CHARMM c30b1 qmmm.doc



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      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:

* Syntax::       Syntax of QM/MM Commands
* Description::  Brief Description of Quantum Commands



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                    Syntax for QUANTUM commands
    
QUANtum [atom-selection] [GLNK atom-selection] [LEPS int1 int2 int3]
        [DECO]
        [PERT REF0 lambda0 PER1 lambda1 PER2 lambda2 TEMP finalT]

        [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] 

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     }




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                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 from one format to  another.
           The input geometry  is printed in various formats at the
           end of a 0SCF calculation.  If NOINTER is absent, cartesian
           coordinates are printed.
           Unconditionally, MOPAC Z-matrix internal coordinates are
           printed, and if AIGOUT is present, Gaussian Z-matrix
           internal coordinates  are  printed. 0SCF should now be used
           in place of DDUM.
   

1SCF       When users want to examine the results of a single SCF  
           calculation of a geometry, 1SCF should be used.  1SCF can 
           be used in conjunction with RESTART, in which case a single
           SCF calculation will be done, and the results printed.
   
           When 1SCF is used on its own (that is, RESTART is not also
           used) then derivatives will only be calculated if GRAD is 
           also specified.  1SCF is helpful in a learning situation.
           MOPAC  normally performs many SCF calculations, and in
           order to minimize output when following the working of the 
           SCF calculation, 1SCF is very useful.

AM1        The AM1 method is to be used.  By default MNDO is run.

PM3        The PM3 method is to be used.  By default MNDO is run.

NOCUtoff   QM/MM cutoffs are disabled, such that the QM region
           interacts with all MM charges. By default the QM region
           only interacts with those charges that are within the
           standard CHARMM nonbond cutoffs.

ANALYTical By default, finite difference derivatives of energy with 
           respect  to geometry  are  used.  If ANALYT is specified,
           then analytical derivatives are used instead.  Since the 
           analytical  derivatives  are  over  Gaussian functions  --
           a  STO-6G  basis set is used -- the overlaps are also over
           Gaussian functions.  This will result in a  very  small
           (less  than  0.1 Kcal/mole)  change  in heat of formation.
           Use analytical derivatives (a) when the mantissa used is
           less than about 51-53  bits, or (b) when comparison with 
           finite difference is desired.  Finite difference
           derivatives are still used when non-variationally optimized
           wavefunctions are present.
   
BIRADical  NOTE:  BIRADICAL is a redundant keyword, and represents a 
           particular configuration  interaction calculation.  
           Experienced users of MECI (q.v.) can duplicate the effect 
           of the  keyword  BIRADICAL by using the MECI keywords 
           OPEN(2,2) and SINGLET.  For molecules which are believed to
           have biradicaloid character the option exists to optimize 
           the lowest singlet energy state which results from the 
           mixing of three states.  These states are, in order, (1) the
           (micro)state  arising from a one electron excitation from
           the HOMO to the LUMO, which is combined with the microstate
           resulting from the time-reversal operator acting on the 
           parent microstate, the result being a full singlet state; 
           (2) the state resulting from de-excitation from the formal 
           LUMO to the HOMO; and (3) the state resulting from the single
           electron in the formal HOMO being excited into the LUMO.
   
                          Microstate 1         Microstate 2      Microstate 3
                     Alpha Beta   Alpha Beta    Alpha  Beta       Alpha  Beta
   
   
           LUMO       *                 *                           *    *
                     ---  ---     ---  ---       ---  ---          ---  ---

                                +
      
           HOMO            *       *              *    * 
                     ---  ---     ---  ---       ---  ---          ---  ---
   
           A configuration interaction calculation is involved  here.
           A  biradical calculation  done  without  C.I. at the RHF 
           level would be meaningless.  Either rotational invariance 
           would be lost, as in the D2d form of ethylene, or very 
           artificial barriers to rotations would be found, such as in
           a methane molecule "orbiting" a D2d ethylene.  In both
           cases the inclusion of limited configuration interaction 
           corrects  the  error.  BIRADICAL should not be used if 
           either the HOMO or LUMO is degenerate; in
           this case, the full  manifold of HOMO x LUMO should be
           included in the  C.I., using MECI options.  The user should
           be aware  of  this  situation.  When the biradical
           calculation is performed correctly, the result is normally 
           a net stabilization.  However,  if  the  first  singlet  
           excited state is much higher in energy than the
           closed-shell ground state, BIRADICAL can lead to a 
           destabilization.  Abbreviation:  BIRAD.  See also MECI,
           C.I., OPEN, SINGLET.
   
CAMKINg

CHARge     When the system being studied is an ion, the charge, n, on
           the ion must be supplied by CHARGE=n.  For cations n can be
           1 or 2 or 3, etc, for anions -1 or -2 or -3, etc.

                                      EXAMPLES
   
           ION               KEYWORD              ION          KEYWORD
   
           NH4(+)           CHARGE=1             CH3COO(-)      CHARGE=-1
           C2H5(+)          CHARGE=1             (COO)(=)       CHARGE=-2
           SO4(=)           CHARGE=-2            PO4(3-)        CHARGE=-3
           HSO4(-)          CHARGE=-1            H2PO4(-)       CHARGE=-1

C.I.       Normally configuration interaction is invoked if any of the
           keywords which imply a C.I. calculation are used, such as 
           BIRADICAL, TRIPLET or QUARTET.  Note that ROOT= does not 
           imply a  C.I. calculation: ROOT= is only used when a C.I. 
           calculation is done.  However, as these implied C.I.'s
           involve the minimum number of configurations practical,
           the user may want to define a larger than minimum C.I., in 
           which case the keyword C.I.=n can be used. When C.I.=n is 
           specified, the n M.O.'s which "bracket" the occupied-
           virtual energy levels will be used.  Thus, C.I.=2 will 
           include both the HOMO and the LUMO, while C.I.=1 (implied 
           for odd-electron  systems)  will  only include the HOMO 
           (This will do nothing for a closed-shell system, and leads 
           to Dewar's half-electron correction for odd-electron
           systems).  Users should be aware of the rapid increase
           in the size of the C.I. with increasing numbers of M.O.'s 
           being  used.  Numbers of microstates implied by the use of 
           the keyword C.I.=n on its own are as follows:
   
           Keyword        Even-electron systems         Odd-electron systems
                       No. of electrons, configs     No. of electrons, configs
                       Alpha   Beta                  Alpha Beta
       
            C.I.=1       1      1          1          1     0             1
            C.I.=2       1      1          4          1     0             2
            C.I.=3       2      2          9          2     1             9
            C.I.=4       2      2         36          2     1            24
            C.I.=5       3      3        100          3     2           100
            C.I.=6       3      3        400          3     2           300
            C.I.=7       4      4       1225          4     3          1225
            C.I.=8   (Do not use unless other keywords also used, see below)
   
           If a change of spin is defined, then larger numbers of
           M.O.'s can be used up to a maximum of 10.  The C.I. matrix 
           is of size 100 x 100.  For calculations involving up to 100
           configurations,  the  spin-states  are exact eigenstates of
           the spin operators.  For systems with more than 100 
           configurations, the 100 configurations of lowest energy are
           used.   See also MICROS and the keywords defining spin-states.
   
           Note that for any system, use of C.I.=5 or higher normally
           implies the diagonalization of a 100 by 100 matrix.  As a 
           geometry optimization using a C.I. requires the derivatives
           to be calculated using derivatives of the C.I. matrix,  
           geometry  optimization with large C.I.'s will require more 
           time than smaller C.I.'s.
   
           Associated keywords:  MECI, ROOT=, MICROS, SINGLET, DOUBLET, etc.
   
   
C.I.=(n,m) In addition to specifying the number of M.O.'s in the
           active space, the number of electrons can also be defined.
           In C.I.=(n,m), n is the number of M.O.s in the active
           space, and m is the number of doubly filled levels to be used.
   
                                        EXAMPLES
           Keywords           Number of M.O.s  No. Electrons
   
           C.I.=2                   2             2 (1)
           C.I.=(2,1)               2             2 (3)
           C.I.=(3,1)               3             2 (3)
           C.I.=(3,2)               3             4 (5)
           C.I.=(3,0) OPEN(2,3)     3             2 (N/A)
           C.I.=(3,1) OPEN(2,2)     3             4 (N/A)
           C.I.=(3,1) OPEN(1,2)     3           N/A (3)
   
           Odd electron systems given in parentheses.
   

DEBUG      Certain keywords have specific output control meanings, such as
           FOCK, VECTORS and DENSITY.  If they are used, only the final 
           arrays of the relevant type are printed.  If DEBUG is supplied,
           then all arrays are printed.   This is useful in debugging
           ITER.  DEBUG can also increase the amount of output produced 
           when certain output keywords are used, e.g. COMPFG.

DCART      The cartesian derivatives which are calculated in DCART for
           variationally optimized systems are printed if the keyword 
           DCART is present.  The derivatives are in units of 
           kcals/Angstrom, and the coordinates are displacements 
           in x, y, and z.

DENSITY    At the end of a job, when the results are being printed, 
           the density matrix  is  also  printed.  For RHF the normal 
           density matrix is printed.  For UHF the sum of the alpha 
           and beta density matrices is printed.
           If density is not  requested, then the diagonal of the 
           density matrix, i.e., the electron density on the atomic 
           orbitals, will be printed.
   
DOUBLet    When a configuration interaction calculation is done,  
           all spin states are calculated simultaneously, either 
           for component of spin = 0 or 1/2.  When only doublet states
           are of interest, then DOUBLET can be specified, and all 
           other spin states, while calculated, are ignored in the 
           choice of root to be used.
   
           Note that while almost every odd-electron system will have 
           a doublet ground state, DOUBLET should still be specified 
           if the desired state must be a doublet.
   
           DOUBLET has no meaning in a UHF calculation.

EIGS
EIG2
ENERGY

ESR        The unpaired spin density arising from an odd-electron
           system can be calculated  both RHF and UHF.  In a UHF 
           calculation the alpha and beta M.O.'s have different
           spatial forms, so unpaired spin density can naturally 
           be present on in-plane hydrogen atoms such as in the phenoxy
           radical.
   
           In the RHF formalism a MECI calculation is performed.  If the
           keywords OPEN and C.I.=  are both absent then only a single
           state is calculated.  The unpaired spin density is then 
           calculated from the state function.  In order to have 
           unpaired spin density on the hydrogens in, for example, 
           the phenoxy radical, several states should be mixed.

EXCIted    The state to be calculated is the first excited open-shell
           singlet state.  If the ground state is a singlet, then the 
           state calculated will be S(1); if the ground state is a 
           triplet, then S(2).  This  state  would normally be the 
           state resulting from a one-electron excitation from the
           HOMO to the LUMO.  Exceptions would be if the lowest
           singlet state were a biradical, in which case the EXCITED 
           state could be a closed shell.
   
           The EXCITED state will be calculated from a BIRADICAL 
           calculation in which the second root of the C.I. matrix is 
           selected.  Note that the eigenvector of the C.I. matrix is 
           not used in the current formalism.
           Abbreviation:  EXCI.
   
           NOTE:  EXCITED is a redundant keyword, and represents a  
           particular configuration interaction calculation.   
           Experienced  users of MECI can duplicate the effect of the 
           keyword EXCITED by using the MECI keywords OPEN(2,2), 
           SINGLET, and ROOT=2.

FOCK

FORCE      A force-calculation is to be run.  The Hessian, that is 
           the  matrix (in millidynes per Angstrom) of second 
           derivatives of the energy with respect to displacements of 
           all pairs of atoms in x, y, and z directions, is
           calculated.  On diagonalization this gives the force 
           constants for the molecule.  The force matrix, weighted 
           for isotopic masses, is then used for calculating the 
           vibrational frequencies.  The system can be characterized
           as a ground state or a transition state by the presence  of
           five (for a linear system) or six eigenvalues which are
           very small (less than about 30 reciprocal centimeters).  A
           transition  state is further characterized by one, and 
           exactly one, negative force constant.
   
           A FORCE calculation is a prerequisite for a THERMO calculation.
           Before a FORCE calculation is started, a check is made to  
           ensure that a stationary point is being used.  This check 
           involves calculating the gradient norm (GNORM) and if it is
           significant, the GNORM will be reduced using BFGS.
   
           All internal coordinates are optimized, and any symmetry 
           constraints are ignored at this point.   An implication of
           this is that if the specification of the geometry relies on
           any angles being exactly 180 or zero degrees, the
           calculation may fail.
   
           The geometric definition supplied to FORCE should not rely 
           on angles or dihedrals  assuming  exact  values.  (The test
           of exact linearity is sufficiently slack that most
           molecules that are linear, such as acetylene and but-2-yne,
           should  not  be  stopped.)  See also THERMO, LET, TRANS,
           ISOTOPE.
   
           In a FORCE calculation, PRECISE will eliminate quartic 
           contamination (part  of  the anharmonicity).  This is
           normally not important, therefore PRECISE should not
           routinely be used.
   
           In a FORCE calculation, the SCF criterion is automatically 
           made more stringent; this is the main cause of the SCF 
           failing  in a FORCE calculation.
   
ITER       The default maximum number of SCF iterations is 200.   
           When  this limit presents difficulty, ITRY=nn can be used 
           to re-define it.  For example, if ITRY=400 is used, the 
           maximum number of iterations will be set to 400. ITRY 
           should normally not be changed until all other means of
           obtaining a SCF have been exhausted, e.g.  PULAY CAMP-KING etc.

INTERP
LPULAY

LARGE      Most of the time the  output invoked by keywords is  
           sufficient. LARGE  will cause less-commonly wanted, but 
           still useful, output to be printed.
   
           1. To save space, DRC and IRC outputs will, by default,
           only print the line with the percent sign.  Other output 
           can be obtained by use of the keyword LARGE, according to 
           the following rules:

           Keyword     Effect
           LARGE       Print all internal and cartesian coordinates 
                       and cartesian velocities.
           LARGE=1     Print all internal coordinates.
           LARGE=-1    Print all internal and cartesian coordinates 
                       and cartesian velocities.
           LARGE=n     Print every n'th set of internal coordinates.
           LARGE=-n    Print every n'th set of internal and cartesian 
                       coordinates and cartesian velocities.
   
           If LARGE=1 is used, the output will be the same as that of
           Version 5.0, when LARGE was not used. If LARGE is used, the
           output will be the same as that of Version 5.0, when LARGE 
           was used.  To save disk space, do not use LARGE.

MECI       At the end of the calculation  details of the Multi Electron
           Configuration Interaction calculation are printed if MECI
           is specified. The state vectors can be printed by
           specifying  VECTORS.  The MECI calculation is either
           invoked automatically, or explicitly invoked by the use of 
           the C.I.=n keyword.

MICRos     The microstates used by MECI are normally generated by use
           of a permutation operator.  When individually defined 
           microstates are desired, then MICROS=n can be used, where 
           n defines the number of microstates to be read in.
   
                          Format for Microstates
   
           After the geometry data plus any symmetry data are read in,
           data defining each microstate is read in, using format
           20I1, one microstate per line.  The microstate data is 
           preceded by the word "MICROS" on a line by itself.   There 
           is at present no mechanism for using MICROS with a reaction path.
   
           For a system with n M.O.'s in the C.I. (use OPEN=(n1,n) or 
           C.I.=n to do this), the populations of the n alpha M.O.'s 
           are defined, followed by the n beta M.O.'s.  Allowed 
           occupancies are zero and one.  For n=6 the closed-shell 
           ground  state would be defined as 111000111000, meaning one
           electron in each of the first three alpha M.O.'s, and one 
           electron in each of the first three beta M.O.'s.
   
           Users are warned that they are responsible for completing 
           any  spin manifolds.  Thus while the state 111100110000 
           is a triplet state with component of spin = 1, the state 
           111000110100, while having a component of spin = 0 is
           neither a singlet nor a triplet.  In order to complete the 
           spin manifold the microstate 110100111000 must also be included.
   
           If a manifold of spin states is not complete, then the 
           eigenstates of the spin operator will not be quantized.  
           When and only when 100 or fewer microstates are supplied, 
           can spin quantization be conserved.

           There are two other limitations on possible microstates.  
           First, the number of electrons in every microstate should 
           be the same.  If they differ, a warning message will be 
           printed, and the calculation continued (but the results
           will almost certainly be nonsense).   Second, the component
           of spin for every microstate must be the same, except for
           teaching  purposes.  Two microstates of different
           components of spin will have a zero matrix element
           connecting them.  No warning will be given as this is a 
           reasonable operation in a teaching situation.  For example, if
           all states arising from two electrons in two levels are to 
           be calculated say for teaching Russel-Saunders coupling, 
           then the following microstates would be used:

            Microstate   No. of alpha, beta electrons  Ms  State
   
              1100            2             0          1   Triplet
              1010            1             1          0   Singlet
              1001            1             1          0   Mixed
              0110            1             1          0   Mixed
              0101            1             1          0   Singlet
              0011            0             2         -1   Triplet
   
           Constraints on the space manifold are just as rigorous, but
           much easier to satisfy.  If the energy levels are
           degenerate, then all components of a manifold of degenerate
           M.O.'s should be either included or excluded.  If only
           some, but not all, components are used, the required 
           degeneracy of the states will be missing.
   
           As an example, for the tetrahedral methane cation, if the user
           supplies the microstates corresponding to a component of
           spin = 3/2, neglecting Jahn-Teller distortion, the minimum 
           number of states that can be supplied is 90 = (6!/(1!*5!))*
           (6!/(4!*2!)).
           
           While the total number of electrons should be the same for all
           microstates, this number does not need to be the same as 
           the number of electrons supplied to the C.I.; thus in the 
           example  above, a cationic state could be 110000111000.
   
           The format is defined as 20I1 so that spaces can be used  
           for empty M.O.'s.

MNDO       The default Hamiltonian within MOPAC is MNDO, with the  
           alternatives of AM1 and MINDO/3.  To use the MINDO/3 
           Hamiltonian the keyword MINDO/3 should be used.  Acceptable
           alternatives to the keyword MINDO/3 are MINDO and MINDO3.

PRECISE    The criteria for terminating all optimizations, electronic and
           geometric, are to be increased by a factor, normally, 100.
           This can be used where more precise results are wanted.  If
           the results are going to be used in a FORCE calculation,
           where the geometry needs to be known quite precisely, then 
           PRECISE is recommended; for small systems the extra cost in
           CPU time is minimal.
   
           PRECISE is not recommended for experienced users, instead 
           GNORM=n.nn and SCFCRT=n.nn are suggested.  PRECISE should
           only very rarely be necessary in a FORCE calculation: all 
           it does is remove quartic contamination, which only affects
           the trivial modes significantly, and is very expensive 
           in CPU time.

PULAy      The default converger in the SCF calculation is to be 
           replaced by Pulay's procedure as soon as the density matrix
           is sufficiently stable.  A considerable improvement in
           speed can be achieved by the use of PULAY.  If a large 
           number of SCF calculations are envisaged, a sample calculation
           using 1SCF and PULAY should be compared with using 1SCF on 
           its own, and if a saving in time results, then PULAY should
           be used in the full calculation.  PULAY should be used with
           care in that its use will prevent the combined package of 
           convergers  (SHIFT,  PULAY  and the CAMP-KING convergers) 
           from automatically being used in the event that the system
           fails to go SCF in (ITRY-10) iterations.
   
           The combined set of convergers very seldom fails.

QUARTet    RHF interpretation:  The desired spin-state is a quartet, 
           i.e., the state with component of spin = 1/2 and spin =
           3/2. When a configuration interaction calculation is done, 
           all spin states of spin equal to, or greater than 1/2 are 
           calculated simultaneously, for component of spin = 1/2.  
           From these states the quartet states are selected when  
           QUARTET is specified, and all other spin states, while 
           calculated, are ignored in the choice of root to be used.
           If QUARTET is used on its own, then a single state, 
           corresponding to an alpha electron in each of three M.O.'s
           is calculated.
   
           UHF interpretation:  The system will have three more alpha 
           electrons than beta electrons.
   
QUINTet    RHF interpretation: The desired spin-state is a quintet,  
           that is, the state with component of spin = 0 and spin = 2.
           When a configuration interaction calculation is done, all 
           spin states of spin equal to, or greater than 0 are 
           calculated simultaneously, for component of spin = 0.
           From these states the quintet states are selected when 
           QUINTET is specified, and the septet states, while 
           calculated, will be ignored in the choice of root to be
           used.  If QUINTET is used on its own, then a single state, 
           corresponding to an alpha electron in each of four M.O.'s
           is calculated.
   
           UHF interpretation:  The system will have three more alpha 
           electrons than beta electrons.

ROOT       The n'th root of a C.I. calculation is to be used in  the
           calculation.  If a keyword specifying the spin-state is
           also present, e.g. SINGLET or TRIPLET, then the n'th root 
           of that state will be selected. Thus ROOT=3 and SINGLET
           will select the third singlet root.  If ROOT=3 is used on
           its own, then the third root will be used, which may be a 
           triplet, the third singlet, or the second singlet (the
           second root might be a triplet).  In normal use, this 
           keyword would not be used.  It is retained for educational 
           and research purposes.  Unusual care should be exercised 
           when ROOT= is specified.
   
SCFCrt     The default SCF criterion is to be replaced by that defined
           by SCFCRT=.  The SCF criterion is the change in energy in  
           kcal/mol on two successive iterations.   Other minor 
           criteria may make the requirements for an SCF slightly more
           stringent.  The SCF criterion can be varied from about
           0.001 to 1.D-25, although numbers in the range 0.0001 to 
           1.D-9 will suffice for most applications.
   
           An overly tight criterion can lead to failure to achieve a 
           SCF, and consequent failure of the run.
   
   
SEXTet     RHF interpretation:  The desired spin-state is a sextet:  
           the state with component of spin = 1/2 and spin = 5/2.
           The sextet states are the highest spin states normally  
           calculable using MOPAC in its unmodified form.  If SEXTET
           is used on its own, then a single state, corresponding to 
           one alpha electron in each of five M.O.'s, is calculated.
           If several sextets are to be calculated, say the second
           or third, then OPEN(n1,n2) should be used.
   
           UHF interpretation:  The system will have five more alpha  
           electrons than beta electrons.

SHIFt      In an attempt to obtain an SCF by damping oscillations
           which slow down the convergence or prevent an SCF being 
           achieved, the virtual M.O. energy levels are shifted up or 
           down in energy by a shift technique.  The principle is that
           if the virtual M.O.'s are changed in energy relative to
           the occupied set, then the polarizability of the occupied  
           M.O.'s  will change pro rata.  Normally, oscillations are 
           due to autoregenerative charge fluctuations.
   
           The SHIFT method has been re-written so that the value of  
           SHIFT changes automatically to give a critically-damped  
           system.  This can result in a positive or negative shift  
           of the virtual M.O. energy levels.  If a non-zero SHIFT 
           is specified, it will be used to start the SHIFT technique,
           rather than the default 15eV.  If SHIFT=0 is  specified,
           the SHIFT technique will not be used unless normal
           convergence techniques fail and the automatic "ALL 
           CONVERGERS..." message is produced.

SINGLet    When a configuration interaction calculation is done, all spin
           states are calculated simultaneously, either for component 
           of spin = 0 or 1/2.  When only singlet states are of
           interest, then SINGLET can be specified, and all other spin
           states, while calculated, are ignored in the choice of root
           to be used.
   
           Note that while almost every even-electron system  will
           have a singlet ground state, SINGLET should still be 
           specified if the desired state must be a singlet.
   
           SINGLET has no meaning in a UHF calculation, but see also TRIPLET.

TRIPLet    The triplet state is defined.  If the system has an odd  
           number of electrons, an error message will be printed.
   
           UHF interpretation.  The number of alpha electrons exceeds 
           that of the beta electrons by 2.  If TRIPLET is not
           specified, then the numbers of alpha and beta electrons are
           set equal.  This does not necessarily correspond to a singlet.
   
           RHF interpretation.
   
           An RHF MECI calculation is performed to calculate the 
           triplet state.  If no other C.I. keywords are used, then 
           only one state is calculated by default.  The occupancy of 
           the M.O.'s in the SCF calculation is defined as 
           (...2,1,1,0,..), that is, one electron is put in each of 
           the two highest occupied M.O.'s.
   
           See keywords C.I.=n and OPEN(n1,n2).

UHF        The unrestricted Hartree-Fock Hamiltonian is to be used.

VECTors    The eigenvectors are to be printed.  In UHF calculations 
           both alpha and beta eigenvectors are printed; in all cases 
           the full set, occupied and virtual, are output.  The
           eigenvectors are normalized to unity, that is the sum of 
           the squares of the coefficients is exactly one.  If DEBUG
           is specified, then ALL eigenvectors on every iteration of  
           every  SCF calculation will be printed.  This is useful in 
           a learning context, but would normally be very undesirable.



File: qmmm ]-[ Node: GLNK
Up: Top -=- Previous: Description -=- Next: LEPS\n

                Description of the GLNK Command

[GLNK atom-selection]

atom-selection: contains a list of atoms that are boundary atoms.

Restrictions: The current implementation of the method requires that
ALL boundary atoms are placed at the end of the QM residue, or at
the end of the QM atom list.  It is also strongly advised to treat
the entire QM fragment as a single residue, without any GROUPping
of atoms.  This is because the delocalized nature of molecular
orbitals does not allow for arbitrarily excluding a particular
fragment or orbitals from interacting with other parts of the system.


Description: In addition to the link atom approach, a generalized 
hybrid orbital (GHO) approach for the treatment of the division across
a covalent bond between the QM and MM region.  The method recognizes
a frontier atom, typically carbon which is the only atom that has
its parameters optimized at this time, both as a QM atom and an MM
atom.  Thus, standard basis orbitals are assigned to this atom.
These atomic orbitals on the frontier atoms are transformed into a
set of equivalent hybrid orbitals (typically the frontier atom is
of sp3 hybridization type).  One of the four hybrid orbitals, which 
points directly to the direction of the neighboring QM atom, is
included in QM-SCF orbital optimizations, and is an active orbital.  
The other three hybrid orbitals are not optimized. Thus, they are the
auxillary orbitals.  Since hybridization (contributions from s and
p orbitals to the hybrid orbitals) is dependent on the local geometry,
change of bond angles will lead to bond polarization in the active
orbital.  Also, since the active orbital is being optimized in the
SCF procedure, charge transfer between the frontier atom and the
QM fragment is allowed.  Consequently, the GHO method provides a
convenient way for smooth transition of charge distribution from the
QM region into the MM region.

The charge density on the auxilary orbitals are determined by equally
distributing the MM partial charge on the frontier atom.  Thus,
P(mu mu) = 1 - q(mm)/3.  The neutral group convention adopted by
the CHARMM force field makes it possible not to alter, to add, or 
to delete any MM charges.  Furthermore, no extra degrees of freedom
is introduced in the GHO approach.

The GHO method based on Unrestricted HF theory (GHO-UHF) is implemented 
at semiempirical level (AM1, PM3) in the quantum module.  With this
extension, GHO boundary treatment can be used for open shell QM fragments
in combined QM/MM calculations.
 
For a GHO-UHF wavefunction, we have two sets of auxiliary hybrid 
orbitals for alpha spin and beta spin electrons respectively.
The charge density assigned to each of these auxiliary hybrid orbitals 
is 0.5(1.0-q(mm)/3.0), while q(mm) denotes the MM partial charge of the 
GHO boundary atom. Similar to GHO-RHF, the hybridization basis
transformation is carried out between the density matrix and Fock matrix,
both for the alpha and the beta sets.
 
Analytical gradients and Mulliken population analysis are also implemented 
for GHO-UHF.

Limitations: The present implementation allows up to 5 QM-boundary
atoms, which uses psuedo-atomic numbers 91-95.  Thus, elements 91
through 95 can not be used in QM calculations.

Reference: Reference made to the following paper, which contains
a more thorough description and discussion of test cases, is appreciated.

Jiali Gao, Patricia Amara, Cristobal Alhambra, and Martin J. Field,
J. Phys. Chem. 102, 4714-4721 (1998). "A Generalized Hybrid Orbital
(GHO) Approach for the Treatment of Link-Atoms using Combined
QM/MM Potentials."



File: qmmm ]-[ Node: LEPS
Up: Top -=- Previous: GLNK -=- Next: Top\n

                Description of the LEPS Command

[LEPS LEPA int LEPB int LEPC int -
 D1AB real D1BC real D1AC real -
 R1AB real R1BC real R1AC reat -
 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]

Description: The motivation behind the semiempirical valence bond term (SEVB)
is to improve the quality of the potential energy surface (PES) when using
semiempirical hamiltonians (AM1 or PM3) to model the reactive event in
enzyme active sites. NDDO based hamiltonias represent a cheap alternative
to describe reactions in enzyme active sites. They allow for a quantum
mechanical description of the active site together with an extensive sampling
of the protein configurational space when combined qmm/mm techniques are used.
However the savings in computer time come with sacrifices in the quality of
the PES due to the NDDO approximation. The SEVB term is introduced in the
hamiltonian of the system to palliate this problem. It contains two extended
London-Eiring-Polany-Sato (LEPS) equations for the three body subsystem
{A,B,C}.  This reduced subsystem mimics the transfer of the particle B
between centers A and C in the active site. In most of the applications
B is a light atom like hydrogen and A and C correspond to the donor and
acceptor sites,

          A-B + C ---> A + B-C

Each of the two extended LEPS functions have different parameters and depend
on the distances r(A-B), r(B-C), and r(A-C). One LEPS potential (V(ref))is
fitted to reproduce high ab initio or experimental data for a model reaction
whilst the second one (V(NDDO)) is fitted to the NDDO hamiltonian in use.
Finally the SEVB correction is introduced in the hamiltonian of the system
as the difference V(ref)-V(NDDO).

Syntaxis: The keyword LEPS in the command line QUANtum turns on the
routine that evaluates the SEVB correction. The three atoms needed to
evaluate the distances r(A-B), r(B-C), and r(A-C) are indicated by,

 LEPA - donor center. 
 LEPB - transferred atom. 
 LEPC - acceptor center.

 int  - corresponds to the psf number of the respective atom.

 The value of the parameters to build the functions V(NDDO) and V(ref) are,

 . for the NDDO LEPS functions,

 D1AB - dissociation energy for the diatomic A-B 
 D1BC - dissociation energy for the diatomic B-C
 D1AC - dissociation energy for the diatomic A-C 
 R1AB - equilibrium distance for the diatomic A-B 
 R1BC - equilibrium distance for the diatomic B-C 
 R1AC - equilibrium distance for the diatomic A-C 
 B1AB - beta exponent for the diatomic A-B 
 B1BC - beta exponent for the diatomic B-C 
 B1AC - beta exponent for the diatomic A-C 
 S1AB - Sato parameter for the diatomic A-B 
 S1BC - Sato parameter for the diatomic B-C 
 S1AC - Sato parameter for the diatomic A-C 

 . for the reference LEPS functions, 

 D2AB - dissociation energy for the diatomic A-B 
 D2BC - dissociation energy for the diatomic B-C
 D2AC - dissociation energy for the diatomic A-C 
 R2AB - equilibrium distance for the diatomic A-B 
 R2BC - equilibrium distance for the diatomic B-C 
 R2AC - equilibrium distance for the diatomic A-C 
 B2AB - beta exponent for the diatomic A-B 
 B2BC - beta exponent for the diatomic B-C 
 B2AC - beta exponent for the diatomic A-C 
 S2AB - Sato parameter for the diatomic A-B 
 S2BC - Sato parameter for the diatomic B-C 
 S2AC - Sato parameter for the diatomic A-C 

 A real value is expected after each one of them.

Limitations: The current implementation is only intended for a single SEVB
correcting term.

Reference: A detailed description of the LEPS potential energy functionals
as well as the application to an enzymatic hydride transfer can be found in, 

C. Alhambra, J. Corchado, M. L. Sanchez, J. Gao & D. G. Truhlar, 
JACS (in press). "Quantum Dynamics of Hydride Transfer in Enzyme
Catalysis."

^_

File: qmmm ]-[ Node: GLNK
Up: Top -=- Previous: LEPS Description -=- Next: PERT\n

                Description of the DECO Command

[DECO]

     The lone command DECO initiates an qm/mm interaction energy
decomposition calculation on the fly during a molecular dynamics simulation
using the QUANtum command.  It is currently implemented only for 
semiempirical Hamiltonians.  The analysis is based on the method reported
in J. Gao and X. Xia, Science, 258, 631 (1992).  It decomposes the total
QM/MM electrostatic interaction energy into a vertical interaction energy
Evert, and a polarization term Epol.  The latter is further separated into
electrostatic stabilization Estab, and charge distortion Edist.  These
terms are defined as follows (Y is the wave function of the qm system
in the presence of mm charges, and Yo is the wave function of the qm
system in the absence of mm charges, i.e., in the gas phase):

Eqm/mm = <Y|Hqm+Hqmmm(elec)|Y>
       = Evert + Epol
Evert  = <Yo|Hqmmm(elec)|Yo>
Epol   = Eqm/mm - Evert

Epol   = Estab + Edist
Estab  = <Y|Hqmmm(elec)|Y> - <Yo|Hqmmm(elec)|Yo>
Edsit  = <Y|Hqm|Y> - <Yo|Hqm|Yo>

where Hqm is the Hamiltonian of the qm system, and Hqmmm(elec) is
the electrostatic part of the QM/MM interaction Hamiltonian.  Note that
the van der Waals term is kept track of separately within CHARMM's
general energy terms.  In addition, the decomposition also averages
the average "gas-phase" energy <Egas> of the QM system during the QM/MM
simulation.  Egas, of course, is NOT the true average gas-phase energy,
but it is one that is restrained by the presence of the MM field.
It is, however, interesting to note that <Egas> - <Yo|Hqm|Yo> gives
the "strain energy" due to geometrical strain in the condensed 
phase/protein environment.  JG 12/00


^_

File: qmmm ]-[ Node: GLNK
Up: Top -=- Previous: DECO Description -=- Next: Top\n

                Description of the PERT Command

[PERT REF0 lambda0 PER1 lambda1 PER2 lambda2 TEMP finalT]

REF0 lambda0     the reference Lambda value in a FEP calculation
PER1 lambda1     the forward perturbation Lambda value in a FEP calculation
PER2 lambda2     the reverse perturbation Lambda value in a FEP calculation
TEMP finalT      the target or final temperature of the MD simulation
                 NOTE: this is required. Otherwise an error will occur.

     The PERT command performs electrostatic free energy decoupling
calculation for QM/MM interactions on the fly of a molecular dynamics
simulation.  The algorithm is based on a method described in J. Gao,
J. Phys. Chem. 96, 537 (1992).  Through a series of simulations, the
electrostatic component of the free energy of solvation can be determined.
See, other free energy simulation documents.

Delta G(L0->L1) = -RT < exp(-[E{H(L1)}-E{H(L0)}]/RT > _E{H(L0)}

where

E{H(Li)} = <Y|Hqm + Li * Hqmmm(elec) + Hqmmm(vdW)|Y>

JG 12/00

^

File: qmmm ]-[ Node: pBOUNd
Up: Top -=- Previous: PERT Description -=- Next: GROUp\n

                 Simple Periodic Boundary Conditions for QM/MM calculations

          This code is an extension of the algorithm already implemented in 
CHARMM for MM calculations. The reason for making this extention is to avoid
duplication of coordinates to save memory in QM/MM calculations.  It takes 
advantage of the minimum image convention for a periodic cubic (or rectangular
or any other shapes) box such that crystallographic images are not required to
be generated in the psf (see images.doc).

[Syntax]

BOUNd {CUBOUNdary } {BOXL <real> } CUTNB <real>

       CUBOUN = CUbicBOUNd
       BOXL   = length of the box edge
       CUTNB  = cutoff for generating "virtual" images

       Note:  QM/MM PBOUND is INCOMPATIBLE with atom based non-bonded list.

RESTRICTIONS:

     1.  Information about the periodic boundary must be given 
         to the program through the command READ IMAGE (see image.doc)

     2.  The system must be centered using commands:
         a)  IMAGE (see image.doc) when solute and solvent
             are small molecules (3-5 atoms) 
         b)  CENT keyword in DYNA command line (see dynamc.doc) when solute is
             a protein or large organic molecule.
      
     3. The mm and  qm/mm nonbonded lists (electrostatic and Van der Waals
        interactions)
        must be generated by groups, i.e:

        update group fswitch vdw vswitched vgroup ...

     4. Compile with PBOUND in pref.dat

Example:

     ...

! Set-up image information for cubic periodic boundaries
! cubig.img file in the /test/data/ directory
set 6 58.93044
set 7 58.93044
set 8 58.93044
open unit 1 read form name cubic.img
read image card unit 1
close unit 1


IMAGe byseg xcen 0.0 ycen 0.0 zcen 0.0 select segid prot end
IMAGe byres xcen 0.0 ycen 0.0 zcen 0.0 select sol end


BOUNd CUBOUND BOXL 58.93044  CUTNB 12.0


UPDAte group  fswitch noextend  cdie vdw vswitched eps 1.0  -
           cutnb 12.0 ctofnb 11.5 ctonnb 10.5 vgroup  WMIN 1.2  -
           inbf 25  imgfrq 1000  cutim 12.0

QUANtum group  sele qms end glnk sele bynu 68:69 end  am1 charge 1 - 
                 scfc 0.000001 

DYNAmics vverlet rest nstep 15000 timestp 0.001 -
                ilbfrq 0 iseed 324239 firstt  239.0 finalt 298.15 -
                teminc 5.0  ihtfrq  5.0   iasor 0 iasvel 1 iscvel 0 -
                ichecw 1 ieqfrq 200 nprint 100 nsavc 00 -
                nose tref 298.15 qref 50.0 isvfrq 100 -
                tstruc 298.15 -
                twindh 5 twindl -5  iprfrq 2000 wmin 0.9 -
                iunrea 9 iunwri 10 iuncrd 11 iunvel -1 kunit -12 -
                CENT ncres 162

    ....

             
^

File: qmmm ]-[ Node: GROUp
Up: Top -=- Previous: pBOUNd -=- Next: CHDYn\n

                Description of the GROUp keyword 

[ GROUp]

      The QM/MM module that was initially implemented into CHARMM allows
for separate QM group and MM group interactions, where a "QM" molecule
can be divided into several groups.  The GROUp option allows the QM 
molecule to be partitioned into separate groups for generating non-bonded
list, but keeps the interactions between the ENTIRE QM molecule and any 
MM group that is whithin the cutoff of any one qm group, avoiding the 
possibility that some MM group only interact with part of the QM molecule.
This is necessary because the QM molecule is not divisible as the wave
function is delocalized over the entire molecule.  (June, 2001)

      See also description of the GLNK keyword.

^

File: qmmm ]-[ Node: CHDYn
Up: Top -=- Previous: GROUp -=- Next: SVB \n

               Description of the CHDYn keyword  

[CHDYn]

     CHDYn allows the computation of average Mulliken population charges 
on quantum atoms during a molecular dynamics simulation. It prints the 
averaged atomic charges at every IPRFRQ steps.
     When CHDYn is used along with DECO it will result in the calculation
of average atomic charges for the same trajectory in the presence of
the MM bath (condensed phase) and absence of the MM charges (gas phase).

RESTRICTIONS: CHDYn is only implemented for molecular dynamics calculations 
              with the Leapfrog Verlet and Velocity Verlet integrators.

TESTCASE : qmfep.inp 

^

File: qmmm ]-[ Node: SVB
Up: Top -=- Previous: CHDYn -=- Next: DAMP \n

               Description of SVB command

[ LEPS SVB LEPA int LEPB int LEPC int -
       D1AB real D1BC real D1AC real -
       R1AB real R1BC real R1AC reat -
       B1AB real B1BC real B1AC real ]  

Description: A simple analytical function is included in combined QM/MM 
potential energy functions using semiempirical Hamiltonian for enzyme
reactions to obtain more accurate energetic results.  The motivation 
behind the simple valence bond (SVB) term is to introduce small energy 
corrections at critical points (reactants, transition state, and products)
on the QM potential energy surface. The underlying assumption is that the
general shape of the QM potential energy surface at the semiempirical level
is in reasonable accord with high-level ab initio result.  The SVB term 
is a simplified version of the semiempirical valence bond term (SEVB) 
invoked by the command LEPS.

The SVB term is a combination of two Morse potentials, which depend on 
the bond distances of the breaking and making bonds, respectively, and 
a coupling term that is typically (but not exclusively) a function of 
the donor-acceptor distance.

Specifically, for the reaction   A-B + C ---> A + B-C   

with r1 = distance A-B
     r2 = distance B-C
     r3 = distance A-C

the SVB correction along a given reaction coordinate that depends on r1 and r2 
is:

VSVB = 1/2 [ M1(r1)+M2(r2) - [(M2(r2)-M1(r1))**2+4V12**2)]**1/2]

where M1(r1) and M2(r2) are  Morse potentials:

M1(r1) = D1AB [ exp(-2*B1AB*(r1-R1AB))-2*exp(-B1AB*(r1-R1AB)) ]

M2(r2) = D1BC [ exp(-2*B1BC*(r2-R1BC))-2*exp(-B1BC*(r1-R1BC)) ] 

and the coupling term has the form:

V12 = D1AC * exp(-B1AC*(r3-R1AC))

where,

D1AB = difference in dissociation energy between the reference calculation 
       or experimental value and the dissociation energy given by 
       semiempirical method (for the AB bond)

D1BC = difference in dissociation energy between reference calculation 
       or experimental value and the dissociation energy given by 
       the semiempirical method (for the BC bond)

B1AB and B1BC = related to the bond force constants  (kij)
              and to the bond dissociation energies (D1ij) by
              B1ij = sqrt (kij/2*D1ij). These values can be obtained from 
              experimentally determined frequencies or from high level
              calculations.

R1AB, R1BC and R1AC = equilibrium bond length for bonds AB, BC, and AC,
                      respectively.
  
D1AC,R1AC  = adjustable parameters to obtain the desired barrier height.

Note: D1AB and D1BC may be also adjusted to obtain the desired reaction energy.
The difference D1AB-D1BC is the relative correction of the product state energy
respect to the reactant state energy. It is recommended to avoid negative values
for these variables.

Reference: A detailed description of the SVB method
as well as the application to the nucleophilic addition reaction catalized by  
haloalkane dehalogenase is found in:

Devi-Kesavan, L.S.; Garcia-Viloca, M.; Gao, J. Theor.Chem.Acc. 2002, in press.


Example:

  ...

QUANtum group  sele qms end glnk sele bynu 68:69 end  am1 charge 1 -
                  scfc 0.000001 -
         LEPS SVB  LEPA 57 LEPB 58 LEPC 13   -   ! atoms involved
         D1AB 36.0   D1BC 15.0   D1AC  15.0 - !  energies
         R1AB   1.101   R1BC   1.1011  R1AC  2.707  - ! equil. bond lenghts
         B1AB   1.393   B1BC   1.409   B1AC  1.0  - !  exponents

  ...



File: qmmm ]-[ Node: DAMP
Up: Top -=- Previous: SVB -=- Next: Top \n


[ DAMP real ]

A simple density damping option is added to the SCF driver for the quantum module.
The motivation of adding this option is to provide a possibility to overcome SCF
convergence difficulties. Currently, this damping accelerator is only used to limit
oscillation behavior in GHO-UHF type calculations.
 
For an SCF iteration with density damping turned on, the actual density matrix used
for next iteration is computed by a linear combination of the current density with
the previous one:
 
       P    = a x P     + (1-a) x P
        i          i-1             i
 
The damping factor "a" is a user defined floating point number between 0 and 1. One
can specify this damping factor as "DAMP a" in the QUANtum command line.
The default of this damping factor is 0.0, i.e., no damping at all. Any
damping factor being less than 0 or greater than 1 will incur a level -5 warning.
 
In the current implementation, several "damped" steps (with a user defined damping
factor "a" ) are carried out until the alpha and beta density matrices 
are partially converged (density changes are smaller than 100 times the density
convergence criterion), then "undamped" steps (a=0.0) follow until the final
convergence is reached.


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