CORRELATION BOUND ANION STATES OF MOLECULES
AND CLUSTERS
K. D. Jordan
Department of Chemistry
University of Pittsburgh
Pittsburgh, PA
Cavity state of (H2O)45-
. QMC in Apuan Alps VIII, July, 2013
Charge flow in C60
induced by an electric field
Acknowledgements and Projects
National Science Foundation
Department of Energy
Group members who
contributed to the work in this
area:
F. Wang (U. Arkansas)
T. Sommerfeld
(Southeastern Lousiana Univ.)
T.-H. Choi (Choongnam National
Univ.)
V. Voora
Collaborators
M. Johnson (Yale Univ.)
Reduction of CO2 using (H2O)n- clusters*
Experiment starts with a cold cluster (T ~ 50K) with the e- localized
on (H2O)6
Following vibrational excitation of either water (OH stretch or bend)
or CO2 (asymm stretch) the electron jumps to the CO2
Ab initio MD simulations reveal that there are a large number of
different reaction pathways.
But in each case ET is triggered by formation of a H-bond to CO2
*J. Breen, A. F. DeBlase, T. L. Guasco, V. K. Voora, K. D. Jordan, T. Nagata and M.
A. Johnson, J. Phys. Chem., 116, 903 (2012)
Classification of anion states
• Unbound: temporary anions (resonances)
• Bound
Bound at KT/HF level
Unbound at KT/HF level
Pose some of the same problems
as resonances
In this talk I focus on non-valence correlation-bound anions
E.g., certain cavity-bound anion states of (H2O)n clusters and
the s-type anion state of C60
Model system comprised of four
water molecules
Electron binding energy (EBE)
calculated vs. R
R
EBE = EEES + Econf + Edisp
EES = exch. plus electrostatic; conf. = effect of confinement on KE; disp=dispersion
Hartree-Fock: essentially the sum of the first two terms
Methods considered
MP2
MP2 for anion and neutral
CCSD(T)
CCSD(T) for anion and neutral
EOM-CCSD
1p + 2p1h CI for anion using transformed H
EOM-MP2
1p + 2p1h CI for anion using transformed H
ADC(2)
second-order self energy with off-diagonal coupling
Diag-ADC(2)
second-order self energy without off-diagonal coupling
OO-MP2
orbital-optimized MP2 for anion and neutral
OO-CCD
orbital-optimized coupled cluster doubles for anion and neutral
B-CCD
Bruekner orbital coupled cluster doubles for anion and neutral
QMC
quantum Monte Carlo
Methods in blue: allow for relaxation of the singly occupied orbital in
response to correlation effects
Results for a basis set with very diffuse functions: aug-cc-pVDZ+6s6p
180.0
eom-ccsd
eom-mp2
160.0
Electron Binding Energy (meV)
delta_ccsd(t)
140.0
delta_ccsd
delta_mp2
120.0
delta_hf
kt
100.0
80.0
60.0
40.0
20.0
0.0
0
2
4
6
8
10
-20.0
Distance between dimers (Ang)
MP2 and coupled cluster methods fail when HF cease to bind the e-.
Coupled cluster methods still useful as long as HF gives binding.
12
Results for basis set without highly diffuse functions: aug-cc-pVDZ
200.0
Electron Binding Energy (meV)
100.0
0.0
0.00
2.00
4.00
6.00
8.00
10.00
12.00
eom-ccsd
-100.0
eom-mp2
delta_ccsd(t)
-200.0
delta_ccsd
delta_mp2
-300.0
delta_hf
kt
-400.0
-500.0
-600.0
Distance between dimers (Ang)
In the absence of diffuse functions, even MP2 binds the e- near R = 4 A, because
singly occ. orbital has appreciable weight in molecular region (fortuitous)
Overall shape of the binding curve is not correct
Singly occ. NO from HF and EOM-CCSD natural orbital analysis (in
latter case ~ Dyson orbital from Green's function treatment)
2.5 Ang
3.5 Ang
hf
Psi (arbitrary units)
Psi (arbitrary units)
hf
nat
0
5
10
15
20
25
nat
It ceases to bind
around R = 4.2 Å
0
5
"z " Dist (Bohrs)
10
Psi (arbitrary units)
Psi (arbitrary units)
15
"z " Dist (Bohrs)
25
hf
nat
10
20
8.5Ang
hf
5
15
"z " Dist (Bohrs)
4.5 Ang
0
At large R, the
anion is bound in
the HF approx.
20
25
nat
0
5
10
15
"z " Dist (Bohrs)
20
25
Turns into an
approximate
continuum
function
ADC(2), OO-MP2, and B-CCD all give for (H2O)4 EBEs reasonably close
to the EOM values even when using large flexible basis sets
• Establishes that for binding of an e- to (H2O)n clusters, high-order
correlation effects are not of major importance
• More important is the relaxation of the singly-occupied orbital in
response to the correlation effects
As we will see later, for many other systems, high-order correlation
effects play a more significant role
The ab initio results for the (H2O)n- clusters, have been used to test
model potential approaches that we have been developing
Our most sophisticated approach employs three mutually interacting,
atom-centered polarizable sites per water, and allows for self-consistent
treatment of e--water and water-water polarization
Consider a (H2O)24 (W24a) cluster
In addition consider W4, W8, W12, W16, and W20 cut out of W24.
Surfaces that enclose
70% of the charge density
of the excess electron
(from pol. model )
1V.
Voora, T. Sommerfeld, K. Jordan, V. Vysotskiy, L. Cederbaum, JTCT, 2012
EBEs of W24a and subclusters extracted from W24a
ADC refers to ADC(2)
Green's function method.
1200
1000
800
ADC/aTZ+C
600
pol3-sc
pol1
400
200
0
4
8
12
16
20
24
C = large
set of
diffuse s + p
functions at
COM
Pol1 decouples einteracting with induced
dipoles from water-water
interactions and edirectly inducing dipoles.
Pol3-SC treats these
interactions selfconsistently.
• For all clusters our self-consistent polarization model gives EBEs in
excellent agreement with the ab initio results
• Self-consistent treatment of e--water and water-polarization is essential
for the cavity-type anion states
Any system with sufficient polarizability should support nonvalence correlation-bound anions
This includes species such as C60
Evidence in electron-scattering and
Rydberg atom collision experiments that
C60 captures 0 eV electrons
One possible interpretation is the
existence of an s-like polarization
bound anion
Not identified in ab initio calculations
carried out to date.
STM dI/dV images of so-called superatom states of a C60
monomer and dimer on the copper surface (Petek group)1
Monomer
Dimer
However, the existence of such an anion for a C60 adsorbed on a
metal surface does not mean it would be bound in the gas phase
(image potential stabilization)
1Feng
et al. Science 320, 359 (2008)
One-particle energy levels of C60
Ag (?)
Hg (-1.0 eV)
T2u (-1.4 eV
Negatives of electron
affinities
Energy
T1g (-2.0 eV)
T1u (-3.1 eV)
Hu (-7.1eV)
Hg (-8.2 eV)
Negatives of
ionization potentials
Gg
Gu
for valence levels, calculated IP's and EAs are in good agreement
with experiment
Ab initio search for a polarization bound anion state of C60.
The anion is not bound in the Hartree-Fock approximation, so cannot use
approaches that assume Hartree-Fock provides a good starting point.
Instead we adopted the EOM-CCSD method, with a large flexible basis
set of Gaussian functions
Integrated
probability
Ψ2*r2
ψ2
The calculations predict the s-type anion to be bound by about 130 meV,
5
10
15
20
25
30
R (Bohrs)
5
10
15
20
25
30
35
40
R (Bohrs)
About 9% of the charge is located inside the C60 based on
analysis of the dominant natural orbital for the excess electron
Occ. number of s-type natural orbital 0.985
Several "filled" natural orbitals have occupations of about 1.9 and
several empty natural orbitals have occupations 0.05 – 0.10
These describe dispersion interactions between excess e- and
the electrons of C60
Dominant dispersion interactions when the excess e- is
within ~ 4 Å of the C60 surface
About ~50 % of the excess electron density is further way
The long-range tail of the wavefunction of the excess
electron is relatively unimportant for the dispersion
interactions
Unlike the (H2O)n clusters, ADC(2) overbinds the anion of C60 by ~2X
(compared to EOM-CCSD): lack of screening?
EOM-MP2 underbinds by about 40%.
High-order correlation effects are more important for C60 than for the
water clusters.
Electrostatic and polarization potentials for C60.
Shaded area indicates
the size of the C atoms
as given by vdW radii
Fit to the short range
electrostatic and
polarization potentials
The polarization potential
is not  r-4 except at very
large distances.
Radial distribution
Model potential
Charge distribution is
similar to that from the
EOM-CCSD calculations
Repulsive potential at the
C60 radius builds in
orthogonality
We are now working on developing a one-electron model
Hamiltonian for describing polarization bound anions of C60,
aggregates of C60, and other fullerenes
Here the challenge is to account for the charge-flow
component of the polarizability of C60
Induced Dipole moment = 0.49 a.u.
Charge range
E_field = 0.001 a.u.
+0.03
-0.03
A dipole moment of 0.49 a.u (1.2 D) is developed in a field of 0.001 a.u.
in the +x direction. Much of this is due to charge-flow.
STM measurements of C6F6 on Cu(110) also displays electron
capture into an extended orbital (Petek et al.)
Has been interpreted in terms of e- capture into valence σ*
Our work suggests that a non-valence correlation bound anion may be
responsible
It is well known that C6F6 has a bound valence anion with a buckled
geometry
EOM calculations bind the
e- for both the planar and
buckled structures
but give very different
charge distributions
for the two structures
Clearly non-valence in the
planar structure
Electrostatic and polarization potentials of C6F6 in the z-direction
(perpendicular to the molecule)
Both the polarization and the electrostatic potentials are essential for
the binding of the e- to the planar molecule
The quadrupole moment is of opposite sign in benzene, and as a
result, it does not have a quadrupole-bound anion
Diabatic and adiabatic
states of C6F6- along the
buckling coordinate
There is an avoided crossing between the valence and non-valence
diabatic anion states
CO2- shares a lot of characteristics with C6F6The anion is valence in nature for highly bent structures (OCO
angle < 148 deg), and is very extended for larger angles
Neutral
When using a large
basis set, e.g., ANO
+3s3p on each
atom, the anion
potential bends over
for angles > 150
deg, when using
methods that do not
depend on the
suitability of HF as a
starting
wavefunction.
First elucidated by
Sommerfeld et al.
Just beyond the crossing point of the neutral and anionic HF
potentials, one can find two HF solutions to for the anion:
One with the excess electron localized and the other with it
collapsed onto the continuum
The figure to the left
depicts the potentials
for the latter case.
Note that with a large
basis set, the bending
potential of CO2- does
NOT correlate with the
π* anion of the linear
molecule
Walsh's rule breaks
down
Has been discussed in
papers by McCurdy and
Rescigno
Correlation bound anions of Xen clusters
Of interest since correlation effects dominate the binding
(electrostatics of little importance)
Dipole Polarizability (a.u.)
70
60
EBE (meV)
50
40
600
500
400
300
200
100
0
0
10
20
30
Size, Xen
30
Results for EOM calculations.
ADC(2) overbinds by up to 3x
20
Is problem screening, or
breakdown of use of uncoupled
"HF" polarizabilities
10
0
5
7
9
11
13
Size, Xen
15
17
19
21
Xe20 and C60 have similar polarizabilities and similar EBEs when
electrostatics suppressed in the latter
PISCES
(Pittsburgh InfraStructure for Clusters with excess ElectronS)
http://www.pisces.pitt.edu/
• PISCES is a code for describing the interaction of excess electrons with atomic
and molecular clusters. It uses of a model Hamiltonian so that only the excess
electron is treated explicitly. (Developed with the support from NSF)
• Release 1.0:
 Characterizes excess electrons
interacting with water clusters using
a DVR basis set
 Polarizable DPP force-field for water
 Self-consistent electron-water
polarization with gradients
 Ground and electronically excited
states
 Readily coupled with molecular
dynamics and pathway searching
codes
• Planned Additions:
 Excess electron states of inert gas
atoms and fullerenes
 Drude oscillator treatment of water
molecules
 Periodic boundary conditions
Summary
• Molecules or clusters with sufficiently high polarizability will have
non-valence correlation bound anions
These are closely related to the image potential states of metals and
graphene
• If the polarizability is not sufficiently high, the balance can be
tipped by favorable electrostatics
• In general EOM-MP2 is adequate for such anions (i.e, gives
results close to EOM-CCSD)
• One can develop one-electron model Hamiltonian approaches that
accurately describe these non-valence ions
Tetramethyleneethane (TME)
Non-kekule, disjoint diradical
6 π electrons with orbitals 3
and 4 being essentially
degenerate
Considerable debate in the
literature as to the spacing
between the lowest singlet
and triplet states
A major complication, is that the molecule can rotate
relatively freely about the central CC bond
In our DMC calculations we use the dominant configurations from
CASSCF(6,6) calculations on the singlet and triplet states
About 25 determinants for each state
CI coefficients optimized together with the Jastrow factors
TME twisting potentials
For the singlet state, the DMC
potential has a rather different
shape than the corresponding
cas(6,6) potential
CAS(6,6)PT2 results very
similar to DMC if cc-pVTZ or
better basis set is used
CAS
CASPT2
DMC
Two shortcomings of earlier work on TME
1. Basis sets lacked f functions on C atoms
2. A two-configuration reference space is inadequate for
CASPT2 or MRCC
The energy gap between the first two π orbitals
and the 2nd pair of π is not very large