army research office military university research initiative oct 16, 2003
DESCRIPTION
ARMY RESEARCH OFFICE Military University Research Initiative Oct 16, 2003. Rodney J. Bartlett. Co-Workers Mr. Andrew Taube Mr. Josh McClellan Mr. Tom Hughes Mr.Luis Galiano Dr. Stefan Fau. Dr. DeCarlos Taylor (ARL) Dr. Ariana Beste (ORNL). Quantum Theory Project - PowerPoint PPT PresentationTRANSCRIPT
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
Mr. Andrew Taube Mr. Josh McClellanMr. Tom Hughes Mr.Luis Galiano
Dr. Stefan FauDr. DeCarlos Taylor (ARL)Dr. Ariana Beste (ORNL)
Identify and characterize the initial steps in nitramine and other detonation in the condensed phase.
Progress requries NEW ab initio quantum mechancial techniques that have the accuracy and appicability to provide reliable results for unimolecular and bimolecular reaction paths.
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, particularly for RDX.
Study the nitromethane molecule and its various isomers as a prototype for nitroalkanes.
Generate ‘transfer Hamiltonians’ to enable direct dynamics simulations as a QM compliment to classical potentials, and to be able to reliably describe many units of a condensed phase explosive.
Provide high-level QM results to facilitate the development of classical PES for large scale simulations.
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
Quantum Mechanics IIBi(tri...)molecular reactionsLong range (condensed phase, pressure) effectsActivation Barriers, Spectroscopy
Classical Mechanics-- Representation E(R)
Large Molecule QM--Simplified Representationof H(R) Transfer HamiltonianElectronic State Specific
Reactions of one Me2N-NO2
Me2N-NO2 Me2N. + NO2
.
MeN.-NO2 + Me.
H2C.-N(Me)-NO2 + H.
[ H2C=N+(Me)-N(O-)OH] H2C=NMe + HONO
Reactions of two Me2N-NO2
Same reactions as before, causing a slight change in the interaction
energy with the second Me2N-NO2.
Additionally:
Me2N-NO2 + Me2N-NO2 Me2N-ONO + Me2N. + NO2
.
Me2N-NMe2 + NO2. + NO2
.
Me2N-Me + Me-N.-NO2 + NO2.
Me2N-N(Me)-NO2 + Me. + NO2.
Me2N-H + H2C.-N(Me)-NO2 + NO2
.
Me2N-CH2-N(Me)-NO2 + H. + NO2.
products from CH3., H. (HONO, H-Me, …)
In reposne to Bob Shaw’s comment abouterror bars in theoretical applications….
It is clear that if we want to know the right answerfor activation barriers competitive decompisiton paths..
We need a high-level of theory like CCSD(T), with a large basis set.
Coupled Cluster Calculation of De’s
De (kcal/mol)
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
(De)
From K. L. Bak et al., J. Chem. Phys. 112, 9229-9242 (2000)
Last year…
•Reported the detailed theory for the compressed (SVD) CC, which ‘contracts’ the CC amplitudes in an optimum way to make it possible to perform much higher level CC calculations for large molecules.
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
MRCI
CCSD
CCSD(T)
CCSDT-1
COMP.SDT-1
(E+
10
0)*
10
00
(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
MRCI
CCSD
CCSD(T)
COMP.SDT-1
CCSDT-1
(E+
76
)*1
00
0 (
a.u
.)
r(OH)/r(eq)
r(eq)=1.809 bohr=0.25
•Detailed a new extrapolation procedure for energies and forces that has a mean error of nearly zero, and a maximum error of0.75 kcal/mol for nitramne and its components.
•Reported on a series of CC studies of nitramine to assess its decomposition paths.
This year….
I.A NEW APPROACHE TO HIGH-LEVEL COUPLED-CLUSTER THEORY FOR LARGER MOLECULES.
A. A natural orbital coupled-cluster method.
B. Comparisons to Compressed coupled-cluster theory.
II. NUMERICAL ILLUSTRATIONS FOR DMNA, DMNA DIMERS AND RDX.
Iii. CONCEPT OF A TRANSFER HAMILTONIAN AS A MEANS TO DESCRIBE COMPLEX SYSTEMS WITH QUANTUM MECHANCIAL FORCES FOR MD APPLICATIONS.
A. Illustration for nitromethane and its isomers.
University of Florida: Quantum Theory Project
OUTLINEOUTLINE
How can we retain the accuracy of CCSD(T), ie an ~n7
method, but make it applicable to large molecules?
Dimer (bimolecular sytem) is 28 times as difficult as the monomer, without modification.
I. Natural orbital coupled-cluster theory
II. Compressed coupled-cluster using Singular Value Decomposition.
Frozen Natural Orbital Coupled Cluster Theory
• Dependence on size of virtual sector of basis set limits high-level CC to small molecules:
• CCSD ~ V4; CCSD(T) ~ V4; CCSDT ~ V5
• Natural Orbitals (NOs) are known to be the best possible set of orbitals to truncate
• Too costly to get exact – use approximate MBPT(2) NOs
• To maintain advantages of a HF reference, only perform truncation in virtual space – leaving occupied space alone – Frozen Natural Orbitals (FNOs)
FNO Procedure SCF gives Molecular Orbitals U Construct MBPT(2) Density Matrix D in MO
Basis Solve DV=Vn Truncate V to V’ throwing out less occupied
virtuals, as measured by their occupation numbers.
Construct new Fock Matrix in FNO Virtual Space Diagonalize for new orbital energies Perform higher level (CC) calculation in
truncated virtual space For an estimate of truncation error, define:∆MBPT(2) = MBPT(2) (Full) – MBPT(2)
(Truncated)
Note: On the following slides, the percentage listed indicated the number of FNOs retained. For example, 20% DZP means that there are only 20% of the original number of DZP virtual orbitals left.
Computational Details: Calculations were performed on an IBM RS/6000 375 MHz POWER3 processor with 3 GB RAM and 18 GB disk using the ACES II electronic structureprogram.
Three Different Bases. Same Number of Orbitals.
-100.45
-100.4
-100.35
-100.3
-100.25
-100.2
-100.15
-100.1
-100.05
0.5 1 1.5 2 2.5 3
Bond Length (Angstroms)
To
tal E
ner
gy
(Har
tree
)
100% DZP
40% cc-pVTZ
20% cc-pVQZ
100% cc-pVQZ
FNO RHF CCSD(T) PES for Hydrogen Fluoride
Reference
*F2, HF, CO, N2, NH3, H2O – PES of symmetric dissociation
*Relative to 20% DZP Basis Calculation
Average Timings for Determination of CCSD(T) PES for Six Small Molecules* with FNO Truncation
Truncated Large Bases are Better than Similar-sized Small Bases
20
40
60
80
100
0 0.5 1 1.5 2 2.5 3 3.5LOG (Relative** Time)
% C
orr
ela
tio
n E
ne
rgy
*
DZP
cc-pVTZ
cc-pVQZ
* Total Correlation Energy Determined by 100% cc-pVQZ calculation
** Times Relative to 20% DZP Calculation
Points are in increments of 20% of basis set
Dimethylnitramine• Model compound for RDX and HMX.• Two possible conformers:
• C2v – X-ray crystallography / gas-phase e- diffraction1;
• Cs – predicted by theory at SCF, MBPT(2), DFT, QCISD levels with moderate basis sets2. It has been argued that theoretical predictions are more accurate than experimental values.
• Dimer interactions are important to model dominant interaction in the solid phase. Given X-ray structure, best to use C2v monomer. Calculations have been done at SAPT level on fixed monomers3.
• DMNA can undergo decomposition via NO2 and HONO elimination. HONO Elimination estimated to be exothermic by ~1-3 kcal/mol at standard conditions4, therefore need high-level calculations, zero-point energy corrections, etc.These have been investigated theoretically locating transition states at the QCISD, MBPT(2) and DFT levels2.1) Stolevik, Rademacher, Acta Chem Scand 1969 23 672
2) Harris, Lammertsma, JPCA 1997 101 1370; Smith, et al., JPCB 1999 103 705; Johnson, Truong, JPCA 1999 103 8840
3) Bukowski, Szalewicz, Chabalowski, JPCA 1999 103 7322
4) Shaw, Walker, JPC 1977 81 2572
DMNA Equilibrium Structure
C2v*Cs**
9.29-339.1180-339.1032cc-pVTZ – 60%
7.00 hr1.80 hrcc-pVTZ – 60% Time
9.29-339.1431-339.1283cc-pVTZ – 60% + ∆MBPT(2)
39.5 hr13.1 hrcc-pVTZ – 100% Time
9.24-339.1399-339.1252cc-pVTZ – 100%
8.91
7.66
9.09
C2v – Cs (kcal/mol)
-338.8220-338.8078DZP – 60% + ∆MBPT(2)
0.19 hr0.06 hrDZP – 60% Time
-338.8302-338.8157DZP – 100%
-338.7671-338.7549DZP – 60%
1.22 hr0.39 hrDZP – 100% Time
CsC2vCCSD(T) RHF Drop Core
Total Energies in Hartree
*Experimental geometry with HCH angles optimized at MBPT(2) Bukowski et.al. JPCA 1999 103 7322
**Theoretical prediction QCISD cc-pVDZ basis Johnson & Truong JPCA 1999 103 8840
M1
M2
M3
M4
DMNA Dimer Structures† - fixed monomer geometry
† Monomer geometries are experimental methyl angles, optimized at MBPT(2) level. Dimer structures are minima of SAPT method –Bukowski, Szalewicz, Chabalowski JPCA 1999 103 7322
DMNA Dimer Interaction Energies
† Bukowski, Szalewicz, Chabalowski JPCA 1999 103 7322
0
2
4
6
8
10
12
-Ein
t (k
cal/
mo
l)
M1 M2 M3 M4
SAPT Minima
SAPTThis work*
†
* CCSD(T) FNO 60% DZP with core occupieds dropped and ∆MBPT(2) correction
Background information for RDX
Decomposition Mechanisms:● NO2 Elimination: B3LYP/6-3311G** (1), DSC closed pan(liquid-like) (2)
● HONO Elimination (3)
● Triple Bond fission: IRMPD(4), DSC open pan(gas-like)(2)
● Other mechanisms: NO elimination (MALDI)(5), internal ring formation, -OH loss
Conformers of RDX:● Solid α-RDX: AAE (Cs) (6)
● Solid β-RDX: AAA● Vapor phase(e- diffraction): AAA(C3v)● Gas/liquid dynamically averaged structure(7)
The energy difference between minima is on the order of 1 Kcal/mol (B3LYP/6-311G**) with AAE being the most stable(1)
1)N. Harris, K. Lammertsma., J. Am. Chem. Soc. 119,6583 (1997)2) G. Long, S. Vyazovkin, B. A. Brems, C.A. Wight, J. Phys. Chem. B., 104, 2570 (2000)3) D. Chakraborty, R.P. Muller, S. Dasgupta, W. Goddard III, J. Phys. Chem. A., 104,2261 (2000)4) X. Zhao, E. Hintsa, Y. Lee, J. Chem. Phys., 88, 2 ,801 (1988)5) H.S. Im and E.R. Bernstein. J.Chem.Phys., 113, 18 ,7911 (2000)6)B. Rice, C. Chabalowski, J. Phys. Chem. A., 101, 8720 (1997)7) T. Vladimiroff, B. Rice J. Phys. Chem. A., 106, 10437 (2002)
RDX Minima*
-1.4
-0.25
Chair-Boat
(kcal/mol)
14530CC Time (hr)
1000200Estimated Time for Full Basis (hr)
-895.3289-895.3311DZP – 60% + ∆MBPT(2)
-895.1728-895.1732DZP – 60%
AAA BoatAAA Chair
CCSD(T) RHF Drop Core
Total Energies in Hartree
*Conformations determined by B3LYP 6-31G(d) Calculations –
Chakraborty, et al JPCA 2004 104 2261
AAA ChairAAA Boat
Triples at a Fraction of the Cost
Compressed Coupled Cluster &
FNO CC for DMNA
CCSD(T) FNO Timings for
AAA Chair Conformer of RDX
** Estimated.
Basis Time
FNO* 60% DZP 30 hours
100% DZP 200 hours**
FNO* 60% cc-pVTZ 50 days**
100% cc-pVTZ 1 year**
FNO* 60% cc-pVQZ 2.5 years**
100% cc-pVQZ 20 years**
*FNO Speed-up ~ 8x faster with 50% truncation. For large numbers of occupied orbitals, FNO speed-up determined by o3v3 term in CCSD equations – Not by o2v4 term
CCSDT-1 RHF DZ Basis Frozen Core:
MethodCC Speed-up
Factor
Comp. CC 8.6
60% FNO CC 5.96.3
Transfer Hamiltonian for large clusters of molecules.
Basic idea: Represent the CC Hamitonian in itsone-particle form by a low-rank operator, that permitsrapid generation of forces for MD, but can (hopefully)retain the accuracy of CC theory, in the process.
University of Florida: Quantum Theory Project
TRANSFER HAMILTONIANTRANSFER HAMILTONIAN
In CC theory we have the equations…
exp(-T) Hexp(T) = Ĥ
Ĥ|0 = E|0 Where E is the exact correlated energy
m |Ĥ|0 =0 Where m| is a single, double, triple, etc excitation which provides the equations for the coefficients in T, ie ti
a, tijab,
etc.
(R)E(R) = F(R) Provides the exact forces
(x)= 0| exp(-T)(x-x’)exp(T) |0 gives the exact density
and m| Ĥ |n Ĥ and ĤRk = kRk Gives the excitation (ionization, electron attached) energies k and eigenvectors Rk
ACCURACY
1
10-2
10-4
10-6
10-8
10-10
CC
DFT
SE
TB
CPC
OS
T
COMPARATIVE APPLICABILITY OF METHODS
TH
TRANSITION FROM MANY-PARTICLE HAMILTONIAN TO EFFECTIVE ONE-PARTICLE HAMILTONIAN...
Wavefunction Approach0|{i†a}Ĥ|0=0= a| Ĝ |i=0
Ĝ|i=i|i iParameterize Ĝ with a GA to satisfy E= 0|Ĥ|0,
E=F(R), (r), (Fermi) = IDensity Functional Approach
Ĝ|i=i|i i where Ĝ =t+E/(x)
and E[]=E, E=F(R), (r)= |i i|, (Fermi) = IFuture? Remove orbital dependence
and/or self-consistency?
Second Quantized Ĝ
Ĝ =gpq{p†q} +ZAZB /RAB
Transition from orbital based to atom based-- (hAA + AA)+ hAB(R) + AB(R)
+ Z’AZ’B /RAB{akAexp[-bkA(RAB-ckA)2] +akBexp[-bkB(RAB- ckB)2]}
hAB(R)= ( + )KS(R)
AB(R) = [( RAB)2 +0.25(1/AA+1/BB)2]-1/2
RELATIONSHIP BETWEEN COUPLED-CLUSTER/DFT HAMILTONIAN AND SIMPLIFIED THEORY
University of Florida: Quantum Theory Project
aci-nitromethane
• Proper description of NMT unimolecular rearrangement is required for adequate description of combustion, detonation and pollution chemistry. • NMT is a model system for energetic materials, e.g. FOX-7, TNAZ.• NMT→ CH3∙ +NO2∙ most energetically favored, ~63 kcal/mol*.• NMT→MNT→ CH3O∙ +NO∙ second most energetically favored, ~69 kcal/mol*.• Molecular beam experiments** demonstrate NMT → MNT
nitromethane (NMT)methylnitrite (MNT)
*CCSD(T)/cc-PVTZ, Nguyen et al., J. Phys. Chem. A 2003, 107, 4286**Wodtke et al., J. Chem. Phys. 1986, 90, 3549
Nitromethane Background
Unimolecular Decomposition Pathways of NMT and MNT
CH3-NO2 CH3. + NO2
.
TS1 CH3ONO Rearrangement
CH3ONO CH3O . + NO.
TS2 CH2O + HNO Rearrangement
•G2MP2*•CCSD/TZP•CCSD(T)/cc-PVTZ**
* Hu et al., J. Phys. Chem. A 2002, 106, 7294** Nguyen et al., J. Phys. Chem. A 2003, 107, 4286
Energies relative to NMT
Nitromethane HT
Force of C-N bond breaking
-0.1
-0.05
0
0.05
0.1
0.15
1.3 1.8 2.3 2.8 3.3
R (A)
F (
H/B
oh
r) CCSD/TZP
AM1
TH-CCSD
B3LYP/6-31G*
Nitromethane PES for C-N rupture
-10
0
10
20
30
40
50
60
70
80
90
0.9 1.9 2.9 3.9
R_C-N (A)
En
erg
y(k
ca
l/m
ol)
CCSD(UHF)/TZP
AM1(UHF)
TH(UHF)
B3LYP/6-31G*(UHF)
NMT Energy (UHF)
-10
40
90
0.9 2.9R_C-N (A)
E-E
_rel
(kca
l/mo
l)
CCSD(UHF)/TZP
MNT Energy
-10
40
90
0.9 2.9R_C-O (A)
E-E
_rel
(kca
l/mo
l)
CCSD(RHF)/DZP
aci-NMT Energy
-10
40
90
0.9 1.9R_C-N (A)
E-E
_rel
(kca
l/mo
l)CCSD(RHF)/TZP
NMT Energy (RHF)
-10
40
90
0.9 2.9R_C-N (A)
E-E
_rel
(kca
l/mo
l)
CCSD(RHF)/TZP
Reference Data
Nitromethane Clusters
• Our nitromethane dimer and trimer calculations used local minima found by Li, Zhao, and Jing in their application of BSSE corrected DFT/B3LYP with 6-31++G** basis*. This reference also concludes that a proper description of three body effects is needed for accurate determination of potential energy surfaces for bulk nitromethane.
• The most stable dimer configuration was that in which two hydrogen bonds of length 2.427Å are formed while trimer involved a ring structure in which the three hydrogen bonds of lengths 2.329Å, 2.313Å, and 2.351Å. This configuration for the dimer minimum is also supported by CP corrected SDQ-MBPT/DZP in which the hydrogen bonding distance is found to be 2.25Å**.
• With TH-CCSD we observe the formation of methoxy radical in the dimer and the formation of methylnitrite in the trimer, similar to predicted unimolecular mechanisms found at the G2MP2/B3LYP/6-311++G(2d,2p) level of theory ***.
* J. Li, F. Zhao, and F. Jing, JCC 24 (2003) 345.** S. J. Cole, K. Szalewicz, G. D. Purvis III, and R. J. Bartlett, JCP 12 (1986) 6833. S. J. Cole, K. Szalewicz, and R. J. Bartlett, IJQC (1986) 695.*** W.F. Hu, T.J. He, D.M. Chen, and F.C. Liu, JPCA 106 (2002) 7294.
Breaking of H-Bonds in Nitromethane Dimers with Frozen Monomers
SAPT equilibrium OH distance*
Nitromethane Decomposition in DimerH3CNO2
* + H3CNO2 H3CNO + H3CO + NO2
UHF TH-CCSD predicts thatrearrangement
occurs when C-N bond is 2.42 Å
UHF AM1 prediction
* Indicates bond rupture
Nitromethane Rearrangement in TrimerH3CNO2* + 2 H3CNO2 3H3CONO
UHF AM1 prediction
* Indicates bond rupture
UHF TH-CCSD predicts thatrearrangement
occurs when C-N bond is 1.94 Å
0
0.5
1
1.5
2
2.5
3
% e
rro
r fr
om
CC
SD
/TZ
P
R_CH R_CN R_NO AHCN AONC
Property
TH/CCSD
AM1
Equilibrium Geom of NMT
Force of C-N bond breaking
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
1.3 1.8 2.3 2.8
R (A)
F (
H/B
oh
r)
B3LYP/6-31G
AM1
TH-CCSD
TNAZ C-N Bond Rupture
*C-N bond breaking trans to N-NO2
SUMMARY
•Derived and illustrated the NO-CC methodwith applications to DMNA and RDX. Savings is ~7 out of theoretical 16. With rapid processors, will make state-of-the-art CC resutls possible ina week, instead of a year.
•Awaiting analytical gradients (programmed) to enable geometry and transition state searches.
•Illustrated tranfer Hamiltonian approach to retain the accuracy of CC theory, but for much more complicated representations of the condensed phase.
•Establsihed rigor of the theory. We are working on alternative,and better realizations of the concept.
Energy of N-N bond breaking
-20
0
20
40
60
80
100
1.1 1.6 2.1 2.6 3.1
R (A)
(E-E
eq)
(kca
l/m
ol)
CCSD(T)/cc-PVTZ
B3LYP/6-31G*
⇒ Forces from DFT are qualitatively and quantitatively wrong at non-equilibrium geometries!
Nitramine: Dangers of DFT