Bryan Changala JILA amp Dept of Physics Univ of Colorado Boulder Joshua Baraban Dept of Chemistry Univ of Colorado Boulder ISMS 2017 Rigid vs nonrigid polyatomic molecules Well defined unique equilibrium geometry ID: 627207
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Slide1
Ab initio effective rovibrational Hamiltonians for non-rigid molecules via curvilinear VMP2
Bryan ChangalaJILA & Dept. of Physics, Univ. of Colorado BoulderJoshua BarabanDept. of Chemistry, Univ. of Colorado Boulder
ISMS 2017Slide2
Rigid vs. non-rigid polyatomic molecules
Well defined, unique equilibrium geometryRigid
Non-rigid
Possibly no unique eq. geometry
Total rotations approximately separable from internal motion (e.g.
Eckart conditions)Small amplitude, approximately harmonic normal modes
Structure
Vibrational
dynamics
Rotational
dynamics
Large amplitude, highly anharmonic, tunneling
Potentially significant rotation-vibration interaction (e.g. internal rotors)Slide3
General approaches to solving
VariationalPerturbative
Converge numerically exact energies and wavefunctions
Non-rigidity handled naturally BUT
Very expensive (ca. 103+ per atom)
Computationally economicalNear spectroscopic accuracy in favorable cases
BUT
Standard methods (e.g. VPT2) geared for
semi-rigid
systems.
Alternative perturbative rovibrational approach for non-rigid molecules?Slide4
Disilicon carbide, Si2C
Si
Si
C
Mode
Variational
(“exact”) / cm
-1
Standard
VPT2 */ cm
-1
ν
2
(Si-C-Si bend)
140.49
148.82
ν
1
(sym. stretch)
828.24
846.62
ν
3
(
asym
. stretch)
1198.14
1213.94
RMS error
14.80
Soft, anharmonic bending mode
N. Reilly, et al,
J. Chem. Phys.
142
, 231101 (2015)
M. McCarthy, et al, J. Phys. Chem. Lett. 6, 2107 (2015)PBC & J. Baraban, J. Chem. Phys. 145, 174106 (2016)
*with rectilinear quartic force fieldSlide5
Rectilinear (Cartesian)
normal modes Q
i
are not natural choices
Q
2
bend
1
Perturbative theories are only as good as
Ψ
0
Standard zeroth order picture:
3N-6 harmonic oscillator normal modes
Use
curvilinear
internal coordinates (e.g. bond angles & lengths, …)
Vibrational factors are
harmonic oscillator
wavefunctions
Allow
arbitrary, anharmonic
1D vibrational wavefunctions
2Slide6
Holding all other fixed, vary one to minimize
…___……….
Do this for each factor.
Vibrational SCF & MP2
How do we choose
the factors??
Guess some initial
Repeat
… until converged
J. Bowman,
Acc. Chem. Res.
19
, 202 (1986); Gerber & Ratner,
Adv. Chem. Phys.
70
, 97 (1988)
Strobusch
&
Scheurer
,
J. Chem. Phys.
135
, 124102 (2011)
L.S. Norris et al,
J. Chem. Phys.
105
, 11261 (1996); O. Christiansen,
J. Chem. Phys.
119
, 5773 (2003
)
Perturbatively
correct for remaining vibrational correlation (
VMP2
)Slide7
How does VMP2 fare for Si2C?
Mode
Variational (“exact”) / cm-1
Standard VPT2 / cm-1Curvilinear VMP2*/ cm-1
ν2 (Si-C-Si bend)140.49148.82
140.48ν1 (sym. stretch)
828.24
846.62
828.29
ν
3
(
asym
. stretch)
1198.14
1213.94
1198.17
RMS error
14.80
0.03
Why such an improvement?
VSCF/VMP2 zeroth order approximation =
separability
of 3N-6 q
i
vibrational degrees of freedom (which we choose …
critical user input
!)
All “diagonal anharmonicity” and “mean-field cross anharmonicity” are accounted for already at zeroth order.
Remaining vibrational correlations tend to be “small”; handled well by VMP2.
PBC & J. Baraban,
J. Chem. Phys.
145
, 174106 (2016)
*with
curvilinear
normal coords.Slide8
Typically: so let’s treat them perturbatively
as well. Important: choice of body-fixed frame! For well defined eq. geometry, use Eckart frame for curvilinear KEO.
If no well defined eq. geometry, more elaborate schemes are used.
Details: J. Chem. Phys. 145, 174106 (2016). Adding molecular rotation to VMP2
After a bunch of machinery, we get A/B/C rotational constants and quartic centrifugal distortion constants.
NEWSlide9
Rotational constant
Variational
(“exact”)/MHz
VPT2 |rel. error| x 104VMP2 |rel. error| x 104
Av=06362749.3
2.1Bv=0
4339
2.9
0.3
C
v
=0
4051
2.3
0.7
A
bend
70668
315.8
5.8
Si
2
C rotational constants
aSlide10
Unhindered internal rotation in nitromethane
E
5.5 cm
-1
V = 2 cm
-1
22 cm
-1
50 cm
-1
So far, we’ve assumed
But in the torsional manifold
Uh-oh!!!Slide11
Dealing with near-resonant interactions with rotational-VMP2
Energy
Target state
well isolated
Energy
Target state
n
ot isolated
Treat subset of states non-
perturbatively
Account for remaining (weak) interactions
perturbatively
(via contact/Van
Vleck
transformation)
Standard perturbative correction sum
PBC
& J. Baraban,
J. Chem. Phys.
145
, 174106 (2016)Slide12
Parameter
Expt. / MHzVPT2 VMP2
A
133421219013330B
105441046410507C
587658495862
F
166703
---
166896
A’
13283
---
13249
Δ
JK
x 10
3
17.8
953
17.8
Δ
K
x 10
3
-7.5
-949
-10.7
δ
K
x 10
3
15.8
-268
15.8
All the “problem” parameters involve internal or total rotation about the CH
3
top axis (a-axis)
CH3NO2 torsion-rotation effective HamiltonianF. Rohart
,
J. Mol. Spec.
57
301 (1975); G.
Sørensen
et al
J. Mol.
Struct
.
97
, 77 (1983).
PBC & J. Baraban,
J. Chem. Phys.
145
, 174106 (2016)
aSlide13
Conclusions
Rotational curvilinear VMP2 is a flexible and efficient tool for accurate rovibrational predictions for non-rigid molecules displaying various types of non-trivial nuclear motion dynamics.Applications to tunneling gauche-1,3,-butadiene (10 atom molecule, see talk
TK07 this afternoon) and c-C
3H2 (see talk WF08 by H. Gupta)Future work:inclusion of rotations in SCF stage (explicit RVSCF)
extensions to vibronic/JT systems???Thanks for your attention!!!Slide14
Si2C experimental molecular constants
Mode
Variational (“exact”) / cm
-1Standard VPT2 / cm-1Curvilinear VMP2 / cm-1
Expt / cm-1ν2
(Si-C-Si bend)140.49148.82140.48140(2)
ν
1
(sym. stretch)
828.24
846.62
828.29
830(2)
ν
3
(
asym
. stretch)
1198.14
1213.94
1198.17
---
RMS error
14.80
0.03
Rotational constant
Variational
(“exact”)/MHz
VPT2
|rel. error| x 10
4
VMP2
|rel. error| x 10
4
Expt
/ MHz
Av=06362749.3
2.164074
Bv=043392.90.34396
C
v
=0
4051
2.3
0.7
4102
A
bend
70668
315.8
5.8
71230
N. Reilly, et al,
J. Chem. Phys.
142
, 231101 (2015)
M. McCarthy, et al,
J. Phys. Chem. Lett.
6
, 2107 (2015)
J.
Cernicharo
, et al,
ApJL
,
806
, L3 (2015)