We introduce vibrational heat-bath configuration interaction (VHCI) as an accurate and efficient method for calculating vibrational eigenstates of anharmonic systems. Inspired by its origin in electronic structure theory, VHCI is a selected CI approach that uses a simple criterion to identify important basis states with a pre-sorted list of anharmonic force constants. Screened second-order perturbation theory and simple extrapolation techniques provide significant improvements to variational energy estimates. We benchmark VHCI on four molecules with 12–48 degrees of freedom and use anharmonic potential energy surfaces truncated at fourth and sixth orders. When compared to other methods using the same truncated potentials, VHCI produces vibrational spectra of tens or hundreds of states with sub-wavenumber accuracy at low computational cost.

1.
R. B.
Gerber
,
B.
Brauer
,
S. K.
Gregurick
, and
G. M.
Chaban
, “
Calculation of anharmonic vibrational spectroscopy of small biological molecules
,”
PhysChemComm
5
,
142
(
2002
).
2.
G. M.
Chaban
,
J. O.
Jung
, and
R. B.
Gerber
, “
Ab initio calculation of anharmonic vibrational states of polyatomic systems: Electronic structure combined with vibrational self-consistent field
,”
J. Chem. Phys.
111
,
1823
1829
(
1999
).
3.
S.
Carter
,
J. M.
Bowman
, and
N. C.
Handy
, “
Extensions and tests of ‘multimode’: A code to obtain accurate vibration/rotation energies of many-mode molecules
,”
Theor. Chem. Acc.
100
,
191
198
(
1998
).
4.
S.
Carter
,
S. J.
Culik
, and
J. M.
Bowman
, “
Vibrational self-consistent field method for many-mode systems: A new approach and application to the vibrations of CO adsorbed on Cu(100)
,”
J. Chem. Phys.
107
,
10458
10469
(
1997
).
5.
J. M.
Bowman
,
S.
Carter
, and
X.
Huang
, “
Multimode: A code to calculate rovibrational energies of polyatomic molecules
,”
Int. Rev. Phys. Chem.
22
,
533
549
(
2003
).
6.
T. K.
Roy
and
R. B.
Gerber
, “
Vibrational self-consistent field calculations for spectroscopy of biological molecules: New algorithmic developments and applications
,”
Phys. Chem. Chem. Phys.
15
,
9468
(
2013
).
7.
V.
Barone
, “
Anharmonic vibrational properties by a fully automated second-order perturbative approach
,”
J. Chem. Phys.
122
,
014108
(
2005
).
8.
O.
Christiansen
, “
Møller–Plesset perturbation theory for vibrational wave functions
,”
J. Chem. Phys.
119
,
5773
5781
(
2003
).
9.
E. L.
Sibert
, “
Theoretical studies of vibrationally excited polyatomic molecules using canonical Van Vleck perturbation theory
,”
J. Chem. Phys.
88
,
4378
4390
(
1987
).
10.
S.
Banik
,
S.
Pal
, and
M. D.
Prasad
, “
Calculation of vibrational energy of molecule using coupled cluster linear response theory in bosonic representation: Convergence studies
,”
J. Chem. Phys.
129
,
134111
(
2008
).
11.
P.
Seidler
and
O.
Christiansen
, “
Automatic derivation and evaluation of vibrational coupled cluster theory equations
,”
J. Chem. Phys.
131
,
234109
(
2009
).
12.
O.
Christiansen
, “
Vibrational coupled cluster theory
,”
J. Chem. Phys.
120
,
2149
2159
(
2004
).
13.
J. M.
Bowman
,
K.
Christoffel
, and
F.
Tobin
, “
Application of SCF-SI theory to vibrational motion in polyatomic molecules
,”
J. Phys. Chem.
83
,
905
920
(
1979
).
14.
T. C.
Thompson
and
D. G.
Truhlar
, “
SCF CI calculations for vibrational eigenvalues and wavefunctions of systems exhibiting fermi resonance
,”
Chem. Phys. Lett.
75
,
87
90
(
1980
).
15.
K. M.
Christoffel
and
J. M.
Bowman
, “
Investigations of self-consistent field, SCF CI and virtual state configuration interaction vibrational energies for a model three-mode system
,”
Chem. Phys. Lett.
85
,
220
224
(
1982
).
16.
G.
Avila
and
T.
Carrington
, “
Using nonproduct quadrature grids to solve the vibrational Schrödinger equation in 12D
,”
J. Chem. Phys.
134
,
054126
(
2011
).
17.
A.
Leclerc
and
T.
Carrington
, “
Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices
,”
J. Chem. Phys.
140
,
174111
(
2014
).
18.
M.
Odunlami
,
V.
Le Bris
,
D.
Bégué
,
I.
Baraille
, and
O.
Coulaud
, “
A-VCI: A flexible method to efficiently compute vibrational spectra
,”
J. Chem. Phys.
146
,
214108
(
2017
).
19.
A.
Baiardi
,
C. J.
Stein
,
V.
Barone
, and
M.
Reiher
, “
Vibrational density matrix renormalization group
,”
J. Chem. Theory Comput.
13
,
3764
3777
(
2017
).
20.
B.
Huron
,
J. P.
Malrieu
, and
P.
Rancurel
, “
Iterative perturbation calculations of ground and excited state energies from multiconfigurational zeroth-order wavefunctions
,”
J. Chem. Phys.
58
,
5745
5759
(
1973
).
21.
R. J.
Buenker
and
S. D.
Peyerimhoff
, “
Individualized configuration selection in CI calculations with subsequent energy extrapolation
,”
Theor. Chim. Acta
35
,
33
58
(
1974
).
22.
R. J.
Harrison
, “
Approximating full configuration interaction with selected configuration interaction and perturbation theory
,”
J. Chem. Phys.
94
,
5021
5031
(
1991
).
23.
J. B.
Schriber
and
F. A.
Evangelista
, “
Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy
,”
J. Chem. Phys.
144
,
161106
(
2016
).
24.
N. M.
Tubman
,
J.
Lee
,
T. Y.
Takeshita
,
M.
Head-Gordon
, and
K. B.
Whaley
, “
A deterministic alternative to the full configuration interaction quantum Monte Carlo method
,”
J. Chem. Phys.
145
,
044112
(
2016
).
25.
N. M.
Tubman
,
C. D.
Freeman
,
D. S.
Levine
,
D.
Hait
,
M.
Head-Gordon
, and
K. B.
Whaley
, “
Modern approaches to exact diagonalization and selected configuration interaction with the adaptive sampling CI method
,”
J. Chem. Theory Comput.
16
,
2139
2159
(
2020
).
26.
A. A.
Holmes
,
N. M.
Tubman
, and
C. J.
Umrigar
, “
Heat-bath configuration interaction: An efficient selected configuration interaction algorithm inspired by heat-bath sampling
,”
J. Chem. Theory Comput.
12
,
3674
3680
(
2016
).
27.
A. A.
Holmes
,
C. J.
Umrigar
, and
S.
Sharma
, “
Excited states using semistochastic heat-bath configuration interaction
,”
J. Chem. Phys.
147
,
164111
(
2017
).
28.
S.
Sharma
,
A. A.
Holmes
,
G.
Jeanmairet
,
A.
Alavi
, and
C. J.
Umrigar
, “
Semistochastic heat-bath configuration interaction method: Selected configuration interaction with semistochastic perturbation theory
,”
J. Chem. Theory Comput.
13
,
1595
1604
(
2017
).
29.
J.
Li
,
M.
Otten
,
A. A.
Holmes
,
S.
Sharma
, and
C. J.
Umrigar
, “
Fast semistochastic heat-bath configuration interaction
,”
J. Chem. Phys.
149
,
214110
(
2018
).
30.
K. T.
Williams
,
Y.
Yao
,
J.
Li
,
L.
Chen
,
H.
Shi
,
M.
Motta
,
C.
Niu
,
U.
Ray
,
S.
Guo
,
R. J.
Anderson
,
J.
Li
,
L. N.
Tran
,
C. N.
Yeh
,
B.
Mussard
,
S.
Sharma
,
F.
Bruneval
,
M.
Van Schilfgaarde
,
G. H.
Booth
,
G. K. L.
Chan
,
S.
Zhang
,
E.
Gull
,
D.
Zgid
,
A.
Millis
,
C. J.
Umrigar
, and
L. K.
Wagner
, “
Direct comparison of many-body methods for realistic electronic Hamiltonians
,”
Phys. Rev. X
10
,
011041
(
2020
).
31.
Y.
Yao
,
E.
Giner
,
J.
Li
,
J.
Toulouse
, and
C. J.
Umrigar
, “
Almost exact energies for the Gaussian-2 set with the semistochastic heat-bath configuration interaction method
,”
J. Chem. Phys.
153
,
124117
(
2020
).
32.
J. J.
Eriksen
,
T. A.
Anderson
,
J. E.
Deustua
,
K.
Ghanem
,
D.
Hait
,
M. R.
Hoffmann
,
S.
Lee
,
D. S.
Levine
,
I.
Magoulas
,
J.
Shen
,
N. M.
Tubman
,
K. B.
Whaley
,
E.
Xu
,
Y.
Yao
,
N.
Zhang
,
A.
Alavi
,
G. K.-L.
Chan
,
M.
Head-Gordon
,
W.
Liu
,
P.
Piecuch
,
S.
Sharma
,
S. L.
Ten-no
,
C. J.
Umrigar
, and
J.
Gauss
, “
The ground state electronic energy of benzene
,”
J. Phys. Chem. Lett.
11
,
8922
8929
(
2020
).
33.
G.
Rauhut
, “
Configuration selection as a route towards efficient vibrational configuration interaction calculations
,”
J. Chem. Phys.
127
,
184109
(
2007
).
34.
M.
Neff
and
G.
Rauhut
, “
Toward large scale vibrational configuration interaction calculations
,”
J. Chem. Phys.
131
,
124129
(
2009
).
35.
P.
Carbonnière
,
A.
Dargelos
, and
C.
Pouchan
, “
The VCI-P code: An iterative variation-perturbation scheme for efficient computations of anharmonic vibrational levels and IR intensities of polyatomic molecules
,”
Theor. Chem. Acc.
125
,
543
554
(
2010
).
36.
M.
Sibaev
and
D. L.
Crittenden
, “
Balancing accuracy and efficiency in selecting vibrational configuration interaction basis states using vibrational perturbation theory
,”
J. Chem. Phys.
145
,
064106
(
2016
).
37.
Y.
Scribano
and
D. M.
Benoit
, “
Iterative active-space selection for vibrational configuration interaction calculations using a reduced-coupling VSCF basis
,”
Chem. Phys. Lett.
458
,
384
387
(
2008
).
38.
E.
Lesko
,
M.
Ardiansyah
, and
K. R.
Brorsen
, “
Vibrational adaptive sampling configuration interaction
,”
J. Chem. Phys.
151
,
164103
(
2019
).
39.
E. G.
Kratz
, LOVCI: Ladder operator vibrational configuration iteraction, https://github.com/kratman/VibCI,
2016
.
40.
J. H.
Fetherolf
, VHCI: Vibrational heat-bath configuration interaction v0.1, https://github.com/berkelbach-group/VHCI,
2020
.
41.
G.
Guennebaud
,
B.
Jacob
 et al., Eigen v3, http://eigen.tuxfamily.org,
2010
.
42.
Y.
Qiu
, SPECTRA: Sparse eigenvalue computation toolkit as a redesigned ARPACK, https://spectralib.org/,
2015
.
43.
J.
Brown
and
T.
Carrington
, “
Using an expanding nondirect product harmonic basis with an iterative eigensolver to compute vibrational energy levels with as many as seven atoms
,”
J. Chem. Phys.
145
,
144104
(
2016
).
44.
P. S.
Thomas
,
T.
Carrington
,
J.
Agarwal
, and
H. F.
Schaefer
, “
Using an iterative eigensolver and intertwined rank reduction to compute vibrational spectra of molecules with more than a dozen atoms: Uracil and naphthalene
,”
J. Chem. Phys.
149
,
064108
(
2018
).
45.
D.
Begue
,
P.
Carbonniere
, and
C.
Pouchan
, “
Calculations of vibrational energy levels by using a hybrid ab initio and DFT quartic force field: Application to acetonitrile
,”
J. Phys. Chem. A
109
,
4611
4616
(
2005
).
46.
R.
Garnier
,
M.
Odunlami
,
V.
Le Bris
,
D.
Bégué
,
I.
Baraille
, and
O.
Coulaud
, “
Adaptive vibrational configuration interaction (A-VCI): A posteriori error estimation to efficiently compute anharmonic IR spectra
,”
J. Chem. Phys.
144
,
204123
(
2016
).
47.
T.
Delahaye
,
A.
Nikitin
,
M.
Rey
,
P. G.
Szalay
, and
V. G.
Tyuterev
, “
A new accurate ground-state potential energy surface of ethylene and predictions for rotational and vibrational energy levels
,”
J. Chem. Phys.
141
,
104301
(
2014
).
48.
M.
Sibaev
and
D. L.
Crittenden
, “
The PyPES library of high quality semi-global potential energy surfaces
,”
J. Comput. Chem.
36
,
2200
2207
(
2015
).
49.
M.
Sibaev
and
D. L.
Crittenden
, “
PyVCI: A flexible open-source code for calculating accurate molecular infrared spectra
,”
Comput. Phys. Commun.
203
,
290
297
(
2016
).
50.
D.
Bégué
,
N.
Gohaud
,
C.
Pouchan
,
P.
Cassam-Chenaï
, and
J.
Liévin
, “
A comparison of two methods for selecting vibrational configuration interaction spaces on a heptatomic system: Ethylene oxide
,”
J. Chem. Phys.
127
,
164115
(
2007
).
51.
E.
Cané
,
A.
Miani
, and
A.
Trombetti
, “
Anharmonic force fields of naphthalene-h8 and naphthalene-d8
,”
J. Phys. Chem. A
111
,
8218
8222
(
2007
).
52.
I.
Baraille
,
C.
Larrieu
,
A.
Dargelos
, and
M.
Chaillet
, “
Calculation of non-fundamental IR frequencies and intensities at the anharmonic level. I. The overtone, combination and difference bands of diazomethane, H2CN2
,”
Chem. Phys.
273
,
91
101
(
2001
).
53.
R.
Burcl
,
S.
Carter
, and
N. C.
Handy
, “
Infrared intensities from the MULTIMODE code
,”
Chem. Phys. Lett.
380
,
237
244
(
2003
).
54.
V.
Le Bris
,
M.
Odunlami
,
D.
Bégué
,
I.
Baraille
, and
O.
Coulaud
, “
Using computed infrared intensities for the reduction of vibrational configuration interaction bases
,”
Phys. Chem. Chem. Phys.
22
,
7021
7030
(
2020
).
55.
K.
Kim
,
K. D.
Jordan
, and
T. S.
Zwier
, “
Low-energy structures and vibrational frequencies of the water hexamer: Comparison with benzene-(H2O)6
,”
J. Am. Chem. Soc.
116
,
11568
11569
(
1994
).
56.
Q.
Yu
and
J. M.
Bowman
, “
Classical, thermostated ring polymer, and quantum VSCF/VCI calculations of IR spectra of H7O3+ and H9O4+ (eigen) and comparison with experiment
,”
J. Phys. Chem. A
123
,
1399
1409
(
2019
).
57.
Z.
Bačić
and
J. C.
Light
, “
Theoretical methods for rovibrational states of floppy molecules
,”
Annu. Rev. Phys. Chem.
40
,
469
498
(
1989
).
58.
M. J.
Bramley
,
J. W.
Tromp
,
T.
Carrington
, and
G. C.
Corey
, “
Efficient calculation of highly excited vibrational energy levels of floppy molecules: The band origins of H+3 up to 35000 cm−1
,”
J. Chem. Phys.
100
,
6175
6194
(
1994
).

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