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

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 }

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.

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."

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." ^_

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 ^_

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 ^

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 .... ^

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. ^

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 ^

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 ...

[ 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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