Equation-of-motion (EOM) is a versatile electronic structure approach
that allows one to describe many multi-configurational wave functions
within a single-reference formalism. For example, EOM for excitation
energies (EOM-EE) method accurately describes electronically excited
states, while ionized/electron attached EOM models (EOM-IP/EA) can
tackle doublet radicals, including notorious cases of symmetry breaking.
We have extended EOM approach to diradicals, triradicals, and
bond-breaking.
In our approach, which is called the Spin-Flip (SF method) problematic
low-spin states are treated as spin-flipping excitations from the
high-spin reference state.
Equation-of-motion excitation energies (EOM-EE) determinants
Ψ(Ms = 0) = R(Ms = 0)Ψ0(Ms = 0)
Equation-of-motion ionization potential (EOM-IP) determinants
Ψ(N) = R(-1)Ψ0(N + 1)
Equation-of-motion electron attachment (EOM-EA) determinants
Ψ(N) = R(+1)Ψ0(N - 1)
Equation-of-motion spin-flip (EOM-SF) determinants
Ψ(Ms = 0) = R(Ms = -1)Ψ0(Ms = 1)
Diradicals and the spin-flip method
From the electronic structure point of view, diradicals are molecules
in which two electrons are distributed in two nearly degenerate molecular
orbitals. For such a system, six Slater determinants can be generated as
in the picture:
Determinants (a) – (d) have zero projection of the total
spin (Ms = 0). High-spin determinants (e) and (f)
correspond to Ms = +1 and
Ms = -1 configurations, respectively. From these
determinants, three singlet and three triplet wave functions can be
constructed as follows (coefficient λ is large when the energy gap
between orbitals is small):
Singlets
Ψs1 = (a) - λ(b)
Ψs2 = λ(a) - (b)
Ψs3 = (c) - (d)
|
Triplets
Ψt1 = (c) + (d)
Ψt2 = (e)
Ψt3 = (f)
|
All of the above singlet wave functions are two-determinantal. The
Ms = 0 component of the triplet is also
two-determinantal, however, the high-spin triplets
(Ms = 1/Ms = -1) are
single-determinantal. Note that all the Ms = 0
determinants are formally single electron excitations with a spin-flip
from the Ms = 1/Ms = -1
configurations. Therefore, the Ms = 0 states
can be described as spin-flipping excited states from the high-spin
|α α> triplet reference. This is the essence
of the Spin-Flip (SF) method. The SF method describes ground and excited
states of diradicals (or potential energy surfaces along bond-breaking
coordinate) as spin-flipping, e. g., α→β, excitations
from a high spin |α α> triplet reference.
Similarly, electronic states of triradicals are described as spin-flipping
excitations from the high-spin component of the quartet state. The SF
approach allows one to describe multi-configurational wave functions in
a size-consistent fashion and within a single-reference formalism thus
resulting in efficient, accurate, and robust computational scheme.
Modeling of charge transfer reactions by EOM methods
Electron transfer reactions are common in biological and synthetic
polymers. The rates of these processes can be related to the coupling
between the diabatic electronic states that correspond to reactant and
product states. Calculations on these systems are difficult due
to the propensity of Hartree-Fock solutions to overlocalize charge and
break symmetry.
Positively charged ethylene dimer is an often-studied prototype
system for perpendicular hole conductance. The reaction coordinate
slowly interpolates between neutral and cationic geometries of
monomers in the dimer.
Electron hopping in ethylene dimer
The EOM-CCSD method relies on the unstable Hartree-Fock solution
for the open-shell doublet system, which is the positively charged
dimer. It predicts excessive charge localization and a cusp on the
potential energy surface. In contrast, EOM-IP-CCSD predicts a smooth
charge flow along the reaction coordinate as well as smooth PESs.
This method employs stable reference wave function of the neutral,
which is a closed-shell singlet system, and describes both
charge-transfer states in a balanced fashion.
Electron hopping in ethylene dimer by EOM methods
Current research
Current research includes development of reduced scaling methods and novel EOM models to deal with other types of open shell systems.
Related Publications
130. K.B. Bravaya, D. Zuev, E. Epifanovsky, and A.I. Krylov
Complex-scaled equation-of-motion coupled-cluster method with single
and double substitutions for autoionizing excited states:
Theory, implementation, and examples
J. Chem. Phys., submitted
(2013)
Abstract
PDF Supporting info
129. D. Ghosh, D. Kosenkov, V. Vanovschi, J. Flick, I. Kaliman, Y. Shao, A.T.B. Gilbert, A.I. Krylov, and L.V. Slipchenko
Effective Fragment Potential method in Q-Chem: A guide for users
and developers
J. Comp. Chem., in press
(2013)
Abstract
PDF Supporting info
128. S. Gozem, A.I. Krylov, and M. Olivucci
Conical intersection and potential energy surface features of a
model retinal chromophore: Comparison of EOM-CC and multireference methods
J. Chem. Theor. Comp 9, in press
(2013)
Abstract
PDF Supporting info
125. A.I. Krylov and P.M.W. Gill
Q-Chem: An engine for innovation
WIREs Comput. Mol. Sci., in press
(2012)
Abstract
PDF
122. T. Kus and A. I. Krylov
De-perturbative corrections for charge-stabilized double ionization
potential equation-of-motion coupled-cluster method
J. Chem. Phys. 136, 244109
(2012)
Abstract
PDF
121. Y.A. Bernard, Y. Shao, and A.I. Krylov
General formulation of spin-flip time-dependent density
functional theory using non-collinear kernels: Theory, implementation,
and benchmarks
J. Chem. Phys. 136, 204103
(2012)
Abstract
PDF Supporting info
120. D. Ghosh, A. Roy, R. Seidel, B. Winter, S.E. Bradforth, and A.I. Krylov
First-principle protocol for calculating ionization energies and redox
potentials of solvated molecules and ions: Theory and application to aqueous
phenol and phenolate
J. Phys. Chem. B 116, 7269 – 7280
(2012)
Abstract
PDF Supporting info
107. T. Kus and A. I. Krylov
Using the charge stabilization technique in the double ionization potential equation-of-motion calculations with dianion references
J. Chem. Phys. 135, 084109
(2011)
Abstract
PDF Supporting info
86. A. Landau, K. Khistyaev, S. Dolgikh, and A.I. Krylov
Frozen natural orbitals for ionized states within equation-of-motion coupled-cluster formalism
J. Chem. Phys. 132, 014109
(2010)
Abstract
PDF
85. C.M. Oana and A.I. Krylov
Cross sections and photoelectron angular distributions
in photodetachment from negative ions using
equation-of-motion coupled-cluster Dyson orbitals
J. Chem. Phys. 131, 124114
(2009)
Abstract
PDF
84. P.U. Manohar, J.F. Stanton, and A.I. Krylov
Perturbative triples correction for the
equation-of-motion coupled-cluster wave functions
with single and double substitutions for ionized states:
Theory, implementation, and examples
J. Chem. Phys. 131, 114112
(2009)
Abstract
PDF
76. A.A. Golubeva, P.A. Pieniazek, and A.I. Krylov
A new electronic structure method for doublet states:
configuration interaction in the space of ionized 1h and 2h1p determinants
J. Chem. Phys. 130, 124113
(2009)
Abstract
PDF Supporting info
73. D. Casanova, L.V. Slipchenko, A.I. Krylov, and M. Head-Gordon
Double spin-flip approach within equation-of-motion coupled
cluster and conguration interaction formalisms: Theory,
implementation and examples
J. Chem. Phys. 130, 044103
(2009)
Abstract
PDF
70. P.U. Manohar and A.I. Krylov
A non-iterative perturbative triples correction for
the spin-flipping and spin-conserving equation-of-motion coupled-cluster
methods with single and double substitutions
J. Chem. Phys. 129, 194105
(2008)
Abstract
PDF
67. P.A. Pieniazek, S.E. Bradforth, and A.I. Krylov
Charge localization and Jahn-Teller distortions in the
benzene dimer cation
J. Chem. Phys. 129, 074104
(2008)
Abstract
PDF
62. A. I. Krylov
Equation-of-motion coupled-cluster methods for open-shell
and electronically excited species: The hitchhiker's guide to Fock
space
Ann. Rev. Phys. Chem. 59, 433 – 462
(2008)
Abstract
Full text
59. C.M. Oana and A.I. Krylov
Dyson orbitals for ionization from the ground and electronically
excited states within equation-of-motion coupled-cluster formalism:
Theory, implementation, and examples
J. Chem. Phys. 127, 234106
(2007)
Abstract
PDF (873 kB)
58. A.A. Golubeva, A.V. Nemukhin, S.J. Klippenstein, L.B. Harding, and A.I. Krylov
Performance of the spin-flip and multi-reference methods for
bond-breaking in hydrocarbons: A benchmark study
J. Phys. Chem. A 111, 13264 – 13271
(2007)
Abstract
PDF (162 kB)
57. P. A. Pieniazek, S. A. Arnstein, S. E. Bradforth, A. I. Krylov, and C. D. Sherrill
Benchmark full configuration interaction and EOM-IP-CCSD
results for prototypical charge transfer systems: Noncovalent ionized dimers
J. Chem. Phys. 127, 164110
(2007)
Abstract
PDF (1542 kB)
55. E. Epifanovsky and A. I. Krylov
Direct location of the minimum point on intersection seams
of potential energy surfaces with equation-of-motion coupled-cluster
methods
Mol. Phys. 105, 2515 – 2525
(2007)
Abstract
PDF (240 kB)
48. Y. Shao, L. F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. Brown, A. T. B. Gilbert, L. V. Slipchenko, S. V. Levchenko, D. P. O'Neil, R. A. Distasio Jr., R. C. Lochan, T. Wang, G. J. O. Beran, N. A. Besley, J. M. Herbert, C. Y. Lin, T. Van Voorhis, S. H. Chien, A. Sodt, R. P. Steele, V. A. Rassolov, P. Maslen, P. P. Korambath, R. D. Adamson, B. Austin, J. Baker, E. F. C. Bird, H. Daschel, R. J. Doerksen, A. Drew, B. D. Dunietz, A. D. Dutoi, T. R. Furlani, S. R. Gwaltney, A. Heyden, S. Hirata, C.-P. Hsu, G. S. Kedziora, R. Z. Khalliulin, P. Klunziger, A. M. Lee, W. Z. Liang, I. Lotan, N. Nair, B. Peters, E. I. Proynov, P. A. Pieniazek, Y. M. Rhee, J. Ritchie, E. Rosta, C. D. Sherrill, A. C. Simmonett, J. E. Subotnik, H. L. Woodcock III, W. Zhang, A. T. Bell, A. K. Chakraborty, D. M. Chipman, F. J. Keil, A. Warshel, W. J. Herhe, H. F. Schaefer III, J. Kong, A. I. Krylov, P. M. W. Gill, and M. Head-Gordon
Advances in methods and algorithms in a modern quantum chemistry
program package
Phys. Chem. Chem. Phys. 8, 3172 – 3191
(2006)
Abstract
PDF (863 kB)
43. L.V. Slipchenko and A.I. Krylov
Efficient strategies for accurate calculations of electronic
excitation and ionization energies: Theory and application to the
dehydro-meta-xylylene anion
J. Phys. Chem. A 110, 291 – 298
(2006)
Abstract
PDF (150 kB)
42. L. V. Slipchenko and A. I. Krylov
Spin-conserving and spin-flipping equation-of-motion coupled-cluster
method with triple excitations
J. Chem. Phys. 123, 84107
(2005)
Abstract
PDF (173 kB)
39. A. I. Krylov
The spin-flip equation-of-motion coupled-cluster electronic
structure method for a description of excited states, bond-breaking,
diradicals, and triradicals
Acc. Chem. Res. 39, 83 – 91
(2006)
Abstract
PDF (246 kB)
38. S. V. Levchenko, T. Wang, and A. I. Krylov
Analytic gradients for the spin-conserving and spin-flipping
equation-of-motion coupled-cluster models with single and double
substitutions
J. Chem. Phys. 122, 224106
(2005)
Abstract
PDF (146 kB)
34. S. V. Levchenko and A. I. Krylov
Equation-of-motion spin-flip coupled-cluster model with single and
double substitutions: Theory and application to
cyclobutadiene
J. Chem. Phys. 120, 175 – 185
(2004)
Abstract
PDF (195 kB)
31. J. S. Sears, C. D. Sherrill, and A. I. Krylov
A spin-complete version of the spin-flip approach to bond breaking:
What is the impact of obtaining spin eigenfunctions?
J. Chem. Phys. 118, 9084 – 9094
(2003)
Abstract
PDF (150 kB)
28. Y. Shao, M. Head-Gordon, and A. I. Krylov
The spin-flip approach within time-dependent density functional
theory: Theory and applications to diradicals
J. Chem. Phys. 118, 4807 – 4818
(2003)
Abstract
PDF (185 kB)
27. A. I. Krylov, L. V. Slipchenko, and S. V. Levchenko
Breaking the curse of the non-dynamical correlation problem: The spin-flip method
ACS Symposium Series 958, 89 – 102
(2007)
PDF (657 kB)
26. L. V. Slipchenko and A. I. Krylov
Singlet-triplet gaps in diradicals by the spin-flip approach: A benchmark study
J. Chem. Phys. 117, 4694 – 4708
(2002)
Abstract
PDF (237 kB)
24. A. I. Krylov and C. D. Sherrill
Perturbative corrections to the equation-of-motion spin-flip SCF model: Application to bond-breaking and equilibrium properties of diradicals
J. Chem. Phys. 116, 3194 – 3203
(2002)
Abstract
PDF (122 kB)
23. A. I. Krylov
Spin-flip configuration interaction: An electronic structure model
that is both variational and size-consistent
Chem. Phys. Lett. 350, 522 – 530
(2001)
Abstract
PDF (148 kB)
20. A. I. Krylov
Size-consistent wave functions for bond-breaking: The
equation-of-motion spin-flip model
Chem. Phys. Lett. 338, 375 – 384
(2001)
Abstract
PDF (114 kB)
19. A. I. Krylov
Spin-contanination in coupled-cluster wavefunctions
J. Chem. Phys. 113, 6052 – 6062
(2000)
Abstract
PDF (144 kB)
18. A. I. Krylov, C. D. Sherrill, and M. Head-Gordon
Excited states theory for optimized orbitals and valence optimized
orbitals coupled-cluster doubles models
J. Chem. Phys. 113, 6509 – 6527
(2000)
Abstract
PDF (212 kB)
17. J. Kong, C. A. White, A. I. Krylov, C. D. Sherrill, R. D. Adamson, T. R. Furlani, M. S. Lee, A. M. Lee, S. R. Gwaltney, T. R. Adams, C. Ochsenfeld, A. T. B. Gilbert, G. S. Kedziora, V. A. Rassolov, D. R. Maurice, N. Nair, Y. Shao, N. A. Besley, P. Maslen, J. P. Dombroski, H. Daschel, W. Zhang, P. P. Korambath, J. Baker, E. F. C. Bird, T. Van Voorhis, M. Oumi, S. Hirata, C.-P. Hsu, N. Ishikawa, J. Florian, A. Warshel, B. G. Johnson, P. M. W. Gill, M. Head-Gordon, and J. A. Pople
Q-Chem 2.0: A high performance ab initio electronic structure
program package
J. Comp. Chem. 21, 1532 – 1548
(2000)
Abstract
PDF (283 kB)
16. S. R. Gwaltney, C. D. Sherrill, M. Head-Gordon, and A. I. Krylov
Second order perturbation corrections to singles and doubles
coupled-cluster methods: General theory and applications to the
valence optimized doubles model
J. Chem. Phys. 113, 3548 – 3560
(2000)
Abstract
PDF (173 kB)
