The Effective Fragment Potential Method
The basic idea behind the effective fragment potential
(EFP) method is to replace the chemically inert part of a
system by EFPs, while performing a regular ab initio
calculation on the chemically active part. Here "inert"
means that no covalent bond breaking process occurs. This
"spectator region" consists of one or more "fragments",
which interact with the ab initio "active region" through
non-bonded interactions, and so of course these EFP
interactions affect the ab initio wavefunction. The EFP
particles can be closed shell or open shell (high spin
ROHF) based potentials. The "active region" can use nearly
every kind of wavefunction available in GAMESS.
A simple example of an active region might be a solute
molecule, with a surrounding spectator region of solvent
molecules represented by fragments. Each discrete solvent
molecule is represented by a single fragment potential, in
marked contrast to continuum models for solvation.
The quantum mechanical part of the system is entered in
the $DATA group, along with an appropriate basis. The EFPs
defining the fragments are input by means of a $EFRAG
group, and one or more $FRAGNAME groups describing each
fragment's EFP. These groups define non-bonded
interactions between the ab initio system and the
fragments, and also between the fragments. The former
interactions enter via one-electron operators in the ab
initio Hamiltonian, while the latter interactions are
treated by analytic functions. The only electrons
explicitly treated (with basis functions used to expand
occupied orbitals) are those in the active region, so there
are no new two electron terms. Thus the use of EFPs leads
to significant time savings, compared to full ab initio
calculations on the same system.
There are two types of EFP available in GAMESS, EFP1 and
EFP2. EFP1, the original method, employs a fitted
repulsive potential. EFP1 is primarily used to model water
molecules to study aqueous solvation effects, at the
RHF/DZP or DFT/DZP (specifically, B3LYP) levels, see
references 1-3 and 26, respectively. EFP2 is a more
general method that is applicable to any species, including
water, and its repulsive potential is obtained from first
principles. EFP2 has been extended to include other
effects as well, such as charge transfer and dispersion.
EFP2 forms the basis of the covalent EFP method described
below for modeling enzymes, see reference 14.
Parallelization of the EFP1 and EFP2 models is described
in reference 32.
MD simulations with EFP are described in reference 31.
The ab initio/EFP1, or pure EFP system can be wrapped in
a Polarizable Continuum Model, see references 23, 43, and
50.
terms in an EFP
The non-bonded interactions currently implemented are:
1) Coulomb interaction. The charge distribution of the
fragments is represented by an arbitrary number of charges,
dipoles, quadrupoles, and octopoles, which interact with
the ab initio hamiltonian as well as with multipoles on
other fragments (see reference 2 and 18). It is possible
to use a screening term that accounts for the charge
penetration (reference 17 and 42). This screening term is
automatically included for EFP1. Typically the multipole
expansion points are located on atomic nuclei and at bond
midpoints.
2) Dipole polarizability. An arbitrary number of dipole
polarizability tensors can be used to calculate the induced
dipole on a fragment due to the electric field of the ab
initio system as well as all the other fragments. These
induced dipoles interact with the ab initio system as well
as the other EFPs, in turn changing their electric fields.
All induced dipoles are therefore iterated to self-
consistency. Typically the polarizability tensors are
located at the centroid of charge of each localized orbital
of a fragment. See reference 41.
3) Repulsive potential. Two different forms are used in
EFP1: one for ab initio-EFP repulsion and one for EFP-EFP
repulsion. The form of the potentials is empirical, and
consists of distributed Gaussian or exponential functions,
respectively. The primary contribution to the repulsion is
the quantum mechanical exchange repulsion, but the fitting
technique used to develop this term also includes the
effects of charge transfer. Typically these fitted
potentials are located on each atomic nucleus within the
fragment (see reference 3). In EFP2, polarization energies
can also be augmented by screening terms, analogous to the
electrostatic screening, to prevent "polarization collapse"
(MS in preparation)
For EFP2, the third term is divided into separate analytic
formulae for different physical interactions:
a) exchange repulsion
b) dispersion
c) charge transfer
A summary of EFP2, and its contrast to EFP1 can be found in
reference 18 and 44. The repulsive potential for EFP2 is
based on an overlap expansion using localized molecular
orbitals, as described in references 5, 6, and 9.
Dispersion energy is described in reference 34, and charge
transfer in reference 39 (which supercedes reference 22's
formulae).
EFP2 potentials have no fitted parameters, and can be
automatically generated during a RUNTYP=MAKEFP job, as
described below.
constructing an EFP1
RUNTYP=MOROKUMA assists in the decomposition of inter-
molecular interaction energies into electrostatic,
polarization, charge transfer, and exchange repulsion
contributions. This is very useful in developing EFPs
since potential problems can be attributed to a particular
term by comparison to these energy components for a
particular system.
A molecular multipole expansion can be obtained using
$ELMOM. A distributed multipole expansion can be obtained
by either a Mulliken-like partitioning of the density
(using $STONE) or by using localized molecular orbitals
($LOCAL: DIPDCM and QADDCM). The dipole polarizability
tensor can be obtained during a Hessian run ($CPHF), and a
distributed LMO polarizability expression is also available
($LOCAL: POLDCM).
In EFP1, the repulsive potential is derived by fitting
the difference between ab initio computed intermolecular
interaction energies, and the form used for Coulomb and
polarizability interactions. This difference is obtained
at a large number of different interaction geometries, and
is then fitted. Thus, the repulsive term is implicitly a
function of the choices made in representing the Coulomb
and polarizability terms. Note that GAMESS currently does
not provide a way to obtain these EFP1 repulsive potential.
Since a user cannot generate all of the EFP1 terms
necessary to define a new $FRAGNAME group using GAMESS, in
practice the usage of EFP1 is limited to the internally
stored H2ORHF or H2ODFT potentials mentioned below.
constructing an EFP2
As noted above, the repulsive potential for EFP2 is
derived from a localized orbital overlap expansion. It is
generally recommended that one use at least a double zeta
plus diffuse plus polarization basis set, e.g. 6-31++G(d,p)
to generate the EFP2 repulsive potential. However, it has
been observed that 6-31G(d) works reasonably well due to a
fortuitous cancellation of errors. The EFP2 potential for
any molecule can be generated as follows:
(a) Choose a basis set and geometry for the molecule of
interest. The geometry is ordinarily optimized at your
choice of Hartree-Fock/MP2/CCSD(T), with your chosen basis
set, but this is not a requirement. It is good to recall,
however, that EFP internal geometries are fixed, so it is
important to give some thought to the chosen geometry.
(b) Perform a RUNTYP=MAKEFP run for the chosen molecule
using the chosen geometry in $DATA and the chosen basis set
in $BASIS. This will generate the entire EFP2 potential in
the run's .efp file. The only user-defined variable that
must be filled in is changing the FRAGNAME's group name, to
$C2H5OH or $DMSO, etc. This step can use RHF or ROHF to
describe the electronic structure of the system.
(c) Transfer the entire fragment potential for the molecule
to any input file in which this fragment is to be used.
Since the internal geometry of an EFP is fixed, one need
only specify the first three atoms of any fragment in order
to position them in $EFRAG. Coordinates of any other atoms
in the rigid fragment will be automatically determined by
the program.
If the EFP contains less than three atoms, you can still
generate a fragment potential. After a normal MAKEFP run,
add dummy atoms (e.g. in the X and/or Y directions) with
zero nuclear charges, and add corresponding dummy bond
midpoints too. Carefully insert zero entries in the
multipole sections, and in the electrostatic screening
sections, for each such dummy point, but don't add data to
any other kind of EFP term such as polarizability. This
trick gives the necessary 3 points for use in $EFRAG groups
to specify "rotational" positions of fragments.
current limitations
1. For EFP1, the energy and energy gradient are programmed,
which permits RUNTYP=ENERGY, GRADIENT, and numerical
HESSIAN. The necessary programing to use the EFP gradients
to move on the potential surface are programmed for
RUNTYP=OPTIMIZE, SADPOINT, IRC, and VSCF, but the other
gradient based potential surface explorations such as DRC
are not yet available. Finally, RUNTYP=PROP is also
permissible.
For EFP2, the gradient terms for ab initio-EFP interactions
have not yet been coded, so geometry optimizations are only
sensible for a COORD=FRAGONLY run; that is, a run in which
only EFP2 fragments are present.
2. The ab initio part of the system must be treated with
RHF, ROHF, UHF, the open shell SCF wavefunctions permitted
by the GVB code, or MCSCF. DFT analogs of RHF, ROHF, and
UHF may also be used. Correlated methods such as MP2 and
CI should not be used.
3. EFPs can move relative to the ab initio system and
relative to each other, but the internal structure of an
EFP is frozen.
4. The boundary between the ab initio system and EFP1's
must not be placed across a chemical bond. However, see
the discussion below regarding covalent bonds.
5. Calculations must be done in C1 symmetry at present.
6. Reorientation of the fragments and ab initio system is
not well coordinated. If you are giving Cartesian
coordinates for the fragments (COORD=CART in $EFRAG), be
sure to use $CONTRL's COORD=UNIQUE option so that the ab
initio molecule is not reoriented.
7. If you need IR intensities, you have to use NVIB=2. The
potential surface is usually very soft for EFP motions, and
double differenced Hessians should usually be obtained.
practical hints for using EFPs
At the present time, we have only two internally stored
EFP potentials suitable for general use. These model
water, using the fragment name H2ORHF or H2ODFT. The
H2ORHF numerical parameters are improved values over the
values which were presented and used in reference 2, and
they also include the improved EFP-EFP repulsive term
defined in reference 3. The H2ORHF water EFP was derived
from RHF/DH(d,p) computations on the water dimer system.
When you use it, therefore, the ab initio part of your
system should be treated at the SCF level, using a basis
set of the same quality (ideally DH(d,p), but probably
other DZP sets such as 6-31G(d,p) will give good results as
well). Use of better basis sets than DZP with this water
EFP has not been tested. Similarly, H2ODFT was developed
using B3LYP/DZP water wavefunctions, so this should be used
(rather than H2ORHF) if you are using DFT to treat the
solute. Since H2ODFT water parameters are obtained from a
correlated calculation, they can also be used when the
solute is treated by MP2.
As noted, effective fragments have frozen internal
geometries, and therefore only translate and rotate with
respect to the ab initio region. An EFP's frozen
coordinates are positioned to the desired location(s) in
$EFRAG as follows:
a) the corresponding points are found in $FRAGNAME.
b) Point -1- in $EFRAG and its FRAGNAME equivalent are
made to coincide.
c) The vector connecting -1- and -2- is aligned with
the corresponding vector connecting FRAGNAME points.
d) The plane defined by -1-, -2-, and -3- is made to
coincide with the corresponding FRAGNAME plane.
Therefore the 3 points in $EFRAG define only the relative
position of the EFP, and not its internal structure. So, if
the "internal structure" given by points in $EFRAG differs
from the true values in $FRAGNAME, then the order in which
the points are given in $EFRAG can affect the positioning
of the fragment. It may be easier to input water EFPs if
you use the Z-matrix style to define them, because then you
can ensure you use the actual frozen geometry in your
$EFRAG. Note that the H2ORHF EFP uses the frozen geometry
r(OH)=0.9438636, a(HOH)=106.70327, and the names of its 3
fragment points are ZO1, ZH2, ZH3.
* * *
Building a large cluster of EFP particles by hand can be
tedious. The RUNTYP=GLOBOP program described below has an
option for constructing dense clusters. The method tries
to place particles near the origin, but not colliding with
other EFP particles already placed there, so that the
clusters grow outwards from the center. Here are some
ideas:
a) place 100 water molecules, all with the same coords
in $EFRAG. This will build up a droplet of water
with particles close together, but not on top of
each other, with various orientations.
b) place 16 waters (same coords, all first) followed by
16 methanols (also sharing their same coords, after
all waters). A 50-50 mixture of 32 molecules will
be created, if you choose the default of picking the
particles randomly from the initial list of 32.
c) to solvate a solute, add the solute in the $DATA
group at or near the origin. Add the solvent
molecules near by (same coords is ok), and run
the globop run with RNDINI as demonstrated below.
(optional, add MCTYP=3 to $GLOBOP input)
Example, allowing the random cluster to have 20 geometry
optimization steps:
$contrl runtyp=globop coord=fragonly $end
$globop rndini=.true. riord=rand mcmin=.true.
mctyp=4 nblock=0 $end
$statpt nstep=20 $end
$efrag
coord=cart
FRAGNAME=WATER
O1 -2.8091763203009 -2.1942725073400 -0.2722207394107
H2 -2.3676165499399 -1.6856118830379 -0.9334073942601
H3 -2.1441965467625 -2.5006167998896 0.3234583094693
...repeat this 15 more times...
FRAGNAME=MeOH
O1 4.9515153249 .4286994611 1.3368662306
H2 5.3392575544 .1717424606 3.0555957053
C3 6.2191743799 2.5592349960 .4064662379
H4 5.7024200977 2.7548960076 -1.5604873643
H5 5.6658856694 4.2696553371 1.4008542042
H6 8.2588049857 2.3458272252 .5282762681
...repeat 15 more times...
$end
$water
...give a full EFP2 potential for water...
$end
$meoh
...give a full EFP2 potential for methanol...
$end
Note that the random cluster generation now proceeds into a
full Monte Carlo simulation.
* * *
The translations and rotations of EFPs with respect to
the ab initio system and one another are automatically
quite soft degrees of freedom. After all, the EFP model is
meant to handle weak interactions! Therefore the
satisfactory location of structures on these flat surfaces
will require use of a tight convergence on the gradient:
OPTTOL=0.00001 in the $STATPT group.
The effect of a bulk continuum surrounding the solute
plus EFP waters can be obtained by using the PCM model, see
reference 23 and 43. To do this, simply add a $PCM group
to your input, in addition to the $EFRAG. The simultaneous
use of EFP and PCM allows for gradients, so geometry
optimization can be performed.
global optimization
If there are a large number of particles to move (EFP
and/or FMO and/or atom groups), it is difficult to locate
the lowest energy structures by hand. Typically these are
numerous, and one would like to have a number of them, not
just the very lowest energy. The RUNTYP of GLOBOP contains
a Monte Carlo procedure to generate a random set of
starting structures to look for those with the lowest
energy at a single temperature. If desired, a simulated
annealing protocol to cool the temperature may be used.
These two procedures may be combined with a local minimum
search, at some or all of the randomly generated
structures. The local minimum search is controlled by the
usual geometry optimizer, namely $STATPT input, and thus
permits the optimization of any ab initio atoms.
The Monte Carlo procedure by default uses a Metropolis
algorithm to move just one of the fragments. The method of
Parks to move all fragments simultaneously is also allowed.
The present program was used to optimize the structure
of water clusters. Let us consider the case of the twelve
water cluster, for which the following ten structures were
published by Day, Pachter, Gordon, and Merrill:
1. (D2d)2 -0.170209 6. (D2d)(C2) -0.167796
2. (D2d)(S4) -0.169933 7. S6 -0.167761
3. (S4)2 -0.169724 8. cage b -0.167307
4. D3 -0.168289 9. cage a -0.167284
5. (C1c)(Cs) -0.167930 10. (C1c)(C1c) -0.167261
A test input using Metropolis style Monte Carlo to examine
300 geometries at each temperature value, using simulated
annealing cooling from 200 to 50 degrees, and with local
minimization every 10 structures was run ten times. Each
run sampled about 7000 geometries. One simulation found
structure 2, while two of the runs found structure 3. The
other seven runs located structures with energy values in
the range -0.163 to -0.164. In all cases the runs began
with the same initial geometry, but produced different
results due to the random number generation used in the
Monte Carlo. Clearly one must try a lot of simulations to
be confident about having found most of the low energy
structures. In particular, it is good to try more than one
initial structure, unlike what was done in this test.
Ab initio atoms can be addressed using FMO, either in
multiple fragments, or perhaps a single large fragment.
Alternatively, ab initio atoms can be put into groups and
used directly in globop, which for small systems has a
lower overhead than FMO. In the case of large molecules
separated into multiple fragments, the keywords NPRBND,
PRSEP, IBNDS, and INDEP are applicable. These specify the
atoms in each set of fragments or groups whose bond is cut
in the fragmentation process. The paired atoms are
constrained during the Monte Carlo procedure to ensure that
the bond is not spacially broken. In the case where a
fragment that is being translated or rotated is paired with
two or more fragments, the movement is repeated on all
attached fragments, after randomly choosing which pair is
the starting point. For example, given a molecule split
into five fragments such that:
A-B-C-D-E
where A,B,C,D,E are the fragments. If C is chosen for a
translation, either B or D will be randomly chosen to be
the starting pair. When B is chosen as the starting pair,
C, D, and E will all be translated by the same amount:
A-B--C-D-E
which maintains the relative position of C, D, and E.
Setting INDEP=1 will not propagate the translation:
A-B--CD-E
So that only C is moved.
The same approach is used for rotations. Since a small
translation or rotation can result in a significant change
in the total system, it is advised that case be taken when
using solvent molecules and to the size of boundary
conditions. If a propagated movement moves a fragment
outside the boundary, a warning will be printed and the
step will be discarded as a proximity alert. Also, the
pair binding is not implemented for RNDINI=.TRUE. To
initialize a set of solvent molecules around pair bonded
fragments, include the pair bonded fragments in IFXFMO.
The Metrpolis Monte Carlo procedure involves the movement
of groups that are internally rigid. To introduce some
internal flexibility for FMO and ab initio groups, a
secondary Monte Carlo search where the entire system is
held rigid while the atoms in one group are moved is
implemented. The secondary Monte Carlo occurs when a FMO
or ab initio group is translated and occurs for that group.
The lowest energy internal configuration for the secondary
Monte Carlo is used when evaluating the step of the primary
Monte Carlo search. The temperature at which the secondary
Monte Carlo is used in the case of simulated annealing is
set by SMTEMP and the number of steps in each secondary
search is given by NSMTP. To turn on this feature, set the
values of SMTEMP and NSMTP to non-zero values.
Monte Carlo references:
N.Metropolis, A.Rosenbluth, A.Teller
J.Chem.Phys. 21, 1087(1953).
G.T.Parks Nucl.Technol. 89, 233(1990).
Monte Carlo with local minimization:
Z.Li, H.A.Scheraga
Proc.Nat.Acad.Sci. USA 84, 6611(1987).
Simulated annealing reference:
S.Kirkpatrick, C.D.Gelatt, M.P.Vecci
Science 220, 671(1983).
The present program is described in reference 15. It is
patterned on the work of
D.J.Wales, M.P.Hodges Chem.Phys.Lett. 286, 65-72 (1998).
QM/MM across covalent bonds
Recent work by Visvaldas Kairys and Jan Jensen has made
it possible to extend the EFP methodology beyond the simple
solute/solvent case described above. When there is a
covalent bond between the portion of the system to be
modeled by quantum mechanics, and the portion which is to
be treated by EFP multipole and polarizability terms, an
additional layer is needed in the model. The covalent
linkage is not so simple as the interactions between closed
shell solute and solvent molecules. The "buffer zone"
between the quantum mechanics and the EFP consists of
frozen nuclei, and frozen localized orbitals, so that the
quantum mechanical region sees a orbital representation of
the closest particles, and multipoles etc. beyond that.
Since the orbitals in the buffer zone are frozen, it need
extend only over a few atoms in order to keep the orbitals
in the fully optimized quantum region within that region.
The general outline of this kind of computation is as
follows:
a) a full quantum mechanics computation on a system
containing the quantum region, the buffer region,
and a few atoms into the EFP region, to obtain the
frozen localized orbitals in the buffer zone.
This is called the "truncation run".
b) a full quantum mechanics computation on a system
with all quantum region atoms removed, and with
the frozen localized orbitals in the buffer zone.
The necessary multipole and polarizability data
to construct the EFP that will describes the EFP
region will be extracted from the wavefunction.
This is called the "MAKEFP run". It is possible
to use several such runs if the total EFP region
is quite large.
c) The intended QM/MM run(s), after combining the
information from these first two types of runs.
As an example, consider a protonated lysine residue
which one might want to consider quantum mechanically in a
protein whose larger parts are to be treated with an EFP.
The protonated lysine is
NH2
+ /
H3N(CH2)(CH2)(CH2)--(CH2)(CH)
\
COOH
The bonds which you see drawn show how the molecule is
partitioned between the quantum mechanical side chain, a
CH2CH group in the buffer zone, and eventually two
different EFPs may be substituted in the area of the NH2
and COOH groups to form the protein backbone.
The "truncation run" will be on the entire system as you
see it, with the 13 atoms in the side chain first in $DATA,
the 5 atoms in the buffer zone next in $DATA, and the
simplified EFP region at the end. This run will compute
the full quantum wavefunction by RUNTYP=ENERGY, followed by
the calculation of localized orbitals, and then truncation
of the localized orbitals that are found in the buffer zone
so that they contain no contribution from AOs outside the
buffer zone. The key input groups for this run are
$contrl
$truncn doproj=.true. plain=.true. natab=13 natbf=5 $end
This will generate a total of 6 localized molecular
orbitals in the buffer zone (one CC, three CH, two 1s inner
shells), expanded in terms of atomic orbitals located only
on those atoms.
The truncation run prepares template input files for
the next run, including adjustments of nuclear charges at
boundaries, etc.
The "MAKEFP" run drops all 13 atoms in the quantum
region, and uses the frozen orbitals just prepared to
obtain a wavefunction for the EFP region. The carbon atom
in the buffer zone that is connected to the now absent QM
region will have its nuclear charge changed from 6 to 5 to
account for a missing electron. The key input for this
RUNTYP=MAKEFP job is the six orbitals in $VEC, plus the
groups
$guess guess=huckel insorb=6 $end
$mofrz frz=.true. ifrz(1)=1,2,3,4,5,6 $end
$stone
QMMMbuf
$end
which will cause the wavefunction optimization for the
remaining atoms to optimize orbitals only in the NH2 and
COOH pieces. After this wavefunction is found, the run
extracts the EFP information needed for the QM/MM third
run(s). This means running the Stone analysis for
distributed multipoles, and obtaining a polarizability
tensor for each localized orbital in the EFP region.
The QM/MM run might be RUNTYP=OPTIMIZE, etc. depending
on what you want to do with the quantum atoms, and its
$DATA group will contain both the 13 fully optimized atoms,
and the 5 buffer atoms, and a basis set will exist on both
sets of atoms. The carbon atom in the buffer zone that
borders the EFP region will have its nuclear charge set to
4 since now two bonding electrons to the EFP region are
lost. $VEC input will provide the six frozen orbitals in
the buffer zone. The EFP atoms are defined in a fragment
potential group.
The QM/MM run could use RHF or ROHF wavefunctions, to
geometry optimize the locations of the quantum atoms (but
not of course the frozen buffer zone or the EFP piece). It
could remove the proton to compute the proton affinity at
that terminal nitrogen, hunt for transition states, and so
on. Presently the gradient for GVB and MCSCF is not quite
right, so their use is discouraged.
Input to control the QM/MM preparation is $TRUNCN and
$MOFRZ groups. There are a number of other parameters in
various groups, namely QMMMBUF in $STONE, MOIDON and POLNUM
in $LOCAL, NBUFFMO in $EFRAG, and INSORB in $GUESS that are
relevant to this kind of computation. For RUNTYP=MAKEFP,
the biggest choices are LOCAL=RUEDENBRG vs. BOYS, and
POLNUM in $LOCAL, otherwise this is pretty much a standard
RUNTYP=ENERGY input file.
Source code distributions of GAMESS contain a directory
named ~/gamess/tools/efp, which has various tools for EFP
manipulation in it, described in file readme.1st. A full
input file for the protonated lysine molecule is included,
with instructions about how to proceed to the next steps.
Tips on more specialized input possibilities are appended
to the file readme.1st.
Simpler potentials
Since the EFP model's electrostatics is a set of
distributed multipoles (monopole to octopole) and
distributed polarizabilities (dipole), it is possible to
generate some water potentials found in the literature by
setting many EFP terms to zero. It is also necessary to
provide a Lennard-Jones 6-12 repulsive potential, and then
make a choice to follow the EFP1 type formula for QM/EFP
repulsion. Accordingly, EFP1 type calculations can be made
with the following water potentials,
FRAGNAME=SPC, SPCE, TIP5P, TIP5PE, or POL5P
The Wikipedia page
http://en.wikipedia.org/wiki/Water_model
defines the first four of these, which are not polarizable
potentials. The same web site references the primary
literature, so that is not repeated here. POL5P is a
polarizable potential, with parameters given by
D.Si and H.Li J.Chem.Phys. 133, 144112/1-8(2010)
references
The first paper is more descriptive, while the second
presents a very detailed derivation of the EFP1 method.
Reference 18 is an overview article on EFP2. Reference 44
is the most recent review.
The model development papers are: 1, 2, 3, 5, 6, 9, 14,
17, 18, 22, 23, 26, 31, 32, 34, 39, 41, 42, 43, 44, 46, 50,
51, 55, 57, 58.
1. "Effective fragment method for modeling intermolecular
hydrogen bonding effects on quantum mechanical
calculations"
J.H.Jensen, P.N.Day, M.S.Gordon, H.Basch, D.Cohen,
D.R.Garmer, M.Krauss, W.J.Stevens in "Modeling the
Hydrogen Bond" (D.A. Smith, ed.) ACS Symposium Series
569, 1994, pp 139-151.
2. "An effective fragment method for modeling solvent
effects in quantum mechanical calculations".
P.N.Day, J.H.Jensen, M.S.Gordon, S.P.Webb,
W.J.Stevens, M.Krauss, D.Garmer, H.Basch, D.Cohen
J.Chem.Phys. 105, 1968-1986(1996).
3. "The effective fragment model for solvation: internal
rotation in formamide"
W.Chen, M.S.Gordon, J.Chem.Phys., 105, 11081-90(1996)
4. "Transphosphorylation catalyzed by ribonuclease A:
Computational study using ab initio EFPs"
B.D.Wladkowski, M. Krauss, W.J.Stevens
J.Am.Chem.Soc. 117, 10537-10545(1995)
5. "Modeling intermolecular exchange integrals between
nonorthogonal orbitals"
J.H.Jensen J.Chem.Phys. 104, 7795-7796(1996)
6. "An approximate formula for the intermolecular Pauli
repulsion between closed shell molecules"
J.H.Jensen, M.S.Gordon Mol.Phys. 89, 1313-1325(1996)
7. "A study of aqueous glutamic acid using the effective
fragment potential model"
P.N.Day, R.Pachter J.Chem.Phys. 107, 2990-9(1997)
8. "Solvation and the excited states of formamide"
M.Krauss, S.P.Webb J.Chem.Phys. 107, 5771-5(1997)
9. "An approximate formula for the intermolecular Pauli
repulsion between closed shell molecules. Application
to the effective fragment potential method"
J.H.Jensen, M.S.Gordon
J.Chem.Phys. 108, 4772-4782(1998)
10. "Study of small water clusters using the effective
fragment potential method"
G.N.Merrill, M.S.Gordon J.Phys.Chem.A 102, 2650-7(1998)
11. "Solvation of the Menshutkin Reaction: A Rigourous
test of the Effective Fragement Model"
S.P.Webb, M.S.Gordon J.Phys.Chem.A 103, 1265-73(1999)
12. "Evaluation of the charge penetration energy between
nonorthogonal molecular orbitals using the Spherical
Gaussian Overlap approximation"
V.Kairys, J.H.Jensen
Chem.Phys.Lett. 315, 140-144(1999)
13. "Solvation of Sodium Chloride: EFP study of NaCl(H2O)n"
C.P.Petersen, M.S.Gordon
J.Phys.Chem.A 103, 4162-6(1999)
14. "QM/MM boundaries across covalent bonds: frozen LMO
based approach for the Effective Fragment Potential
method"
V.Kairys, J.H.Jensen J.Phys.Chem.A 104, 6656-65(2000)
15. "A study of water clusters using the effective fragment
potential and Monte Carlo simulated annealing"
P.N.Day, R.Pachter, M.S.Gordon, G.N.Merrill
J.Chem.Phys. 112, 2063-73(2000)
16. "A combined discrete/continuum solvation model:
Application to glycine" P.Bandyopadhyay, M.S.Gordon
J.Chem.Phys. 113, 1104-9(2000)
17. "Evaluation of charge penetration between distributed
multipolar expansions"
M.A.Freitag, M.S.Gordon, J.H.Jensen, W.J.Stevens
J.Chem.Phys. 112, 7300-7306(2000)
18. "The Effective Fragment Potential Method: a QM-based MM
approach to modeling environmental effects in
chemistry"
M.S.Gordon, M.A.Freitag, P.Bandyopadhyay, J.H.Jensen,
V.Kairys, W.J.Stevens J.Phys.Chem.A 105, 293-307(2001)
19. "Accurate Intraprotein Electrostatics derived from
first principles: EFP study of proton affinities of
lysine 55 and tyrosine 20 in Turkey Ovomucoid"
R.M.Minikis, V.Kairys, J.H.Jensen
J.Phys.Chem.A 105, 3829-3837(2001)
20. "Active site structure & mechanism of Human Glyoxalase"
U.Richter, M.Krauss J.Am.Chem.Soc. 123, 6973-6982(2001)
21. "Solvent effect on the global and atomic DFT-based
reactivity descriptors using the EFP model. Solvation
of ammonia." R.Balawender, B.Safi, P.Geerlings
J.Phys.Chem.A 105, 6703-6710(2001)
22. "Intermolecular exchange-induction and charge transfer:
Derivation of approximate formulas using nonorthogonal
localized molecular orbitals."
J.H.Jensen J.Chem.Phys. 114, 8775-8783(2001)
23. "An integrated effective fragment-polarizable continuum
approach to solvation: Theory & application to glycine"
P.Bandyopadhyay, M.S.Gordon, B.Mennucci, J.Tomasi
J.Chem.Phys. 116, 5023-5032(2002)
24. "The prediction of protein pKa's using QM/MM: the pKa
of Lysine 55 in turkey ovomucoid third domain"
H.Li, A.W.Hains, J.E.Everts, A.D.Robertson, J.H.Jensen
J.Phys.Chem.B 106, 3486-3494(2002)
25. "Computational studies of aliphatic amine basicity"
D.C.Caskey, R.Damrauer, D.McGoff
J.Org.Chem. 67, 5098-5105(2002)
26. "Density Functional Theory based Effective Fragment
Potential" I.Adamovic, M.A.Freitag, M.S.Gordon
J.Chem.Phys. 118, 6725-6732(2003)
27. "Intraprotein electrostatics derived from first
principles: Divid-and-conquer approaches for QM/MM
calculations" P.A.Molina, H.Li, J.H.Jensen
J.Comput.Chem. 24, 1971-1979(2003)
28. "Formation of alkali metal/alkaline earth cation water
clusters, M(H2O)1-6, M=Li+, K+, Mg+2, Ca+2: an
effective fragment potential caase study"
G.N.Merrill, S.P.Webb, D.B.Bivin
J.Phys.Chem.A 107, 386-396(2003)
29. "Anion-water clusters A-(H2O)1-6, A=OH, F, SH, Cl, and
Br. An effective fragment potential test case"
G.N.Merrill, S.P.Webb
J.Phys.Chem.A 107,7852-7860(2003)
30. "The application of the Effective Fragment Potential to
molecular anion solvation: a study of ten oxyanion-
water clusters, A-(H2O)1-4"
G.N.Merrill, S.P.Webb J.Phys.Chem.A 108, 833-839(2004)
31. "The effective fragment potential: small clusters and
radial distribution functions"
H.M.Netzloff, M.S.Gordon J.Chem.Phys. 121, 2711-4(2004)
32. "Fast fragments: the development of a parallel
effective fragment potential method"
H.M.Netzloff, M.S.Gordon
J.Comput.Chem. 25, 1926-36(2004)
33. "Theoretical investigations of acetylcholine (Ach) and
acetylthiocholine (ATCh) using ab initio and effective
fragment potential methods"
J.Song, M.S.Gordon, C.A.Deakyne, W.Zheng
J.Phys.Chem.A 108, 11419-11432(2004)
34. "Dynamic polarizability, dispersion coefficient C6, and
dispersion energy in the effective fragment potential
method"
I.Adamovic, M.S.Gordon Mol.Phys. 103, 379-387(2005)
35. "Solvent effects on the SN2 reaction: Application of
the density functional theory-based effective fragment
potential method"
I.Adamovic, M.S.Gordon J.Phys.Chem.A 109, 1629-36(2005)
36. "Theoretical study of the solvation of fluorine and
chlorine anions by water"
D.D.Kemp, M.S.Gordon J.Phys.Chem.A 109, 7688-99(2005)
37. "Modeling styrene-styrene interactions"
I.Adamovic, H.Li, M.H.Lamm, M.S.Gordon
J.Phys.Chem.A 110, 519-525(2006)
38. "Methanol-water mixtures: a microsolvation study using
the Effective Fragment Potential method"
I.Adamovic, M.S.Gordon
J.Phys.Chem.A 110, 10267-10273(2006)
39. "Charge transfer interaction in the effective fragment
potential method" H.Li, M.S.Gordon, J.H.Jensen
J.Chem.Phys. 124, 214108/1-16(2006)
40. "Incremental solvation of nonionized and zwitterionic
glycine"
C.M.Aikens, M.S.Gordon
J.Am.Chem.Soc. 128, 12835-12850(2006)
41. "Gradients of the polarization energy in the Effective
Fragment Potential method"
H.Li, H.M.Netzloff, M.S.Gordon
J.Chem.Phys. 125, 194103/1-9(2006)
42. "Electrostatic energy in the Effective Fragment
Potential method: Theory and application to benzene
dimer"
L.V.Slipchenko, M.S.Gordon
J.Comput.Chem. 28, 276-291(2007)
43. "Polarization energy gradients in combined Quantum
Mechanics, Effective Fragment Potential, and
Polarizable Continuum Model Calculations"
H.Li, M.S.Gordon J.Chem.Phys. 126, 124112/1-10(2007)
44. "The Effective Fragment Potential: a general method
for predicting intermolecular interactions"
M.S.Gordon, L.V.Slipchenko, H.Li, J.H.Jensen
Annual Reports in Computational Chemistry, Volume 3,
pp 177-193 (2007).
45. "An Interpretation of the Enhancement of the Water
Dipole Moment Due to the Presence of Other Water
Molecules"
D.D.Kemp, M.S.Gordon
J.Phys.Chem.A 112, 4885-4894(2008)
46. "Solvent effects on optical properties of molecules: a
combined time-dependent density functional/effective
fragment potential approach"
S.Yoo, F.Zahariev, S.Sok, M.S.Gordon
J.Chem.Phys. 129, 144112/1-8(2008)
47. "Modeling pi-pi interactions with the effective
fragment potential method: The benzene dimer and
substituents"
T.Smith, L.V.Slipchenko, M.S.Gordon
J.Phys.Chem.A 112, 5286-5294(2008)
48. "Water-benzene interactions: An effective fragment
potential and correlated quantum chemistry study"
L.V.Slipchenko, M.S.Gordon
J.Phys.Chem.A 113, 2092-2102(2009)
49. "Ab initio QM/MM excited-state molecular dynamics study
of Coumarin 151 in water solution"
D.Kina, P.Arora, A.Nakayama, T.Noro, M.S.Gordon,
T.Taketsugu Int.J.Quantum Chem. 109, 2308-2318(2009)
50. "Damping functions in the effective fragment potential
method
L.V.Slipchenko, M.S.Gordon
Mol.Phys. 197, 999-1016 (2009)
51. "A combined effective fragment potential-fragment
molecular orbital method. 1. the energy expression"
T.Nagata, D.G.Fedorov, K.Kitaura, M.S.Gordon
J.Chem.Phys. 131, 024101/1-12(2009)
52. "Alanine: then there was water"
J.M.Mullin, M.S.Gordon
J.Phys.Chem.B 113, 8657-8669(2009)
53. "Water and Alanine: from puddles(32) to ponds(49)"
J.M.Mullin, M.S.Gordon
J.Phys.Chem.B 113, 14413-14420(2009)
54. "Structure of large nitrate-water clusters at ambient
temperatures: simulations with effective fragment
potentials and force fields with implications for
atmospheric chemistry"
Y.Miller, J.L.Thoman, D.D.Kemp, B.J.Finlayson-Pitts,
M.S.Gordon, D.J.Tobias, R.B.Gerber
J.Phys.Chem.A 113, 12805-12814(2009)
55. "Quantum mechanical/molecular mechanical/continuum
style solvation model: linear response theory,
variational treatment, and nuclear gradients"
H.Li J.Chem.Phys. 131, 184103/1-8(2009)
56. "Aqueous solvation of bihalide anions"
D.D.Kemp, M.S.Gordon
J.Phys.Chem.A 114, 1298-1303(2010)
57. "Exchange repulsion between effective fragment
potentials and ab initio molecules"
D.D.Kemp, J.M.Rintelman, M.S.Gordon, J.H.Jensen
Theoret.Chem.Acc. 125, 481-491(2010).
58. Modeling Solvent Effects on Electronic Excited States
A.DeFusco, N.Minezawa, L.V.Slipchenko, F.Zahariev,
M.S.Gordon J.Phys.Chem.Lett. 2, 2184-2192(2011)
created on 7/7/2017