Post on 03-Jan-2016
Calculating Molecular Binding Energiesfrom Chemical Bonds to van der Waals Interactions
Thom H. Dunning, Jr.
Joint Institute for Computational SciencesUniversity of Tennessee – Oak Ridge National Laboratory
Oak Ridge, Tennessee
Joint Institute for Computational Sciences
Outline of Seminar
Statement of the Problem
Theoretical Methods
Basis Sets and Error Analysis Correlation Consistent Basis Sets Errors in Molecular Calculations
Errors in Molecular Binding Energies (for Four Classes) Intrinsic Errors of Methods Basis Set Convergence Errors Statistical Analysis of Errors in Binding Energies
Conclusions
Statement of Problem
Wide Range of Binding Energies
0.01 0.1 1.0 10.0 100.0 1000.0}
He2
De (kcal/mol)
Ne2 Ar2
Ar-HCl
N2-HFH-CO CO
H-CO-
H-C2H2
H-C2Hn
H-CHn
(HF)2
Ar-HF
N2
Statement of Problem
Importance of Electron Correlation
HF Expt’l
HF 100.3 141.6
N2 122.3 228.4
F2 -27.0 39.0
(HF)2 3.7 4.6
N2-HF 1.27 2.22
He2 – 0.0218
De (kcal/mol)
Chemical Bonds
Hydrogen Bonds
van der Waals “Bonds”
Electrostatic “Bonds”
Theoretical Methods
Configuration Interaction
e = 0 + Ciai
a +
Cijabij
ab + …
He C = Ee C
Long history in electronic structure theory
Very flexible, e.g., can describe both ground and excited states
Not size extensive/consistent
Perturbation Theory
He = H0 + H1
e = 0 + 1 + 22 + …
Ee = E0 + E1 + 2E2 + …
Most widely used technique for including electron correlation
Assumes that electron correlation is perturbation to the HF hamiltonian
Recent studies have revealed serious convergence problems
Theoretical Methods
Coupled Cluster Theory
e = eT0
T = t1 + t2 + t3 + …
t1 = tiaaa
+ai
t2 = tijabab
+aa+ajai
t3 =
Recent addition to electronic structure theory
Includes dominant higher-order terms as products of lower order terms
Rapid convergence if wavefunction is dominated by well localized electron pairs
Convergence problems if HF wave-function provides poor zero-order description of molecule
Basis Sets and Error Analysis
Correlation Consistent Basis Setscc-Sets based on detailed study of electron correlation in atoms
Correlation functions added in shells
Hartree-Fock orbitals cc-pVDZ: + (1s1p1d)
cc-pVTZ: + (2s2p2d1f)cc-pVQZ: + (3s3p3d2f1g)…
Augmented with diffuse functions for anions, long range interactions, etc.
Molecular properties often exhibit systematic dependence
Possible to extrapolate properties to complete basis set limit
De(CO)
n (cc-pVnZ)2 3 4 5 6
240.0
245.0
250.0
255.0
260.0
CBS Limit
HFOrbitals
+1s1p1d
+1s1p1d1f
+1s1p1d1f1g
cc-pVDZcc-pVTZ
cc-pVQZ
Basis Sets and Error Analysis
Definition of Errors (Method “M”)
Basis Set Convergence Error
QbsM(n) = Q(M,n) – Q (M,)
Intrinsic Error
QM = Q(M,) – Q(expt’l)
Calculational Error
Qcalc’dM(n) = Q(M,n) – Q (expt’l)
= QbsM(n) + QM
Basis Sets and Error Analysis
Convergence Types
n
Type II
Note:Qcalc’d
M 0
n
Type III
QM()
n
QbsM(n)
Type I
QM
Q(expt’l)
Qcalc’dM
Molecular Binding Energies:Chemical Bonds
T. H. Dunning, Jr., J. Phys. Chem. A 104, 9062- 9080 (2000)
K. L. Bak, P. Jørgensen, J. Olsen, T. Helgaker, and W. Klopper, J. Chem. Phys. 112, 9229- 9242 (2000)
Intrinsic Errors in De
Chemical Bonds
CH HF CO N2
De (kcal/mol)a 83.9 141.6 258.6 227.4
MP2 -2.9 4.2 13.0 12.5
MP3 -1.4 -3.1 -8.5 -11.7
MP4 -0.6 1.1 5.7 4.7
MP5 -1.0
CCSD -1.0 -2.2 -8.1 -9.8
CCSD(T) -0.2 -0.1 0.0 -0.3
CCSDT -0.1 -0.2 -0.6 -1.1a Corrected for core-valence and relativistic effects.
Basis Set Convergence Errors in De
Chemical BondsD
ebs (
n)
(k
cal/
mol
)
n n2 3 4 5 6
-30.0
-25.0
-20.0
-15.0
-10.0
-5.0
0.0
2 3 4 5 6
cc-pVnZ sets
aug-cc-pVnZ Sets
CO
N2
HF
CH
Region of“false positives”
0
Statistical Analysis of Binding Energies
Q (Error in Q)
(Q
)
std = errorvariation
= average error
Intrinsic Errors in De
MP2 , CCSD, CCSD(T) Methods (6Z Set)
De (kcal/mol)
(D
e)
0.0
0.2
0.4
0.6
0.8
1.0
-40.0 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0
MP2
CCSD(T)
CCSD
MP2 CCSD +(T)
6.0 -8.3 -1.0
std 7.5 4.5 0.5
0.0
0.2
0.4
0.6
0.8
1.0
-40.0 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0
DZ TZ
QZ
5Z 6Z
Basis Set Convergence of De
CCSD(T) Method for Chemical Bonds
De (kcal/mol)
(D
e) = -1.0 kcal/molstd = 0.5 kcal/mol
Extrapolation of Binding Energies
Analysis of Electron Correlation in He
Principal ExpansionE = EHF(1s) + E2(2s2p)
corr + E3(3s3p3d)corr + …
Errors in He Atom
Klopper et al. [J. Phys. B. 32, R103 (1999)] showed error in truncating series after nth term in principal expansion is
Extrapolation Formula
€
ΔEncorr ∝
1
n3
€
En−1,n = EnHF +
n3Encorr − (n −1)3En−1
corr
n3 − (n −1)3
Extrapolation of De
CCSD(T) Method for Chemical Bonds
De (kcal/mol)
(D
e)
-40.0 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.00.0
0.2
0.4
0.6
0.8
1.0
DZ-TZ
TZ-QZ
QZ-5Z
5Z-6Z
DT TQ Q5 56
-3.5 -0.1 0.0 -0.1
std 2.0 0.5 0.3 0.2
1.6
Molecular Binding Energies:Hydrogen Bonds
T. H. Dunning, Jr., J. Phys. Chem. A 104, 9062- 9080 (2000)
A. Halkier, W. Klopper, T. Helgaker, P. Jørgensen, and P. R. Taylor, J. Chem. Phys. 111, 9157 (1999)
Intrinsic Errors in De
Hydrogen Bond in HF Dimer
(HF)2
De (kcal/mol) 4.56 0.05 a
MP2 -0.09
MP3 -0.03
MP4 -0.02
CCSD -0.16
CCSD(T) -0.02
a W. Klopper, M. Quack, and M. Suhm, J. Chem. Phys. 108, 10096 (1998).
Basis Set Convergence Errors in De
Hydrogen Bonds in (H2O)2 and Others
Deb
s (n
) (
kca
l/m
ol)
n n
-1.5
-1.0
-0.5
0.0
2 3 4 5
cc-pVnZ
aug-cc-pVnZ
d-aug-cc-pVnZ
(H2O)2
B
B
BB
J
J
J J
H
H
HH
P
P
PP
F
F
F
2 3 4 5
B HF-HF (4.53)
J HCl-HCl (1.95)
H HF-H2O (8.51)
P HF-HCN (7.31)
F H2O-H2O (4.96)
B
BB
B
J
J
JJ
2 3 4 5
uncorrected
corrected
Errors in De
Hydrogen Bonds
De(
n)
(k
cal/
mol
)
n
BS
SE
BS
CE
De(n=∞)
Extrapolation of De
Hydrogen Bond in HF Dimer
De(
n)
(k
cal/
mol
)
n
CalculatedExtrapolated
B
B
BB
J
J J
3.8
4.0
4.2
4.4
4.6
2 3 4 5
Molecular Binding Energies:Electrostatic Interactions
T. H. Dunning, Jr., J. Phys. Chem. A 104, 9062- 9080 (2000)
Intrinsic Errors in De
Electrostatic Interactions
N2-HF Ar-HF Ar-FH Ar-HCl Ar-ClH
De (cm-1) 776 ± 30a 211 ± 4b 109 ± 10b 176 ± 5c 148 ± 10c
MP2 35 -10 -16 31 33
MP3 -36 -31 -31
MP4 38 7 -10 10 7
CCSD -52 -45 -36
CCSD(T) 17 0 -15 0 7
a R. J. Bemish, E. J. Bohac, M. Wu, and R. E. Miller, J. Chem. Phys. 101, 9457 (1994) and references therein. b J. M. Huston, J. Chem. Phys. 96, 6752 (1992) and references therein. c J. M. Huston, J. Chem. Phys. 89, 4550 (1988); J. M. Hutson, J. Chem. Phys. 96, 4237 (1992) and references therein.
Basis Set Convergence Errors in De
Electrostatic InteractionsD
ebs (
n)
(cm
-1)
n n2 3 4 5
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
2 3 4 5
aug-cc-pVnZ
d-aug-cc-pVnZ
Ar-HF Ar-FH
Molecular Binding Energies:van der Waals Interactions
T. H. Dunning, Jr., J. Phys. Chem. A 104, 9062- 9080 (2000)
Intrinsic Errors in De
van der Waals Interactions
He2 Ne2 Ar2
De(cm-1) 7.59 a 29.4 b 99.6 c
MP2 -2.7 -10.5 13.4
MP3 -1.1 -7.1 -17.6
MP4 -0.5 -1.9 0.4
MP5 -0.2
CCSD -1.1 -6.8 -27.6
CCSD(T) -0.2 -1.0 -2.6
CCSDT -0.0a R. A. Aziz and M. J. Slaman, J. Chem. Phys. 94, 8047 (1991); R. A. Aziz, A. R. Janzen, and R. Moldover, Phys. Rev. Lett. 74, 1586 (1995). b R. A. Aziz, W. J. Meath, and A. R. Allnatt, Chem. Phys. 78, 295 (1983); R. A. Aziz and M. J. Slaman, Chem. Phys. 130, 187 (1989). c R. A. Aziz and M. J. Slaman, Mol. Phys. 58, 679 (1986); R. A. Aziz, J. Chem. Phys. 99, 4518 (1993).
Basis Set Convergence Errors in De
van der Waals InteractionsD
ebs (
n)
(cm
-1)
n n2 3 4 5 6
-20.0
-15.0
-10.0
-5.0
0.0
2 3 4 5 6
Ne2
aug-cc-pVnZ
d-aug-cc-pVnZ
t-aug-cc-pVnZ
Ne2
Ar2
Conclusions
Critical Assessment of Methods Coupled cluster method provides reliable means of
computing molecular properties for molecules well described by single configuration
Perturbation method is poorly convergent or even non-convergent; often does not achieve chemical accuracy for chemical bonds
Critical Assessment of Basis Sets Correlation consistent basis sets systematically
approach complete basis set limit, extrapolation possible Choice of cc-basis set family depends on molecular
system Chemically bound covalent molecules—standard sets
Conclusions (cont’d)
Chemically bound ionic, hydrogen-bonded, and electrostaticly bound molecules—singly augmented sets
van der Waals bound molecules—doubly augmented sets
Convergence with basis set is slow Difficult to describe coulomb hole using expansions in one-
electron functions Rate of convergence depends on molecular details
Single, double or triple bonds Chemically bound, hydrogen-bonded, electrostatically bound or van der
Waals bound
Extrapolation substantially improves convergence rate
Acknowledgements
It is a pleasure to acknowledge contributions of …Kirk Peterson, David Woon, David Feller, Ricky Kendall, Tanja van Mourik, and Angela Wilson to this work
It is also a pleasure to acknowledge work of …Poul Jørgensen, Trygve Helgaker, Wim Klopper, Jeppe Olsen and coworkers, whose work has also contributed greatly to calibrating the methods used for molecular calculations
Finally, I would like to thank …Division of Chemical Sciences, Office of Science, U.S. Department of Energy for their support of this work.
End of Presentation
Definitions
De and D0
E
De D0
A+B
ABZero Point Energy
Separated Atoms
Molecule
Higher Order Effects in He2V
(R)
(K
)
R (bohr)
0.0001
0.001
0.01
0.1
1.0
10.0
3 4 5 6 7 8 9 10 11 12
FCI-T
T-(T)
-0.32 K
-0.015 K