ARMY RESEARCH OFFICE Military University Research Initiative Oct 16, 2003 Quantum Theory Project Departments of Chemistry and Physics University of Florida Gainesville, Florida USA Rodney J. Bartlett Co-Workers Dr. Marshall Cory Dr. Stefan Fau Mr. Josh McClellan
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ARMY RESEARCH OFFICE Military University Research Initiative Oct 16, 2003 Quantum Theory Project Departments of Chemistry and Physics University of Florida.
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ARMY RESEARCH OFFICE
Military University Research Initiative Oct 16, 2003
Quantum Theory ProjectDepartments of Chemistry and Physics
University of FloridaGainesville, Florida USA
Rodney J. Bartlett Co-Workers
Dr. Marshall CoryDr. Stefan Fau
Mr. Josh McClellan
I. INTRODUCTIONNature of problem and our objectives
II. NUMERICAL RESULTSDimethylnitramine and tests of quantum chemical methods to be used. (Stefan Fau)
III. PLAN AND PROGRESS FOR RDX (Stefan Fau, Marshall Cory)
IV. COMPRESSED COUPLED CLUSTER THEORY: A NEW APPROACH TO HIGH LEVEL CC FOR LARGE MOLECULES
V. SUMMARY OF PROGRESS AND FUTURE PLANS
University of Florida: Quantum Theory Project
OUTLINEOUTLINE
Identify and characterize the initial steps in nitramine detonation in the condensed phase.
Study the series of molecules, nitramine (gas phase), methyl nitramine(liquid), dimethylnitramine(solid) which have (1) different reaction paths(2) different condensed phase effects
Investigate their unimolecular, secondary, and bimolecular reaction mechanisms.
Obtain definitive results for the comparative activation barriers for different unimolecular paths including those for RDX.
Develop ‘response/dielectric function’ methods to incorporate the condensed phase effects into the quantum mechanical calculations.
Provide high-level QM results to facilitate the development of classical PES for large scale simulations.
Generate ‘transfer Hamiltonians’ to enable the direct dynamics simulations as a QM complement to classical potentials.
University of Florida: Quantum Theory Project
OBJECTIVES
Quantum Mechanics I (Isolated gas phase molecules, 0K)Potential Energy Surface E(R) Different Unimolecular Decomposition PathsActivation BarriersSpectroscopic signatures for intermediates and products
A(l) is the closest rank l matrix to A. SVD is a useful mathematical tool because of this remarkable property. If su (u>l) is nearly equal to zero, we can reconstruct the matrix A without losing much information.
CCD 1ab abij ijt t
Application of SVD to the Coupled Cluster Doubles (CCD) Amplitude (1)
First, we choose an approximate CCD amplitude. The simplest one is MBPT(2) amplitude. We assume the Hartree-Fock reference.
1 2
1
,
W
ab ij abij p p p
p
t s U V W O
The singular values which are less than the threshold are neglected.
SVD
Application of SVD to the Coupled Cluster Doubles (CCD) Amplitude (2)
We can define the following contracted two-electron creation and annihilation operators according to the SVD of the approximate amplitude.
† † † , ab ijA A a b I I j i
ab ij
C V a a A U a a Then we can define the approximate cluster operator.
†2
1
2
W WAI A I
A I
T t C A
Physical meaning of the procedures (1)
1 † †HF
1 † †HF
†HF
1
2
1vac
2
1
2
abij a b j i
abij
abij a b j i
abij
P P PP
t a a a a
t a a a a
s C A
exact HF MBPT(2):
Reduced density matrix for 1 1 1 1
, ,,ab ab ab cdij kl ij kl ab cd ij ij
ab ij
t t t t
Application of SVD to the Coupled Cluster Doubles (CCD) Amplitude (3)
The CCD equation becomes,
2 2HF HF HF, 0.T TA
Ic c
E He He
4 4
,
,
cd C ab cdij B A C
cd C abcd
ab cd t A C t A C V ab cd V
ab cd V A C O
Degrees of freedom of the equation2 2
2 2 2W O
V O V
Most expensive term in CCD calculation
Integral transformation is required only once.
Improvement of the quality of calculated results
Use better approximate amplitude (e.g. MBPT(3)…).
CCD 2 CCD 1, ,ab ab ab abij ij ij ijd t t d t t
Tighten the threshold.
†2
†2
1
2
1,
2
W WAI A I
A I
W WAI A I
A I
T t C A
T t C A W W
・ The CCSD model is one of the most reliable quantum chemical methods. However, it is often necessary to incorporate higher order cluster operators than connected doubles to achieve the chemical accuracy.
Background
・ CCSDT, CCSDTQ, and CCSDTQP are implemented and they produce highly accurate computational results. But they are too expensive to be performed routinely.・ Perturbative approach such as the CCSD(T) or CCSD(TQ) is one possible solution for this problem. But still there is a problem that the perturbative approaches are stable only in the vicinity of equilibrium molecular geometry.
Purpose of this study
To develop theoretical framework (1) including the connected triples (2) accurate(3) less expensive (4) stable under deformed molecular geometry
Compression of the connected triples
2
1
OVabc ai bjckijk X X X
X
t s Q R
(1) Apply SVD to the second order triples
† , 1,2, ,aiX X
ai
C Q a i X K (2) Create contracted mono-excitation operators
(3) Truncate the mono-excitation operator manifold
3 2 2 , 1K O V
(4) Compressed T3 cluster operator
3
1
6 XYZ X Y ZXYZ
T t C C C
Easy to manipulate T3 amplitude
Compressed CCSDT method
1 2 3 1 2 3
1 2 3 1 2 3
HF HF HF
HF HF
HF
e ,0 e
0 e ,0 e
T T T T T Tai
c c
T T T T T Tabij XYZ
c c
XYZ X Y Z
E H H
H H
C C C
(1) Equations
(2) Equations for connected triples
,
abc abc abcijk ijk ijk
XX X YZ YY XY Z ZZ XYZ XYZX X X
a ai aiXX i X X
ai
D t R
D t D t D t R
D D Q Q
Compressed CCSDT-1 method
Approximate treatment for the T3 amplitude
1 2 3 1 2
1 2 3
HF 3 HF
HF 2 HF
0 e 0 e
CCSDT-1a
no approximation for the T2 amplitude
CCSDT-1b
0 e 0 1
T T T T Tabij XYZ
c c
T T TXYZ XYZ cc
H H T
H H T
・ Easiest to implement・ Operation count for T3 amplitude scales as K2V2O・ Iterative counterparts of CCSD[T] and CCSD(T)
Potenrial Energy Curve (1) (HF, aug-cc-pVDZ, HF-bond stretcing)
-300
-250
-200
-150
-100
-50
0
0.5 1 1.5 2 2.5 3 3.5 4
MRCICCSDCCSD(T)CCSDT-1COMP.SDT-1
(E+
100)
*100
0 (a
.u.)
r(HF)/r(eq)
r(eq)=1.733 bohr=0.25
Potential Energy Curve (2) (H2O, aug-cc-pVDZ, OH-bonds stretching)
-300
-200
-100
0
100
0.5 1 1.5 2 2.5 3 3.5
MRCICCSDCCSD(T)COMP.SDT-1CCSDT-1
(E+
76)*
1000
(a.
u.)
r(OH)/r(eq)
r(eq)=1.809 bohr=0.25
SUMMARY OF PROGRESS
• Detailed study of nitramines to establish the accuracy of various quantum-mechanical results for application to uni- and bi-molecular reactions.
• Initial investigation of comparative reaction paths for DMNA with the goal of providing definitive results.
• Application to RDX to help resolve the nature of the initial step in its decomposition.
• Introduced compressed coupled-cluster theory as a new tool that can provide CC quality results at a fraction of the current cost.
PLANS FOR 2003-2004
• Resolve issue of comparative energetics among HONO elimination, loss of .NO2, and NO2 ONO in prototypical nitramines.
• Complete work on primary decomposition of dimethylnitramine and reactions of decomposition products with each other and new dimethylnitramine.
Apply the methods used with dimethylnitramine to RDX and compare to relative reaction rates from established technology.
Extend the compressed CC method to full triples and factorized quadruples.
Formulate analytical gradients for compressed CC.
Backup Slides
Enthalpies of formation for H2N-NO2 et al. (gas-phase)
cis HONO, NO2 (2A1), HN-NO2-, NH3, H2N (2B2),
HN (3g-)
average error [kcal/mol]B3L/6 CBS2M CBS2 CBS3 G2 CBS-Q
all 0.7 0.0 -0.4 -0.7 -2.2 -1.1no HN, HN-NO2
- 0.0 -0.2 -0.5 -0.6 -1.7 -0.6
H2N-NO2 -> H2N. + NO2
. BS dependence
0
20
40
60
80
100
1 2 3 4 5 6 7
rNN
Ere
l [
kca
l/mo
l]
MBPT(2)-fc/DZ
CCSD-fc/DZ
CCSD(T)-fc/DZ
MBPT(2)-fc/CBS2(XZ)
CCSD-fc/CBS2(XZ)
CCSD(T)-fc/CBS2(XZ)
100 * max. T2 (s)
MBPT(2)-fc/ADZ
CCSD-fc/ADZ
CCSD(T)-fc/ADZ
MBPT(2)-fc/CBS2(AXZ)
CCSD-fc/CBS2(AXZ)
CCSD(T)-fc/CBS2(AXZ)
100 * max. T2 (s)
Relative energy in kcal/mol along possible bimolecular reaction paths