VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.)...

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Supporting information: The N( 4 S )+O 2 (X 3 Σ - g ) O( 3 P ) + NO(X 2 Π) Reaction: Thermal and Vibrational Relaxation Rates for the 2 A 0 , 4 A 0 and 2 A 00 States Juan Carlos San Vicente Veliz, 1 Debasish Koner, 1 Max Schwilk, 1 Raymond J. Bemish, 2 and Markus Meuwly 1 1) Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland 2) Air Force Research Laboratory, Space Vehicles Directorate, Kirtland AFB, New Mexico 87117, USA 1 Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is © the Owner Societies 2020

Transcript of VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.)...

Page 1: VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.) Total Caridade (2018, Theo.) FIG. S12. Vibrational relaxation rates for O+NO( = 1)

Supporting information:

The N(4S) + O2(X3Σ−g )↔ O(3P ) + NO(X2Π) Reaction: Thermal and Vibrational

Relaxation Rates for the 2A′, 4A′ and 2A′′ States

Juan Carlos San Vicente Veliz,1 Debasish Koner,1 Max Schwilk,1 Raymond J. Bemish,2

and Markus Meuwly1

1)Department of Chemistry, University of Basel, Klingelbergstrasse 80,

CH-4056 Basel, Switzerland

2)Air Force Research Laboratory, Space Vehicles Directorate, Kirtland AFB,

New Mexico 87117, USA

1

Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2020

Page 2: VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.) Total Caridade (2018, Theo.) FIG. S12. Vibrational relaxation rates for O+NO( = 1)

0

2

4

6

8

En

erg

y [

eV

]

N(4S)+O2(X3Σg-)

N(4S)+O2(a1∆g)

N(4S)+O2(b1Σg+)

N(2D)+O2(X3Σg-)

N(2D)+O2(a1∆g)

NO2(2A′)

NO2(4A′)

NO2(2A″)

NO(X2Π)+O(3P) 2A′

2A′

4A′

2A″

6A′

2A″

4A′

FIG. S1. Correlation plot for the NO2 states (in CS symmetry) investigated in the present work

(middle) and their connection with the atom+diatom states. Only the 2A’ and 2A” states have

attractive wells with respect to dissociation into atom+diatom states. One of the sextett states

discussed in the manuscript is also indicated.

2

Page 3: VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.) Total Caridade (2018, Theo.) FIG. S12. Vibrational relaxation rates for O+NO( = 1)

2

3

4

5

6R

(a0)

2A″

OO+N

2

3

4

5

6

R(a

0)

4A′

0 30 60 90 120 150 1802

3

4

5

6

R(a

0)

2A′

θ (°)

2A″

NO+O

−9−8−7−6−5−4−3−2−10

4A′

−9−8−7−6−5−4−3−2−10

30 60 90 120 150 180

2A′

θ (°)

−9−8−7−6−5−4−3−2−10

MM MM

M

MM

M

M

MM

M

M M

FIG. S2. Two-dimensional cuts through the 3-d PES for the OO+N (left and the NO+O (right)

channels. The OO and NO diatomics are at their equilibrium bond lengths of the respective states,

see text. The three states are 2A′, 4A′, and 2A′′ from bottom to top. Contour increments of 0.1

eV. The zero of energy is for dissociation into atomic fragments. “M” labels the minima described

in the text.

REFERENCES

1G. Henkelman, B. Uberuaga, and H. Jonsson, J. Chem. Phys. 113, 9901 (2000).

2E. L. Kolsbjerg, M. N. Groves, and B. Hammer, J. Chem. Phys. 145, 094107 (2016).

3

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-10

-9

-8

-7

-6

-5

-4

0En

ergy

(eV)

NO(2Π)+O(3P)

2A'

MIN1 MIN2

MIN3

TS1

TS2

TS3

2.33

3.46 θ=112.1°

2.582.27 θ=130.4°

2.862.20 θ=134.1°

4.51

θ=121.1°

4.63

2.19 θ=90.7°

2.262.26

θ=134.2°2.18

O2(3Σg)+N(2D)

FIG. S3. The minima (MINi) and transition states (TSi) for the 2A′ state as found from mini-

mization and the nudged elastic band calculations.1,2 The geometrical parameters are also given

(bond distances in a0).

3R. Sayos, C. Oliva, and M. Gonzalez, J. Chem. Phys. 117, 670 (2002).

4P. J. S. B. Caridade, J. Li, V. C. Mota, and A. J. C. Varandas, J. Phys. Chem. A 122,

5299 (2018).

4

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-6

-5

-4

0En

ergy

(eV)

4A'

MIN1

TS1

TS2

2.60

2.653.07

2.36

2.39

3.26 θ=108.0°

θ=104.0° θ=103.0°

NO(2Π)+O(3P)

O2(3Σg)+N(2D)

FIG. S4. The minima (MINi) and transition states (TSi) for the 4A′ state as found from minimiza-

tion and the nudged elastic band calculations. The geometrical parameters are also given (bond

distances in a0).

5

Page 6: VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.) Total Caridade (2018, Theo.) FIG. S12. Vibrational relaxation rates for O+NO( = 1)

-9

-8

-7

-6

-5

-4

-3

-2

-1

0En

ergy

(eV)

2A''

MIN1

TS2

TS3

TS5MIN2

MIN3

MIN4

2.61

2.88

2.61

2.57 2.57

2.28 2.28

2.38 2.38

θ=130.2°

θ=80.2°

θ=67.1°

2.652.26

2.303.96

θ=111.7°

MIN2

TS4

MIN2 θ=107.5°

2.422.42

θ=109.5°2.232.782.782.23

θ=107.5°0.13 eV

2.31

4.324.36

θ=30.8°TS1

NO(2Π)+O(3P)

O2(3Σg)+N(2D)

FIG. S5. The minima (MINi) and transition states (TSi) for the 2A′′ state as found from min-

imization and the nudged elastic band calculations.1 The geometrical parameters are also given

(bond distances in a0).

6

Page 7: VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.) Total Caridade (2018, Theo.) FIG. S12. Vibrational relaxation rates for O+NO( = 1)

-10

-8

-6

-4

-2

0

2E

RK

HS (

eV

)

-10 -8 -6 -4 -2 0-10

-8

-6

-4

-2

0

-10 -8 -6 -4 -2 0

Eab initio

(eV)-10 -8 -6 -4 -2 0 2

grid 2A′′ grid

4A′ grid

2A′

offgrid 2A′′ offgrid

4A′

offgrid 2A′

FIG. S6. Correlation between MRCI/aug-cc-PVTZ (Eabinitio) and RKHS energies up to a values

of 2 eV for 7435 (2A′), 6869 (4A′) and 7275 (2A′′) grid points and 537, 533 and 596 offgrid points

for the 2A′, 4A′ and 2A′′ surfaces, respectively. The zero of energy is the O+O+N dissociation

limit. The R2 value for the grid points are (0.99984, 0.99989, 0.99965) and for off-grid points

(0.99959, 0.99966, 0.99922) for the (2A′, 4A′, 2A′′) surfaces, respectively. The corresponding root

mean squared errors (RMSE) for the 2A′, 4A′ and 2A′′ surfaces are (0.65, 0.49, 0.99) kcal/mol

(0.028, 0.022, 0.043) eV for the grid points and (0.86, 0.76, 1.31) kcal/mol (0.038, 0.033, 0.057) eV

for offgrid points.

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FIG. S7. MO diagram of the NO +O channel at fixed values of R and r together with details of

the orbital occupancies. This Figure complements Figure 3 in the main text. The most important

configurations with >10% contribution to the CASSCF wave function for each state are given in

the middle panel of the figure. Caption continued on next page.

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Page 9: VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.) Total Caridade (2018, Theo.) FIG. S12. Vibrational relaxation rates for O+NO( = 1)

FIG. S7. Continued: Configurations where three single occupancies in orbitals couple to an overall

doublet state are not distinguished further and so coupled orbitals indicated by an asterisk. Two

configurations involve partially unoccupied bonding orbitals of the π3-systems (orbitals shown in

Figure S8). In these extended MO diagrams, the additional orbitals are given in gray colour.

The bottom panel reports which of the configurations contribute to the states for a given bending

angle θ according to the CI coefficients from the CASSCF wave function (labels A to F). Smaller

font indicates less contribution from a certain configuration. Arrows indicate the evolution of a

configuration contribution to a state. I. e., crossing arrows indicate a change of configuration of a

state, normally resulting in a configuration coupling and an avoided crossing of two states. States

2A′ and 2A′′ are characterized by strong changes in contributing configurations along the path

which is at the origin of the complexity of the shape of the PESs. Contrary to that, the 4A′ state

only contains one configuration along the path which explains its rather simple topology.

FIG. S8. MO diagram of NO2 for the doublet ground state for the two linear configurations (left

OON, right ONO) and for θ = 90 (middle). The full valence orbital basis is shown. The dominant

configurations at selected angles are depicted for the lowest 2A′ and 2A′′ states. Black arrows

for occupancies in both states, red for 2A′ and green for 2A′′. Asterisks for significant additional

occupancies due to strong correlation.

9

Page 10: VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.) Total Caridade (2018, Theo.) FIG. S12. Vibrational relaxation rates for O+NO( = 1)

0 20 40 60 80 100 120 140 160 180 θ (°)

-10

-8

-6

-4

-2

0

2E

MR

CI+

Q (

eV

)8 states 1

2A´

12 states 12A´

8 states 12A´´

12 states 12A´´

8 states 14A´

12 states 14A´

FIG. S9. The MRCI+Q energies for the 3 lowest states along the bending coordinate from an

8- and 12-state active space, see also Figure 3. The curves along the bending coordinate were

determined for R = 3.4 a0 and rNO = 2.183 a0 (equilibrium NO separation).

0 20 40 60 80 100 120 140 160 180θ (°)

-8

-6

-4

-2

0

2

4

E CA

SSC

F(e

V)

12A´12A´´14A´14A´´

0 20 40 60 80 100 120 140 160 180θ (°)

-10

-8

-6

-4

-2

0

2

E MR

CI+

Q(e

V)

12A´12A´´14A´14A´´

CASSCF MRCI+Q

FIG. S10. Comparison of the CASSCF (left panel) and the MRCI+Q (right panel) energies for

the 4 lowest states along the bending coordinate from an 8-state active space and including the

full valence orbital space, see also Figures 3 and S9. The curves along the bending coordinate were

determined for R = 3.4 a0 and rNO = 2.183 a0 (equilibrium NO separation).

10

Page 11: VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.) Total Caridade (2018, Theo.) FIG. S12. Vibrational relaxation rates for O+NO( = 1)

0 1000 2000 3000 4000 5000Temperature (K)

NO+O-> N+OON+OO-> NO+O

4A´

0 1000 2000 3000 4000 5000Temperature (K)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ratio

(pw

/ref)

NO+O-> N+OON+OO-> NO+O

2A´

FIG. S11. Ratio between the present QCT and previously calculated ICVT3 thermal rates as a

function of temperature. For the 2A′ (left) and 4A′ (right) using Gaussian binning for the forward

(N(4S) + O2(X3Σ−g ) → O(3P) +NO(X2Π), solid line) and reverse (O(3P) + NO(X2Π) → N(4S)

+O2(X3Σ−g ), dotted line) reaction.

0 500 1000 1500 2000 2500 3000T (K)

0

1e-11

2e-11

3e-11

4e-11

5e-11

6e-11

7e-11

k ν

=1

→0 (

T )

/cm

3s

-1

Glazer (1975, Exp.)

Hwang (2003, Exp)2A´´ This Work GB

2A´ This Work GB

4A´ This Work GB

Total This Work GB2A´´ Caridade (2018, Theo.)

2A´ Caridade (2018, Theo.)

Total Caridade (2018, Theo.)

FIG. S12. Vibrational relaxation rates for O+NO(ν = 1) → O+NO(ν ′ = 0) computed on 2A′

(triangle down), 2A′′ (triangle up) and 4A′ (triangle right) PESs. Results from this work are shown

as filled symbols while from Ref.4 are shown as open symbols. The black filled symbols with error

bars show the experimental results.

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Page 12: VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.) Total Caridade (2018, Theo.) FIG. S12. Vibrational relaxation rates for O+NO( = 1)

0 2 4 6 8 10 12 14b (a

0)

0

0.1

0.2

0.3

0.4

0.5

P(b

)

298 K530 K640 K825 K1500 K2700 K3000 K

2A´

FIG. S13. Opacity function (probability of vibrational relaxation as a function of impact parameter)

for the relaxing trajectories (O + NO(ν = 1) → O + NO(ν = 0)), with or without oxygen atom

exchange on the 2A′ PES at different temperatures. With increasing T the probability decreases

and bmax - the value for which vibrational relaxation still occurs - shifts to smaller values of b. The

opacity function P (b) indicates that at 300 K ∼ 50 % of all trajectories starting in O + NO(ν = 1)

relax to O + NO(ν = 0) for small values of b whereas at 3000 K only 30 % relax.

12

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0 30

60 90

120 150

180 2.5 3.5

4.5 5.5

6.5 7.5

8.5

Pro

bab

ilit

y

θ (°)R (a0)

FIG. S14. Distribution of the vibrationally nonrelaxing trajectories in (R, θ), i.e. O + NO(ν =

1) → O + NO(ν 6= 0), with or without oxygen atom exchange and N+O2. The distance R

is the oxygen atom-to-NO(center of mass) distance. Probability densities are calculated for all

nonrelaxing trajectories and only up to the time satisfying the criterion that the sum of the three

inter-nuclear distances is less than 9.5 a0.

13

Page 14: VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.) Total Caridade (2018, Theo.) FIG. S12. Vibrational relaxation rates for O+NO( = 1)

0 30

60 90

120 150

180 2.5 3.5

4.5 5.5

6.5 7.5

8.5

Pro

bab

ilit

y

θ (°)R (a0)

FIG. S15. Distribution of the vibrationally relaxing trajectories in (R, θ), i.e. O + NO(ν = 1) →

O + NO(ν = 0), with or without oxygen atom exchange. The distance R is the oxygen atom-to-

NO(center of mass) distance. Probability densities are calculated for all relaxing trajectories and

only up to the time satisfying the criterion that the sum of the three inter-nuclear distances is less

than 9.5 a0.

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Page 15: VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.) Total Caridade (2018, Theo.) FIG. S12. Vibrational relaxation rates for O+NO( = 1)

0 30 60 90 120 150 180 2

3

4

5

6

7

8

9

10R

(a

0)

θ (°) 0 30 60 90 120 150 180

FIG. S16. Projection of vibrationally relaxing (red) and nonrelaxing (black) O+NO collision

trajectories onto the 2A′ PES (blue isocontours) as a function of (R, θ). For each (R, θ) combination

the energy of the structure with lowest energy for r ∈ [2.03, 2.39] (covers the classical turning points

of the vNO = 1 vibration, which are at rmin = 2.046 a0 and rmax = 2.370 a0) is used. Ten random

trajectories are shown for each of the cases. Trajectories are shown only up to the time satisfying

the geometrical criterion that the sum of the three inter-nuclear distances is less than 9.5 a0.

Reactive (oxygen exchange or O2 formation) trajectories are shown as dashed lines.

15

Page 16: VLFV 7KLVMRXUQDOLV WKH2ZQHU6RFLHWLHV · 2A´´ Caridade (2018, Theo.) 2A´ Caridade (2018, Theo.) Total Caridade (2018, Theo.) FIG. S12. Vibrational relaxation rates for O+NO( = 1)

0 30 60 90 120 150 180 1.5

2.5

3.5

4.5

5.5

6.5

7.5R

(a

0)

θ (°) 0 30 60 90 120 150 180

FIG. S17. Contour diagram of the relaxed PES (as a function of R, θ and r = 2.03 − 2.39 a0) of

the 2A′ PES for the O+NO channel. The ab initio grid points used in constructing the RKHS are

shown as red filled circles at which MRCI+Q calculations were carried out.

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