Columbus, OH – June 20-24, 2011
OUTLINE
Laboratory of Millimetre-wave
1) QUANTUM-CHEMICAL
CALCULATIONS:
Some details
385784
2) INTERPLAY between
EXPERIMENT and THEORY:
Spectroscopy
of Bologna
The need: why
385786
385788
FREQUENCY (MHz)
385790
OUTLINE
Laboratory of Millimetre-wave
1) QUANTUM-CHEMICAL
CALCULATIONS:
Some details
385784
2) INTERPLAY between
EXPERIMENT and THEORY:
Spectroscopy
of Bologna
The need: why
385786
385788
FREQUENCY (MHz)
385790
QUANTUM-CHEMICAL
CALCULATIONS of SPECTROSCOPIC
PARAMETERS
For ROTATIONAL SPECTROSCOPY:
the NEED of the INTERPLAY
between EXPERIMENT and THEORY
Int. Symposium on Molecular Spectroscopy
66th Meeting – Columbus, OH – June 20-24, 2011
Rotational Hamiltonian
Laboratory
of
Millimetre-wave
Rotational Hamiltonian
AJ  BJ  CJ
2
A
2
B
2
C
Rotational constants
Spectroscopy of Bologna
Rotational Hamiltonian
Laboratory
of
Millimetre-wave
Rotational Hamiltonian
AJ  BJ  CJ
2
A
2
B
Rotational constants
2
C
RIGID ROTOR
+
CENTRIFUGAL DISTORTION
Spectroscopy of Bologna
Rotational Hamiltonian
Laboratory
of
Millimetre-wave
Rotational Hamiltonian
AJ  BJ  CJ
2
A
2
B
2
C
Rotational constants
+ Centrif.distort. constants
- eQK qJ K

1
3 ( ) 2 2
2
(
)


3I J
IJ -I J 


2 K 2I K (2I K -1) J (2 J -1) 
2

Spectroscopy of Bologna
Nuclear quadrupole coupling
Rotational Hamiltonian
Laboratory
of
Millimetre-wave
Rotational Hamiltonian
AJ  BJ  CJ
2
A
2
B
I
2
C
Rotational constants
+ Centrif.distort. constants
K
CKJ
K
Spin-rotation interactions
- eQK qJ K

1
3 ( ) 2 2
2
(
)


3I J
IJ -I J 


2 K 2I K (2I K -1) J (2 J -1) 
2

Spectroscopy of Bologna
Nuclear quadrupole coupling
Rotational Hamiltonian
Laboratory
of
Millimetre-wave
Rotational Hamiltonian
AJ  BJ  CJ
2
A
2
B
I
2
C
Rotational constants
+ Centrif.distort. constants
K
CKJ
K
Spin-rotation interactions
- eQK qJ K

1
3 ( ) 2 2
2
(
)


3I J
IJ -I J 


2 K 2I K (2I K -1) J (2 J -1) 
2

I
K L
D KL I L
Spin-spin (direct)
interactions
Spectroscopy of Bologna
Nuclear quadrupole coupling
K
Rotational Hamiltonian
Laboratory
of
Millimetre-wave
Rotational Hamiltonian
AJ  BJ  CJ
2
A
2
B
I
2
C
Rotational constants
+ Centrif.distort. constants
K
CKJ
K
Spin-rotation interactions
- eQK qJ K

1
3 ( ) 2 2
2
(
)


3I J
IJ -I J 


2 K 2I K (2I K -1) J (2 J -1) 
2

I
K L
D KL I L
Spin-spin (direct)
interactions
Spectroscopy of Bologna
Nuclear quadrupole coupling
K
Accuracy of Theoretical Rotational
Constants
STATISTICAL ANALYSIS for
• 16 molecules (97 isotopologues)
• 180 rotational constants
Reference values: B0 from experiment
HF, N2, CO, F2, HCN, HNC, O=C=O, H2O, NH3,
CH4, HCCH, HOF, HNO, NH=NH, CH2=CH2, H2C=O
C. Puzzarini, M. Heckert, J. Gauss JCP 128, 194108 (2008)
B0calc vs B0exp
CCSD(T)/VTZ
CCSD(T)/V6Z
CCSD(T)/V6Z
CCSD(T)/VQZ
CCSD(T)/V5Z
CV
CCSD(T)/V6Z
CV ++ fT
fT
CCSD(T)/VZ
CCSD(T)/VZ
++ CV
+ fQ+ +fQ
vib
+++fQ
+fQ
vib
ele
Laboratory of Millimetre-wave
-4
Spectroscopy of Bologna
-3
-2
-1
0
1
2
3
4
normal distributions of relative errors
C. Puzzarini, M. Heckert, J. Gauss JCP 128, 194108 (2008)
B0calc vs B0exp
Laboratory of Millimetre-wave
mean error -0.001%
standard deviation 0.09%
mean error 0.70%
standard deviation 0.75%
CCSD(T)/VZ
+ CV
+ fT
+ fQ
+ vib
+ ele
-4
CCSD(T)/V6Z
+ CV
+ fT
+ fQ
Spectroscopy of Bologna
-3
-2
-1
0
1
2
3
4
normal distributions of relative errors
C. Puzzarini, M. Heckert, J. Gauss JCP 128, 194108 (2008)
COMPOSITE APPROACH extended to large molecule
b
H10
O7
N3
C2
H9
N1
C6
H12
O8
C4
a
C5
H11
URACIL
COMPOSITE APPROACH extended to large molecule
 Equilibrium Rotational Constants
r (CBS  CV  diff  T)  r (CBS)  r (CV)  r (diff)  r (T)
MP2/cc-pV(T,Q)Z
MP2/aug-cc-pVTZ
MP2/cc-pCVTZ
CCSD(T)/cc-pVTZ
 Vibrational Corrections to Rotational Constants
B3LYP/N07D
MP2/cc-pVTZ
URACIL
MHz
Calculated
3885.475
Experiment
3883.873021(60)
B0
MHz
2027.763
2023.732581(45)
C0
MHz
1332.761
1330.928108(33)
DJ
kHz
0.061
DJK
kHz
0.107
DK
kHz
0.447
0.4530(32)
d1
kHz
-0.026
-0.02623(18)
d2
kHz
-0.006
-0.00680(13)
aa
MHz
1.739
1.7600 (25)
bb
MHz
1.952
1.9811(29)
aa
MHz
1.871
1.9255(24)
bb
MHz
1.491
1.5273(32)
A0
Puzzarini
&
<0.2% 0.06336(44)
0.1055(23)
Barone, PCCP 13, 7158 (2011)
COMPOSITE APPROACH extended to large molecule
 Equilibrium Rotational Constants
r (CBS  CV  diff  T)  r (CBS)  r (CV)  r (diff)  r (T)
MP2/cc-pV(T,Q)Z
MP2/aug-cc-pVTZ
MP2/cc-pCVTZ
CCSD(T)/cc-pVTZ
 Vibrational Corrections to Rotational Constants
B3LYP/N07D
MP2/cc-pVTZ
 Centrifugal-Distortion Constants
D(best)  D(CCSD(T)/T Z)  D(MP2/CVTZ, all) - D(MP2/CVTZ, fc)  D(MP2/aVTZ) - D(MP2/VTZ)
CV
Puzzarini
&
Barone, PCCP 13, 7158 (2011)
diffuse
URACIL
MHz
Calculated
3885.475
Experiment
3883.873021(60)
B0
MHz
2027.763
2023.732581(45)
C0
MHz
1332.761
1330.928108(33)
DJ
kHz
0.061
0.06336(44)
DJK
kHz
0.107
0.1055(23)
DK
kHz
0.447
d1
kHz
-0.026
-0.02623(18)
d2
kHz
-0.006
-0.00680(13)
aa
MHz
1.739
1.7600 (25)
bb
MHz
1.952
1.9811(29)
aa
MHz
1.871
1.9255(24)
bb
MHz
1.491
1.5273(32)
A0
Puzzarini
&
~1%
0.4530(32)
Barone, PCCP 13, 7158 (2011)
OUTLINE
Laboratory of Millimetre-wave
1) QUANTUM-CHEMICAL
CALCULATIONS:
Some details
385784
2) INTERPLAY between
EXPERIMENT and THEORY:
Spectroscopy
of Bologna
The need: why
385786
385788
FREQUENCY (MHz)
385790
Laboratory of Millimetre-wave
INTERPLAY
of
Theory and Experiment
in
Rotational Spectroscopy
Spectroscopy of Bologna
Assignment of “unknown” spectra
 Analyze the spectra: ITERATIVE PROCEDURE
Calculated spectrum

Preliminary assignments

Improved calculated spectrum

Further assignments
 AABS package
…… Kisiel, Pszczolkowski, Medvedev, Winnewisser, De Lucia,
Herbst, J. Mol. Spectrosc. 233, 231 (2005)

Complete assignment
Unknown spectrosocpic parameters …
Need: accurate
estimate
of
rotational
35
trans-CH Cl=CHF
parameters, dipole moment &
quadrupole
coupling
constants
- Accurate
equilibrium
structure
(Be)
from
ab
initio
computations
- Accurate centrifugal-distortion constants
- Accurate vibrational corrections (BeB0)
524000
524100
524200
524300
524400
Frequency (MHz)
524500
524600
524700
Unknown spectrosocpic parameters …
Need: accurate
estimate
of
rotational
35
trans-CH Cl=CHF
parameters,
parameters dipole
& dipole
moment
moment
&
quadrupole coupling constants
from ab initio computations
524000
524100
524200
524300
524400
Frequency (MHz)
524500
524600
524700
Laboratory of Millimetre-wave
For a detailed example:
LISTEN to next TALK
“Rotational Spectrum of CH2FI”
Spectroscopy of Bologna
C. Puzzarini et al., JCP 134, 174312 (2011)
Laboratory of Millimetre-wave
INTERPLAY
of
Theory and Experiment
in
Rotational Spectroscopy
Spectroscopy of Bologna
Hyperfine structure of rotational spectra
HFS
of
trans-HCOOH
Laboratory of Millimetre-wave
2 non-equivalent
hydrogens
(I1 = I2 = 1/2)
Spectroscopy of Bologna
Cazzoli, Puzzarini, Stopkowicz & Gauss, A&A 520, A64 (2010)
HCOOH: J = 18
- 18
Laboratory of Millimetre-wave
2,16
2,17
Experiment:
Lamb-dip
J.-C. Chardon, C. Genty, D. Guichon, & J.-G. Theobald, J. Chem. Phys. 64, 1434 (1976)
“rf spectrum and hyperfine structure of formic acid”
RF data:
only SR
Spectroscopy of Bologna
107638.20
107638.25
107638.30
FREQUENCY (MHz)
107638.35
HCOOH: J = 18
- 18
Laboratory of Millimetre-wave
2,16
2,17
Experiment:
Lamb-dip
????
RF data:
only SR
Spectroscopy of Bologna
107638.20
107638.25
107638.30
107638.35
FREQUENCY (MHz)
J.-C. Chardon, C. Genty, D. Guichon, & J.-G. Theobald, J. Chem. Phys. 64, 1434 (1976)
HCOOH: J = 18
- 18
Laboratory of Millimetre-wave
2,16
2,17
Experiment:
Lamb-dip
What does Quantum Chemistry say?
RF data:
only SR
Spectroscopy of Bologna
107638.20
107638.25
107638.30
107638.35
FREQUENCY (MHz)
J.-C. Chardon, C. Genty, D. Guichon, & J.-G. Theobald, J. Chem. Phys. 64, 1434 (1976)
Accurate hyperfine parameters
Laboratory of Millimetre-wave
>>>> Main requirements:
- accurate method [CCSD(T)]
- cc basis set [nQ]
- CV correction [additivity]
- vibrational
correction
[ff:
correlated
Spectroscopy of Bologna
method]
HCOOH: J = 18
- 18
Laboratory of Millimetre-wave
2,16
2,17
Experiment
Theory:
only SR
RF data:
only SR
Spectroscopy of Bologna
107638.20
107638.25
107638.30
FREQUENCY (MHz)
107638.35
HCOOH: J = 18
- 18
Laboratory of Millimetre-wave
2,16
2,17
Experiment
Theory:
SR and SS
Theory:
only SR
RF data:
only SR
Spectroscopy of Bologna
107638.20
107638.25
107638.30
FREQUENCY (MHz)
107638.35
HCOOH: J = 18
- 18
Laboratory of Millimetre-wave
2,16
2,17
Experiment
Theory:
SR and SS
Theory:
only SR
RF data:
only SR
Spectroscopy of Bologna
107638.20
107638.25
107638.30
FREQUENCY (MHz)
107638.35
Hyperfine parameters of trans-HCOOH
Experiment
Theory
Caa [H(C)]
-6.835(46)
-7.02
Cbb [H(C)]
1.037
1.04
Ccc [H(C)]
-0.8014(96)
-0.82
Caa [H(O)]
-6.868(45)
-6.94
Cbb [H(O)]
0.781(20)
0.77
Ccc [H(O)]
-1.290(15)
-1.32
4.49(12)
4.62
RF results
Laboratory of Millimetre-wave
1.5Daa
Spectroscopy
of
Bologna
)/4
-3.53(35)
-3.47
(Dbb – Dcc
Equil: CCSD(T)/CV5Z +
Vib. Corr: CCSD(T)/CVTZ
---
Hyperfine parameters of trans-HCOOH
Experiment
Theory
RF results
Caa [H(C)]
-6.835(46)
-7.02
-7.50(20)
Cbb [H(C)]
1.037
1.04
Ccc [H(C)]
-0.8014(96)
-0.82
Caa [H(O)]
-6.868(45)
-6.94
Cbb [H(O)]
0.781(20)
0.77
Ccc [H(O)]
-1.290(15)
-1.32
4.49(12)
4.62
Laboratory of Millimetre-wave
1.5Daa
-6.55(20)
Spectroscopy
of
Bologna
)/4
-3.53(35)
-3.47
(Dbb – Dcc
Equil: CCSD(T)/CV5Z +
Vib. Corr: CCSD(T)/CVTZ
---
Hyperfine parameters of trans-HCOOH
Experiment
Theory
RF results
Caa [H(C)]
-6.835(46)
-7.02
-7.50(20)
Cbb [H(C)]
1.037
1.04
-7.2(40)
Ccc [H(C)]
-0.8014(96)
-0.82
7.5(40)
Caa [H(O)]
-6.868(45)
-6.94
-6.55(20)
Cbb [H(O)]
0.781(20)
0.77
8.2(40)
Ccc [H(O)]
-1.290(15)
-1.32
-8.6(40)
4.49(12)
4.62
--
Laboratory of Millimetre-wave
1.5Daa
Spectroscopy
of
Bologna
)/4
-3.53(35)
-3.47
(Dbb – Dcc
--
Cazzoli, Puzzarini, Stopkowicz, Gauss, A &A 520, A64 (2010)
H217O:
J = 4
1,4
- 3
2,1
Experiment
Real+Ghost
Real
Ghost
385784
385786
385788
385790
FREQUENCY (MHz)
Puzzarini, Cazzoli, Harding , Vázquez & Gauss, JCP 131, 234304 (2009)
Laboratory of Millimetre-wave
Lamb-dip spectra
recorded
Results
Spectra analysis
& assignment
Hyperfine parameters
Spectroscopy
of
Bologna
computed
Laboratory of Millimetre-wave
INTERPLAY
of
Theory and Experiment
in
Rotational Spectroscopy
Spectroscopy of Bologna
Determination of equilibrium structure
1
B
FIT Be  B0    r
2 r
from EXPERIMENT
(various isotopic species)
from THEORY
(cubic force field)
“Empirical” equilibrium structure
Accuracy: experimental quality
Pawłowski, Jørgensen, Olsen, Hegelund, Helgaker, Gauss, Bak, Stanton JCP 116 6482 (2002)
Semi-exp equilibrium structure of large molecule
Isotopic substitution:
b
16
18
- O  O
- 14N  15H10
N
O713 N3
12
- C  C
C2
H9
O8
C4
a
N1
10 isotopic species
C5
Vaquero, Sanz, López, Alonso,
C6
J. Phys. Chem. Lett. 111A, 3443 (2007).
H11
H12
20 rotational constants
URACIL: 21 independent geometrical parameters
Puzzarini
&
Barone, PCCP 13, 7158 (2011)
Best est. rea
Distances
N1-C2
C2-N3
N3-C4
C4-C5
C5-C6
C6-N1
C2-O7
C4-O8
N1-H9
N3-H10
C5-H11
C6-H12
Angles
C2-N1-C6
N1-C6-C5
C6-C5-C4
C5-C4-N3
C4-N3-C2
N3-C2-N1
N1-C2-O7
C5-C4-O8
C2-N1-H9
C2-N3-H10
C6-C5-H11
N1-C6-H12
Fit 1
1.3785
1.3756
1.3974
1.4539
1.3433
1.3723
1.2112
1.2138
1.0046
1.0090
1.0766
1.0793
123.38
121.91
119.49
113.97
127.75
113.51
123.62
125.83
115.22
115.70
122.11
115.34
1.38175(53)
1.3763
1.39793(40)
1.45500(57)
1.34496(59)
1.37196(55)
1.21025(21)
1.21278(24)




Semi-exp. reb
Fit 2
1.38163(65)
1.3763
1.39823(47)
1.45485(99)
1.34576(107)
1.37160(100)
1.21015(26)
1.21268(34)
1.0004(70)
1.0110(96)


Exp. rsc
Fit 3
1.38161(51)
1.3762
1.39835(45)
1.45481(57)
1.34473(58)
1.37258(66)
1.21015(21)
1.21269(24)


1.0695(52)
1.0856(32)
1.386(5)
1.38(2)
1.451(4)
1.379(4)
1.352(14)
1.219(4)
1.22(2)
123.374(19)
123.394(35)
123.370(21)
123.0(11)
121.924(10)
121.920(10)
121.9237(97)
122.3(6)
119.516(16)
119.501(20)
119.523(16)
118.8(12)
113.860(22)
113.859(33)
113.858(22)
115.4(16)
127.942
127.947
127.945
113.383
113.379
113.380
123.883(44)
123.878(54)
123.874(42)
122.3(8)
125.768(48)
125.765(75)
125.767(45)
118.8(7)




115.52(40)




Non-determinable
Parameters:
fixed at the corresponding
theo values



Laboratory of Millimetre-wave
THANK YOU for your attention!!
Spectroscopy of Bologna
Electronic contribution to B




B0  Be  Bvib  Bel
me  
Bel 
g Be
mp

=x,y,z
princ. inertia system
g = rotational g tensor
me = mass of the electron
mp = mass of the proton
CCSD(T) calc: Gauss, Ruud, Kallay, JCP 127, 074101 (2007)