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

I. INTRODUCTION Nature of problem and our objectives II. NUMERICAL RESULTS Dimethylnitramine 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 OUTLINE

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 Paths Activation Barriers Spectroscopic signatures for intermediates and products Quantum Mechanics II Bi(tri...)molecular reactions Long range (condensed phase, pressure) effects Activation Barriers, Spectroscopy Classical Mechanics-- Representation E(R) Large Molecule QM-- Simplified Representation of H(R) Transfer Hamiltonian Electronic State Specific

SEAMLESS WHOLE… FROM QM [(CC) TO (DFT)TO (TH)] TO ADAPTIVE (CHARGE TRANSFER) POTENTIALS, TO CLASSICAL POTENTIALS (CP), AND BACK, ie INSIST THAT E(R) LEADS BACK TO A H(R), THAT GIVES ELECTRONIC DENSITY AND OTHER QM PROPERTIES

Reactions of one H 2 N-NO 2 H 2 N-NO 2  H 2 N. + NO 2.  H. + HN. -NO 2  H 2 N-ONO [  HN=N(O)OH]  3 HN + 1 HONO (  1 HN + 1 HONO) (  3 HN + 3 HONO)

Reactions of two H 2 N-NO 2 Additionally: H 2 N-NO 2 + H 2 N-NO 2  H 2 N-NH 2 + NO 2. + NO 2.  NH 2. + NH 2. + O 2 N-NO 2  H 2 NH + NO 2. + HN. -NO 2  H 2 N. + HONO + HN. -NO 2 Same reactions as before, causing a slight change in the interaction energy with the second H 2 N-NO 2.

Reactions of one Me 2 N-NO 2 Me 2 N-NO 2  Me 2 N. + NO 2.  MeN. -NO 2 + Me.  H 2 C. -N(Me)-NO 2 + H. [  H 2 C=N + (Me)-N(O - )OH]  H 2 C=NMe + HONO

Reactions of two Me 2 N-NO 2 Same reactions as before, causing a slight change in the interaction energy with the second Me 2 N-NO 2. Additionally: Me 2 N-NO 2 + Me 2 N-NO 2  Me 2 N-ONO + Me 2 N. + NO 2.  Me 2 N-NMe 2 + NO 2. + NO 2.  Me 2 N-Me + Me-N. -NO 2 + NO 2.  Me 2 N-N(Me)-NO 2 + Me. + NO 2.  Me 2 N-H + H 2 C. -N(Me)-NO 2 + NO 2.  Me 2 N-CH 2 -N(Me)-NO 2 + H. + NO 2. products from CH 3., H. (HONO, H-Me, …)

Dimethylnitramine

Overview Immediate goals and methods Dimethylnitramine RDX Other Things We Can Do

Goals of Our Calculations  Provide high quality energies (forces where feasible) at points along various reaction coordinates for testing or fitting of faster methods.  Definitive answers for low energy dissociation reactions of dimethylnitramine (and more reliable ones for RDX).  Use nitramine as a test-case since better methods can be used. (More complete work if desired.)  Environmental effects by including second molecules.

How we do it DFT:  generally good minimum geometries  less good for transition states, vdW,...  cheap CCSD(T):  good energies (and other properties)  expensive. Basis set extrapolation:  necessary for high quality energies,...  Single-point energies with basis set extrapolation on DFT/TZ minima and reaction paths.

Basis Set Extrapolations CBSxf: CBS3: CBSxM:  E CBSx-DZ from MBPT(2) CBS2: (PWD) Let’s introduce empirical parameters...

A Broader Test of Basis Set Extrapolation Schemes (H 3 C) 2 N-NO 2, H 2 C=N-CH 3, cis HONO, 2 A 1 NO 2, 2 A 2 " CH 3, H, H 2 C=NH, HCN, NH 3, 2 B 2 NH 2, 3  g - NH, HNO, 2  NO, N 2 O, 3 B 2 CH 2, H 2 CO, CO, CO 2, H 2 O, 2  HO

Definition of CBS2Mf+ E(CBS2Mf)= E(CCSD(T)-fc/cc-pVDZ) *  E MBPT(2)-fc (CBS2 - cc-pVDZ) For enthalpies of formation (riBP86/TZVP freqs.): H(CBS2Mf+)= H(CBS2Mf)  n R * c R c(H 2 )= c(CH 4 )= c(N 2 )= c(O 2 )= Determined by minimizing RMS of  f H c -  f H e. Average error: 0.00 Standard deviation: 0.75 kcal/mol

Properties of the Extrapolation Scheme Standard deviation 0.75 kcal/mol. Using small reference molecules saves more expensive calculations. T 2 diagnostic allows judgement of reliability for every molecule! (Max. T 2 < 0.15 is good. Calculations with larger T 2 may be unreliable.) Anions need diffuse basis sets in the gas-phase.

A Difficult Reaction Path 



r NN =  N-N bond breaks 

riBP86/TZVP Energies of Some Primary Reaction Pathways in kcal/mol DFTCBS2M (H 3 C) 2 N-NO 2   r E  a E  r H  r H (H 3 C) 2 N · + NO 2 · 46~ H 3 C-N-NO 2 · + CH 3 · 83=7984 H 2 C · -N(CH 3 )-NO 2 + H · 96=9097 H 2 C=N-CH 3 ···HONO-1~ H 3 C-N=NO 2 CH 3 13~ H 2 C=N(CH 3 )-NO 2 H (w. H 2 O)(45)=-

DFT Energies of Secondary Reactions  a E w.r.t. [kcal/mol]  r E  a E  r HDMNA (H 3 C) 2 N   3  H 3 C-N + CH 3  74.7= (H 3 C) 2 N   H 2 C  -NH-CH ~ H 2 C  -NH-CH 3  H 2 C=NH + CH 3  25.1~ (85) H 3 C -N  -NO 2  H 2 C  -NH-NO ~39?122 H 2 C  -NH-NO 2  H 2 C=NH + NO 2  -7.9~4?80 (122) {H 3 C -N  -NO 2  H 2 C=NH + NO 2  -15.1~ }122 H 2 C  -NCH 3 -NO 2  H 2 C=NCH 3 + NO 2  -9.1~ H 2 C  -NCH 3 -NO 2  H 2 C=NNO 2 + CH 3  33.1~

A Small Summary  The CBS2Mf+ extrapolation scheme gives enthalpies of formation with an RMS error of 0.75 kcal/mol.  The T 2 diagnostic indicates reliability of results.  While riBP86/TZVP is usually within 5-10 kcal/mol of the CBS2Mf results, the shape of the curves may be quite different.  Many reactions have been calculated at the CBS2Mf level, but this work is not yet complete.

Other Things We Can Do  Calculate triplet states (possibly important for strongly deformed geometries).  Use excited state methods (not quite fire and forget).

RDX

— Gas Phase Dynamics of RDX — (unimolecular thermal decomposition) Purpose: Investigate/Reproduce the findings of Lee et-al 1 with respect to the primary event Methodology: CCG2MP2/SCFFAF 2 (and SCFSCF) 1) Zhao, Hintsa, Lee; JCP (1988) 2) Runge, Cory, Bartlett; JCP (2001)

RDX (H2C-N-NO2) - concertedC3H6N5O4 + NO2 - simple bond rupture Primary Event 1 1) Zhao, Hintsa, Lee; JCP (1988)

2nd-Order Reactant and Transition State C3v C kcal/mol Upper bound

Current Concerted - CCG2MP2 kinetic barrier and reaction swath information generation SBR - Reactant and TS structure optimizations Future Determine the theoretical reaction rates, k(T), and branching ratios of the primary event The future direction of the dynamics work depends on what we learn from the current effort

Compressed Coupled Cluster

Singular Value Decomposition Approach to Coupled Cluster Calculations Osamu Hino 1, Tomoko Kinoshita 2 and Rodney J. Bartlett 1 Quantum Theory Project University of Florida 1 Graduate University for Advanced Studies and Institute for Molecular Science, Japan 2

Application of the coupled cluster method to larger systems → several bottlenecks (CPU, Memory, Disk) Background Integral direct algorithm Parallelization of programs Local Correlation method Important to exploit another approach Use of Singular Value Decomposition Compressed CC method

Singular Value Decomposition (SVD) (1) singular values left singular vectors right singular vectors

Singular Value Decomposition (SVD) (2) A (l) is the closest rank l matrix to A. SVD is a useful mathematical tool because of this remarkable property. If s u (u>l) is nearly equal to zero, we can reconstruct the matrix A without losing much information.

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. 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. Then we can define the approximate cluster operator.

Physical meaning of the procedures (1) MBPT(2): Reduced density matrix for

Application of SVD to the Coupled Cluster Doubles (CCD) Amplitude (3) The CCD equation becomes, Degrees of freedom of the equation 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)…). Tighten the threshold.

・ 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 (1) Apply SVD to the second order triples (2) Create contracted mono-excitation operators (3) Truncate the mono-excitation operator manifold (4) Compressed T3 cluster operator Easy to manipulate T3 amplitude

Compressed CCSDT method (1) Equations (2) Equations for connected triples

Compressed CCSDT-1 method Approximate treatment for the T3 amplitude ・ Easiest to implement ・ Operation count for T3 amplitude scales as K 2 V 2 O ・ Iterative counterparts of CCSD[T] and CCSD(T)

Potenrial Energy Curve (1) (HF, aug-cc-pVDZ, HF-bond stretcing) r(eq)=1.733 bohr  =0.25

Potential Energy Curve (2) (H 2 O, aug-cc-pVDZ, OH-bonds stretching) 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 Resolve issue of comparative energetics among HONO elimination, loss of. NO 2, and NO 2  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 H 2 N-NO 2 et al. (gas-phase) cis HONO, NO 2 ( 2 A 1 ), HN-NO 2 -, NH 3, H 2 N ( 2 B 2 ), HN ( 3  g - ) average error [kcal/mol] B3L/6CBS2MCBS2CBS3 G2CBS-Q all no HN, HN-NO

Relative energy in kcal/mol along possible bimolecular reaction paths C) 2 Me 2 N-NO 2  MeN-NO 2. + Me 2 N-NO 2 Me. r(CN)r(CO)riBP86 MBPT(2)-fc

The Very End