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CORRELATION BOUND ANION STATES OF MOLECULES AND CLUSTERS K. D. Jordan Department of Chemistry...
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Transcript of CORRELATION BOUND ANION STATES OF MOLECULES AND CLUSTERS K. D. Jordan Department of Chemistry...
CORRELATION BOUND ANION STATES OF MOLECULES AND CLUSTERS
K. D. Jordan
Department of Chemistry
University of Pittsburgh
Pittsburgh, PA
. QMC in Apuan Alps VIII, July, 2013
Cavity state of (H2O)45- Charge flow in C60 induced
by an electric field
National Science Foundation
Department of Energy
Acknowledgements and Projects
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
CollaboratorsM. Johnson (Yale Univ.)
Reduction of CO2 using (H2O)n- clusters*
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)
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
Classification of anion states
• Unbound: temporary anions (resonances)
• Bound
Bound at KT/HF level
Unbound at KT/HF levelPose 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
R
Model system comprised of four water molecules
Electron binding energy (EBE) calculated vs. 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
-20.0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
0 2 4 6 8 10 12
Distance between dimers (Ang)
Ele
ctro
n B
indi
ng E
nerg
y (m
eV)
eom-ccsd
eom-mp2
delta_ccsd(t)
delta_ccsd
delta_mp2
delta_hf
kt
Results for a basis set with very diffuse functions: aug-cc-pVDZ+6s6p
MP2 and coupled cluster methods fail when HF cease to bind the e-.
Coupled cluster methods still useful as long as HF gives binding.
-600.0
-500.0
-400.0
-300.0
-200.0
-100.0
0.0
100.0
200.0
0.00 2.00 4.00 6.00 8.00 10.00 12.00
Distance between dimers (Ang)
Ele
ctro
n B
ind
ing
En
ergy
(m
eV)
eom-ccsd
eom-mp2
delta_ccsd(t)
delta_ccsd
delta_mp2
delta_hf
kt
Results for basis set without highly diffuse functions: aug-cc-pVDZ
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
2.5 Ang
0 5 10 15 20 25
"z " Dist (Bohrs)
Psi
(ar
bit
rary
un
its)
hf
nat
3.5 Ang
0 5 10 15 20 25
"z " Dist (Bohrs)
Psi
(ar
bit
rary
un
its)
hf
nat
4.5 Ang
0 5 10 15 20 25
"z " Dist (Bohrs)
Psi
(ar
bit
rary
un
its)
hf
nat
8.5Ang
0 5 10 15 20 25
"z " Dist (Bohrs)
Psi
(ar
bit
rary
un
its)
hf
nat
Singly occ. NO from HF and EOM-CCSD natural orbital analysis (in latter case ~ Dyson orbital from Green's function treatment)
At large R, the anion is bound in the HF approx.
It ceases to bind around R = 4.2 Å
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
0
200
400
600
800
1000
1200
4 8 12 16 20 24
ADC/aTZ+C
pol3-sc
pol1
EBEs of W24a and subclusters extracted from W24a
• 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
ADC refers to ADC(2) Green's function method.
Pol1 decouples e- interacting with induced dipoles from water-water interactions and e- directly inducing dipoles.
Pol3-SC treats these interactions self- consistently.
C = large set of diffuse s + p functions at COM
Any system with sufficient polarizability should support non-valence 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.
1Feng et al. Science 320, 359 (2008)
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)
Hu (-7.1eV)
Hg (-8.2 eV)
Gg
Gu
T1u (-3.1 eV)
T1g (-2.0 eV)
T2u (-1.4 eV
Hg (-1.0 eV)
Ag (?)
One-particle energy levels of C60E
nerg
y
Negatives of ionization potentials
Negatives of electron affinities
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
The calculations predict the s-type anion to be bound by about 130 meV,
Integrated probability
About 9% of the charge is located inside the C60 based on analysis of the dominant natural orbital for the excess electron
ψ2
Ψ2 *
r2
105 3020 2515 5 10 15 20 3025 35 40R (Bohrs) R (Bohrs)
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
The polarization potential is not r-4 except at very large distances.
Fit to the short range electrostatic and polarization potentials
Model potential
Radial distributionCharge distribution is similar to that from the EOM-CCSD calculations
Repulsive potential at the C60 radius builds in orthogonality
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.
E_f
ield
= 0
.001
a.u
.
Indu
ced
Dip
ole
mom
ent =
0.4
9 a.
u.
-0.03
+0.03
Charge range
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
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 C6F6
-
The anion is valence in nature for highly bent structures (OCO angle < 148 deg), and is very extended for larger angles
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.
Neutral
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)
Xe20 and C60 have similar polarizabilities and similar EBEs when electrostatics suppressed in the latter
Results for EOM calculations.
ADC(2) overbinds by up to 3x
Is problem screening, or breakdown of use of uncoupled "HF" polarizabilities
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
DMC
CAS
CASPT2
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