Supplemental Material for
A practical and efficient diabatization that combines Lorentz and Laplace
functions to approximate nonadiabatic coupling terms
Heesun An and Kyoung Koo Baecka
Department of Chemistry, Gangneung-Wonju National University, Gangwon-do, 25457, Republic of Korea
Table S1. The values of α- and β-parameter of F
to
Lo
F
dr 
La


1 Lo
1
La
 2 F  F dr   2
Lo
and F
F
Lo
La
, their product

2
 F La dr 
FIG. S1. An example of the dependence of the overlap area,
F

2

   , and the overlapped area corresponding
1
2


(FLo  F La )2 dr .
dr , on the change of β for a given α. It shows the
Lo La
numerical procedure maximizing the overlap area between a Lorentz and a Laplace functions.
FIG. S2. The top and middle rows compare the Lorentz (Lo), Laplace (La), and geometric-average (g-av) of the two. The
bottom row shows the mixing angles θLo, θLa, and θg-av obtained by Eqs. (3), (9), and (15), respectively. The left and right
columns corresponds to the cases α = 1.000 (β = 1.397) and α = 10.00 (β = 0.1397), respectively.
FIG. S3. It is exactly the same as Fig. 2 of the main text, and given here just for clearer view of details.
FIG. S4. The same as Fig. 2 of the main text (and therefore FIG. S3), but obtained with not the MRCI/aug-cc-pVTZ but the
CASSCF/aug-cc-pVTZ method. However, the sech-3 fitting in this case used all NACTs between R LiF from 7.5 to 15.0
Bohr, and the fitted parameters are Rc = 10.7 Bohr, Ai213 = 0.4803, 0.3279, 0.1918, ai=1-3 = 2.3390, 0.9298, 0.0368.
a
baeck@gwnu.ac.kr
1
Table S1.
The values of α- and β-parameter of F Lo and F La , their product
corresponding to
F
dr 
Lo La
 2 F
1
Lo
α
0.00100000
0.01000000
0.10000000
0.30000000
0.50000000
0.70000000
0.90000000
1.00000000
3.00000000
5.00000000
10.00000000
100.00000000
1000.00000000

 F La dr  
1
2
F
Lo
β
1397.15473467
139.73432167
13.97359234
4.65747687
2.79453552
1.99597352
1.55261463
1.39710948
0.46579700
0.27948141
0.13972723
0.01397297
0.00139725
Ave.
FIG. S1. An example of the dependence of the overlap area,
F

2
 F La dr 


2


1.39715473
1.39734322
1.39735923
1.39724306
1.39726776
1.39718146
1.39735316
1.39710948
1.39739101
1.39740707
1.39727234
1.39729736
1.39724609
1.39726880
1
2
, and the maximized overlapped area

Overlap
1.41020998
1.41021162
1.41020923
1.41021119
1.41021106
1.41021146
1.41021079
1.41020821
1.41021197
1.41021122
1.41021098
1.41021174
1.41021130
1.41021067
dr , on the change of β for a given α. It shows the
Lo La
numerical procedure maximizing the overlap area between a Lorentz and a Laplace functions.
2

(FLo  F La )2 dr .
FIG. S2. The top and middle rows compare the Lorentz (Lo), Laplace (La), and geometric-average (g-av) of the two. The bottom row
shows the mixing angles θLo, θLa, and θg-av obtained by Eqs. (3), (9), and (15), respectively. The left and right columns corresponds to
the cases α = 1.000 (β = 1.397) and α = 10.00 (β = 0.1397), respectively.
3
FIG. S3. It is exactly the same as Fig. 2 of the main text, and given here just for clearer view of details.
4
FIG. S4. The same as Fig. 2 of the main text (and therefore FIG. S3), but obtained with not the MRCI/aug-cc-pVTZ but the CASSCF/augcc-pVTZ method. However, the sech-3 fitting in this case used all NACTs between RLiF from 7.5 to 15.0 Bohr, and the fitted
parameters are Rc = 10.7 Bohr, Ai213 = 0.4803, 0.3279, 0.1918, ai=1-3 = 2.3390, 0.9298, 0.0368.
5