Recently, we proposed a new orbital analysis method, natural reaction orbital (NRO), which automatically extracts orbital pairs that characterize electron transfer in reaction processes by singular value decomposition of the first-order orbital response matrix to the nuclear coordinate displacements [Ebisawa et al., Phys. Chem. Chem. Phys. 24, 3532 (2022)]. NRO analysis along the intrinsic reaction coordinate (IRC) for several typical chemical reactions demonstrated that electron transfer occurs mainly in the vicinity of transition states and in regions where the energy profile along the IRC shows shoulder features, allowing the reaction mechanism to be explained in terms of electron motion. However, its application has been limited to single configuration theories such as Hartree–Fock theory and density functional theory. In this work, the concept of NRO is extended to multiconfigurational wavefunctions and formulated as the multiconfiguration NRO (MC-NRO). The MC-NRO method is applicable to various types of electronic structure theories, including multiconfigurational theory and linear response theory, and is expected to be a practical tool for extracting the essential qualitative features of a broad range of chemical reactions, including covalent bond dissociation and chemical reactions in electronically excited states. In this paper, we calculate the IRC for five basic chemical reaction processes at the level of the complete active space self-consistent field theory and discuss the phenomenon of electron transfer by performing MC-NRO analysis along each IRC. Finally, issues and future prospects of the MC-NRO method are discussed.

2.
R. S.
Mulliken
,
Phys. Rev.
32
,
186
(
1928
).
3.
K.
Fukui
,
T.
Yonezawa
, and
H.
Shingu
,
J. Chem. Phys.
20
,
722
(
1952
).
4.
K.
Fukui
,
T.
Yonezawa
, and
C.
Nagata
,
Bull. Chem. Soc. Jpn.
27
,
423
(
1954
).
5.
R. B.
Woodward
and
R.
Hoffmann
,
J. Am. Chem. Soc.
87
,
395
(
1965
).
6.
R.
Hoffmann
and
R. B.
Woodward
,
J. Am. Chem. Soc.
87
,
2046
(
1965
).
7.
R.
Hoffmann
and
R. B.
Woodward
,
J. Am. Chem. Soc.
87
,
4388
(
1965
).
8.
R. B.
Woodward
and
R.
Hoffmann
,
Angew. Chem., Int. Ed.
8
,
781
(
1969
).
9.
R.
Hoffmann
and
R. B.
Woodward
,
Science
167
,
825
(
1970
).
10.
G.
Montavon
,
M.
Rupp
,
V.
Gobre
,
A.
Vazquez-Mayagoitia
,
K.
Hansen
,
A.
Tkatchenko
,
K.-R.
Müller
, and
O.
Anatole von Lilienfeld
,
New J. Phys.
15
,
095003
(
2013
).
11.
O. A.
von Lilienfeld
,
K.-R.
Müller
, and
A.
Tkatchenko
,
Nat. Rev. Chem.
4
,
347
(
2020
).
12.
H.
Jónsson
,
G.
Mills
, and
K. W.
Jacobsen
, “
Nudged elastic band method for finding minimum energy paths of transitions
,” in
Classical and Quantum Dynamics in Condensed Phase Simulations
, edited by
B. J.
Berne
,
G.
Ciccotti
, and
D. F.
Coker
(
World Scientific
,
Singapore
,
1998
), Chap. 16, pp.
385
404
.
13.
W.
Quapp
,
M.
Hirsch
,
O.
Imig
, and
D.
Heidrich
,
J. Comput. Chem.
19
,
1087
(
1998
).
14.
K.
Ohno
and
S.
Maeda
,
Chem. Phys. Lett.
384
,
277
(
2004
).
15.
S.
Maeda
and
K.
Ohno
,
J. Phys. Chem. A
109
,
5724
(
2005
).
16.
S.
Maeda
and
K.
Morokuma
,
J. Chem. Phys.
132
,
241102
(
2010
).
17.
M.
Shoji
,
M.
Kayanuma
, and
Y.
Shigeta
,
Bull. Chem. Soc. Jpn.
91
,
1465
(
2018
).
18.
K.
Fukui
,
J. Phys. Chem.
74
,
4161
(
1970
).
20.
T.
Tsutsumi
,
Y.
Ono
,
Z.
Arai
, and
T.
Taketsugu
,
J. Chem. Theory Comput.
14
,
4263
(
2018
).
21.
T.
Tsutsumi
,
Y.
Ono
,
Z.
Arai
, and
T.
Taketsugu
,
J. Chem. Theory Comput.
16
,
4029
(
2020
).
22.
S. R.
Hare
,
L. A.
Bratholm
,
D. R.
Glowacki
, and
B. K.
Carpenter
,
Chem. Sci.
10
,
9954
(
2019
).
23.
A. I.
Krylov
,
J. Chem. Phys.
153
,
080901
(
2020
).
24.
P. O.
Löwdin
,
Phys. Rev.
97
,
1474
(
1955
).
25.
C.
Edmiston
and
K.
Ruedenberg
,
Rev. Mod. Phys.
35
,
457
(
1963
).
26.
K.
Fukui
,
N.
Koga
, and
H.
Fujimoto
,
J. Am. Chem. Soc.
103
,
196
(
1981
).
27.
A. E.
Reed
and
F.
Weinhold
,
J. Chem. Phys.
78
,
4066
(
1983
).
28.
A. E.
Reed
and
F.
Weinhold
,
J. Chem. Phys.
83
,
1736
(
1985
).
29.
G.
Knizia
,
J. Chem. Theory Comput.
9
,
4834
(
2013
).
30.
M. W.
Schmidt
,
E. A.
Hull
, and
T. L.
Windus
,
J. Phys. Chem. A
119
,
10408
(
2015
).
31.
J.-X.
Zhang
,
F. K.
Sheong
, and
Z.
Lin
,
Chem. - Eur. J.
24
,
9639
(
2018
).
32.
K.
Takatsuka
and
Y.
Arasaki
,
J. Chem. Phys.
154
,
094103
(
2021
).
33.
S.
Ebisawa
,
M.
Hasebe
,
T.
Tsutsumi
,
T.
Tsuneda
, and
T.
Taketsugu
,
Phys. Chem. Chem. Phys.
24
,
3532
(
2022
).
34.
K.
Ruedenberg
,
M. W.
Schmidt
,
M. M.
Gilbert
, and
S. T.
Elbert
,
Chem. Phys.
71
,
41
(
1982
).
35.
K.
Ruedenberg
,
M. W.
Schmidt
, and
M. M.
Gilbert
,
Chem. Phys.
71
,
51
(
1982
).
36.
A. T.
Amos
and
G. G.
Hall
,
Proc. Roy. Soc.
A263
,
483
(
1961
).
38.
J.
Gerratt
and
I. M.
Mills
,
J. Chem. Phys.
49
,
1719
(
1968
).
39.
J. A.
Pople
,
R.
Krishnan
,
H. B.
Schlegel
, and
J. S.
Binkley
,
Int. J. Quantum Chem.
16
,
225
(
1979
).
40.
A.
Morita
and
S.
Kato
,
J. Am. Chem. Soc.
119
,
4021
(
1997
).
41.
J. A.
Pople
,
R.
Seeger
, and
R.
Krishnan
,
Int. J. Quantun Chem.
12
,
149
(
1977
).
42.
B. O.
Roos
,
P. R.
Taylor
, and
P. E. M.
Sigbahn
,
Chem. Phys.
48
,
157
(
1980
).
43.
A. D.
McLachlan
and
M. A.
Ball
,
Rev. Mod. Phys.
36
,
844
(
1964
).
44.
R.
Bauernschmitt
and
R.
Ahlrichs
,
Chem. Phys. Lett.
256
,
454
(
1996
).
45.
M. E.
Casida
,
C.
Jamorski
,
K. C.
Casida
, and
D. R.
Salahub
,
J. Chem. Phys.
108
,
4439
(
1998
).
46.
P.
Lancaster
and
M.
Tismenetsky
,
The Theory of Matrices
, 2nd ed (
Academic Press
,
London
,
1985
).
47.
L.
Hogben
,
Handbook of Linear Algebra
, 2nd ed (
Chapman and Hall/CRC
,
Boca Raton, Florida
,
2013
).
48.
H. J.
Werner
and
W.
Meyer
,
J. Chem. Phys.
74
,
5794
(
1981
).
49.
L. N.
Tran
and
E.
Neuscamman
,
J. Phys. Chem. A
124
,
8273
(
2020
).
50.
L.
Kong
,
Int. J. Quantum Chem.
110
,
2603
(
2010
).
51.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
,
G. E.
Scuseria
,
M. A.
Robb
,
J. R.
Cheeseman
,
G.
Scalmani
,
V.
Barone
,
G. A.
Petersson
,
H.
Nakatsuji
,
X.
Li
,
M.
Caricato
,
A. V.
Marenich
,
J.
Bloino
,
B. G.
Janesko
,
R.
Gomperts
,
B.
Mennucci
,
H. P.
Hratchian
,
J. V.
Ortiz
,
A. F.
Izmaylov
,
J. L.
Sonnenberg
,
D.
Williams-Young
,
F.
Ding
,
F.
Lipparini
,
F.
Egidi
,
J.
Goings
,
B.
Peng
,
A.
Petrone
,
T.
Henderson
,
D.
Ranasinghe
,
V. G.
Zakrzewski
,
J.
Gao
,
N.
Rega
,
G.
Zheng
,
W.
Liang
,
M.
Hada
,
M.
Ehara
,
K.
Toyota
,
R.
Fukuda
,
J.
Hasegawa
,
M.
Ishida
,
T.
Nakajima
,
Y.
Honda
,
O.
Kitao
,
H.
Nakai
,
T.
Vreven
,
K.
Throssell
,
J. A.
Montgomery
, Jr.
,
J. E.
Peralta
,
F.
Ogliaro
,
M. J.
Bearpark
,
J. J.
Heyd
,
E. N.
Brothers
,
K. N.
Kudin
,
V. N.
Staroverov
,
T. A.
Keith
,
R.
Kobayashi
,
J.
Normand
,
K.
Raghavachari
,
A. P.
Rendell
,
J. C.
Burant
,
S. S.
Iyengar
,
J.
Tomasi
,
M.
Cossi
,
J. M.
Millam
,
M.
Klene
,
C.
Adamo
,
R.
Cammi
,
J. W.
Ochterski
,
R. L.
Martin
,
K.
Morokuma
,
O.
Farkas
,
J. B.
Foresman
, and
D. J.
Fox
, gaussian 16, Revision C.01,
Gaussian, Inc.
,
Wallingford CT
,
2016
.
52.
A. D.
McLean
,
A.
Weiss
, and
M.
Yoshimine
,
Rev. Mod. Phys.
32
,
211
(
1960
).
53.
G.
Das
and
A. C.
Wahl
,
J. Chem. Phys.
44
,
87
(
1966
).
54.
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
90
,
1007
(
1989
).
55.
R. A.
Kendall
,
T. H.
Dunning
, Jr.
, and
R. J.
Harrison
,
J. Chem. Phys.
96
,
6796
(
1992
).
56.
A.
Szabo
and
N. S.
Ostlund
,
Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory
(
McGraw-Hill
,
New York
,
1989
).
57.
B. H.
Botch
and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
76
,
6046
(
1982
).
58.
S. P.
Walch
,
J. Chem. Phys.
86
,
5670
(
1987
).
59.
C. W.
Bauschlicher
, Jr.
,
S. P.
Walch
,
S. R.
Langhoff
,
P. R.
Taylor
, and
R. L.
Jaffe
,
J. Chem. Phys.
88
,
1743
(
1988
).
61.
H.
Nohira
and
T.
Nohira
,
J. Theor. Comput. Chem.
16
,
1750055
(
2017
).
62.
A. L.
Sobolewski
and
W.
Domcke
,
J. Chem. Phys.
103
,
4494
(
1999
).
63.
T.
Kar
,
S.
Scheiner
, and
M.
Čuma
,
J. Chem. Phys.
111
,
849
(
1999
).
64.
J. D.
Coe
and
T. J.
Martínez
,
J. Phys. Chem. A
110
,
618
(
2006
).
65.
K. R.
Nandipati
,
A. K.
Kanakati
,
H.
Singh
, and
S.
Mahapatra
,
Phys. Chem. Chem. Phys.
21
,
20018
(
2019
).
66.
N. H.
List
,
A. L.
Dempwolff
,
A.
Dreuw
,
P.
Norman
, and
T. J.
Martínez
,
Chem. Sci.
11
,
4180
(
2020
).
67.
R. L.
Martin
,
J. Chem. Phys.
118
,
4775
(
2003
).
68.
F.
Plasser
,
M.
Wormit
, and
A.
Dreuw
,
J. Chem. Phys.
141
,
024106
(
2014
).

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