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Chemistry at Harvard Molecular Mechanics ______ LECTURE 24 CHARMM course 21-MAR-2006 CHARMM ______ Chemistry at HARvard Molecular Mechanics _ ___ _ _ Twenty-Fourth Lecture: _____________________________________________________________ Combined QM/MM Modeling and Simulation Documentation qmmm.doc qchem.doc gamess.doc gamess-uk.doc sccdftb.doc mndo97.doc cadpac.doc diesel.doc charmmrate.doc cheq.doc flucq.doc Examples ------------------------------------------------------- None Available ------------------------------------------------------- No Homework Problem _____________________________________________________________ QM/MM Modeling Approach ● Couple quantum mechanics and molecular mechanics approaches (e.g. QM/MM) ● QM treatment of the active site – reacting center – excited state processes (e.g. spectroscopy) – problem structures (e.g. complex transition metal center) ● Classical MM treatment of environment – enzyme structure – explicit solvent molecules – bulky organometallic ligan ds General QM/MM Methodology ● The QM/MM potential energy is implemented via solving the Schrödinger equation with an effective Hamiltonian H eff r , Ra , RM = E Ra ,R M r , Ra , RM ● Where Heff and HQM/MM are defined as.... H eff = H QM H MM H QM / MM qM Z A qM A A, M B A, M H QM / MM = −∑ ∑ ∑ 12 − 6 i , M ri M A, M R A, M A , M R A , M R A , M ● The total energy is then: 〈 ∣H QM H QM/ MM∣ 〉 Warshel, A.; Levitt, M. J. Mol. Biol. 1976, 103, 227-249. Singh, U. C.; Kollman, P. A. J. Comp. Chem. 1986, 7, 718-730. Etot = EMM Field, M.J.; Bash, P.A.; Karplus, M. J. Comp. Chem. 1990, 11, 700-733. Lyne, P.D.; Hodoscek, M.; Karplus, M. J. Phys. Chem. A 1993, 103, 3462-3471. 〈∣ 〉 Eurenius, K.P.; Chatfield, D.C.; Brooks, B.R.; Hodoscek, M. Int. J. Quant. Chem. 1996, 60, 1189. Implementations of QM/MM Implementations of QM/MM Implementations of QM/MM ● Semi-empirical ● Pros: – AM1 – Fast – PM3 – Simpler than ab initio QM methods – MNDO – In many cases describes – PDP3 (PDDG/PM3) system(s) correctly – PDMN (PDDG/MNDO) ● Cons: – SCCDFTB – Reduced accuracy – Only restricted wavefunctions (caveat...) – Parameters – Ground state methods – Only valence electrons treated explicitly Implementations of QM/MM ● Ab initio ● Pros: – HF – Accuracy – DFT ● Much better description of wavefunction (e.g. ● Pure: BLYP correlation) ● Hybrid: B3LYP – Flexibility ● RI methods ● Cons: – MP2 – Performance ● Local methods ● Speed ● RI methods ● System size limitations – CCSD – More complex than semi- – Multireference methods empirical methods ● CASSCF ● Spin-flip ● EOM Additional Implementations of QM/MM ● Empirical Valence Bond ● SCCDFTB (EVB) – Empirical approximation to – Approximates QM DFT (B3LYP) interactions – QM/MM implementation – Mixes valence bond via CHARMM configurations – Approximately the same ● Must define bonding cost as AM1, PM3 patterns in “QM” ● But better accuracy system – Actively being developed – Requires parameterization ● Q. Cui ● M. Elstner Additional Implementations of QM/MM ● ONIOM: Morokuma et al. – QM/MM, QM/QM, QM/QM/MM and QM/QM/QM – Subtractive method – Pro: Easy to use! – Widely available: Gaussian, Q-Chem 3.0 Additional Implementations of QM/MM ● CPMD: Car-Parrinello Molecular Dynamics – Employees DFT ● Mostly restricted to pure DFT functionals – QM wavefunction is propagated through the dynamics – Electronic motion can become coupled to the nuclear motion ● Should not happen in the Born-Oppenheimer approximation – Employees plane wave basis functions ● Needs a lot of them to describe the wave function accurately – Employees Effective Core Potentials (ECP) QM/MM Boundary Treatments QM/MM Boundary Treatments ● Single Link Atom (Singh and Kollman) ● Double Link Atom (Brooks and coworkers) – Gaussian Blur ● Generalized Hybrid Orbital (GHO) Approximation – Gao and coworkers ● Local Self-Consistent Field (LSCF) – Rivail and coworkers ● Frozen Orbital Approximation – Friesner and coworkers ● Pseudobond Methods – Yang and coworkers Amara and Field; Theor Chem Acc (2003)109:43–52 QM/MM Boundary Treatments QM/MM Boundary Treatments EXGR: QM/MM Electrostatics for link host groups removed Use CHARMM's lone pair facility to keep H (Link) atoms in proper orientation QM/MM Boundary Treatments QM/MM Boundary Treatments DGMM: Delocalized Gaussian MM charges (e.g. Blurred Gaussian functions) QM/MM Boundary Treatments Generalized Hybrid Orbital (GHO) Local Self-Consistent Field (LSCF) Frozen Orbital Approximation Pseudobond Method CHARMM Element doc/qmmm.doc 1.1 # File: qmmm, Node: Top, Up: (chmdoc/commands.doc), Next: Syntax Combined Quantum and Molecular Mechanical Hamiltonian A combined quantum (QM) and molecular (MM) mechanical potential allows for the study of condensed phase chemical reactions, reactive intermediates, and excited state isomerizations. This is necessary since standard MM force fields are parameterized with experimental data on the potential energy surface which may be far removed from the region of interest, or have the wrong analytical form. A full decription of the theory and application is given in J. Computational Chemistry (1990) 6, 700. The effective Hamiltonian, Heff, describes the energy and forces on each atom. It is treated as a sum of four terms, Hqm, Hmm, Hqm/mm, and Hbrdy. Hqm Describes the quantum mechanical particles. The semi- empirical methods available are AM1, PM3 and MNDO. All treat hydrogen, first row elements plus silicon, phosphorus, sulfur, and the halogens. MNDO has additional parameters for aluminium, phosphorus, chromium, germanium, tin, mercury, and lead. Full details concerning these theoretical methods can be found in Dewar's original papers, JACS (1985) 107, 3902, JACS (1977) 99, 4899, Theoret. Chim. Acta. (1977) 46, 89. Hmm The molecular mechanical Hamiltonian is independent of the coordinates of the electrons and nuclei of the QM atoms. CHARMM22 is used to treat atoms in this region. Hqm/mm The combined Hamiltonian describes how QM and MM atoms interact. This is composed of two electrostatic and one van der Waals terms. Each MM atom interacts with both the electrons and nuclei of the QM atoms (therefore two terms). The van der Waals term is necessary since some MM atoms possess no charge and would consequently be invisible to the QM atoms, and in other cases often provide the only difference in the interaction (Cl vs. Br). Hbrdy The usual periodic or stochastic boundary conditions are implemented. The quantum mechanical package MOPAC 4.0 was interfaced with CHARMM22. This was provided by James P. P. Stewart from the Air Force Academy. There are several limitations with the current program implemntation. The current plan is to update the quantum mechanical procedures to MOPAC 6.0, to include vibrational analysis using analytical functions, with the possibility of using free energy perturbation. * Menu: 1) QUANTUM module * Syntax:: Syntax of QM/MM Commands * Description:: Brief Description of Quantum Commands * GLINK:: GHO Method and GLNK Command * DECO:: DECO Command * DAMP:: DAMP Command * PERT:: PERT Command * pBOUNd:: Simple Periodic Boundary Condition * GROUp:: GROUp keyword * CHDYn:: CHDYn keyword * NEWD:: NEWDS Command * EXTE:: EXTErnal File Command * LEPS:: LEPS Command * SVB:: SVB Command * 2DSVB:: 2D Usage of SVB 2) SQUANTM module * SQUANTUM:: SQUANTUM Module * SQM_Syntax:: Syntax of the SQUANTM commands * SQM_Install:: Installation of SQUANTM in CHARMM environment # File: qmmm, Node: Syntax, Up: Top, Previous: Top, Next: Description Syntax for QUANTUM commands QUANtum [atom-selection] [GLNK atom-selection] [LEPS int1 int2 int3] [DECO] [PERT REF0 lambda0 PER1 lambda1 PER2 lambda2 TEMP finalT] [NGUEss int] [NEWD int] ewald-spec [IFIL int] [ITRMax int] [CAMP] [KING] [PULAy] [SHIFt real] [SCFCriteria real] [UHF] [C.I.] [EXCIted] [NMOS int] [MICR int] [TRIPLET|QUARTET|QUINTET|SEXTET] [AM1|PM3|MNDO] [CHARge int] [NOCUtoff] [ALPM real] [RHO0 real] [SFT1 real] [EXCIted] [BIRADical] [C.I.] [ITER] [EIG2] [ENERGY] [ PL ] [DEBUG [1ELEC] [DENSITY] [FOCK] [VECTor]] [LEPS LEPA int LEPB int LEPC int D1AB real D1BC real D1AC real R1AB real R1BC real R1AC real B1AB real B1BC real B1AC real S1AB real S1BC real S1AC real D2AB real D2BC real D2AC real R2AB real R2BC real R2AC real B2AB real B2BC real B2AC real S2AB real S2BC real S2AC real] ewald-spec::= { [ KMAX integer ] } KSQMAX integer { KMXX integer KMXY integer KMXZ integer } MULLiken ADDLinkatom link-atom-name atom-spec atom-spec RELLinkatom link-atom-name atom-spec atom-spec link-atom-name ::= a four character descriptor starting with QQ. atom-spec::= {residue-number atom-name} { segid resid atom-name } { BYNUm atom-number } # File: qmmm, Node: Description, Up: Top, Previous: Syntax, Next: GLNK Description of QUANtum Commands Most keywords preceed an equal sign followed by an appropriate value. A description of each is given below. 1ELECtron The final one-electron matrix is printed out. This matrix is composed of atomic orbitals; the array element between orbitals i and j on different atoms is given by, H(i,j) = 0.5 (beta(i) + beta(j)(overlap(i,j)) The matrix elements between orbitals i and j on the same atom are calculated from the electron-nuclear attraction energy, and also from the U(i) value if i=j. The one-electron matrix is unaffected by (a) the charge and (b) the electron density. It is only a function of the geometry. Abbreviation: 1ELEC. 0SCF The data can be read in and output, but no actual calculation is performed when this keyword is used. This is useful as a check on the input data. All obvious errors are trapped, and warning messages printed. A second use is to convert
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