`By K.Kuczera & J.Wiorkiewicz-Kuczera, May 1991`

MOLVIB is a general-purpose vibrational analysis program, suitable for small to medium sized molecules (say of less than 50 atoms). For larger systems the detail of description may be too great.

The main options are:

- the vibrational problem in internal coordinates (GF)
- the vibrational problem in cartesian coordinates (GFX)
- analysis of GAUSSIAN program output (GFX,GAUS)
- analysis of dependencies in internal coordinate sets (G)
- canonic force field calculations (KANO)
- crystal normal mode analysis for k=0 (CRYS)
- generating cartesian displacements along some interesting directions (STEP)
- the vibrational analysis in presence of Drude particles

The different options use mostly the same package of subroutines called in different order. New applications may thus be easily added when necessary.

Of special interest is the symbolic PED analysis package, enabling a clear and condensed overview of the usually complex PED contributions.

```
[SYNTAX MOLVib command]
MOLVib NDI1 int NDI2 int NDI3 int
[NATOm int] [MAXSymbol int] [NGMAx int] [NBLMax int]
[IZMAx int] [NOTOpology] [SECOnd] [PRINt] [FINIte real]
```

The following section describes the keywords of the MOLVib command.

```
NDI1,NDI2,NDI3 are the MOLVIB variables NQ, NIC, NIC0; their definition
here effectively replaces the MOLVIB 'DIM ' card. Two cases:
a. Molecular vibrations
NIC0 - number of primitive internal coordinates (PIC's), this
must correspond to the number of entries following the
'IC' card
NIC - number of IC's left after transformation by first U matrix
If only one U matrix is used, this should be the same
as NQ; if no U matrices used, NQ=NIC=NIC0
NQ - number of vibrational degrees of freedom. Usually this
is the famous number 3*Nat-6 (3*Nat-5), but also separate
symmetry blocks of the vibrational Hamiltonian may be
entered.
b. Crystal vibrations
NIC0 - no. of primitive molecular coords (MC), i.e. external
coords + primitive IC's
NIC - no. of vibrational degrees of freedom = 3*NAT, where
NAT is the total no. of atoms in unit cell
NQ - here =NIC
NATOm - defines the number of atoms in the system. To be used only in
conjunction with the NOTO flag. If NOTO is not provided, the number
of atoms from the PSF will be used in MOLVIB and will override any
values provided here.
IZMAx - needed for 'CRYS' option only - specifies maximum number
of molecules in unit cell. Default is 10.
MAXSymbol, NGMax, NBLMax - dimensions for PED analysis arrays. They
specify the maximum number of symbols, coordinate groups and
symmetry blocks, respectively. Defaults are NQ (NDI1) for all
three. It is recommended not to modify these defaults.
NOTOpology - if flag is present, CHARMM data structures will not
be used, all information required is to be read in inside the module.
If flag is absent, cartesian coordinates, atomic masses and cartesian
force constants from CHARMM may be passed to MOLVIB, as needed.
SECOnd - calculate second derivatives (force constants in cartesian
coordinates) and pass them to MOLVIB.
This is done through a call to the CHARMM routine ENERGY, so all
preconditions for energy (and second derivative) calculations
must be met.
PRINT - flag for test printout of the CHARMM second derivatives being
passed to MOLVIB.
FINIte - finite step size (default 0.01) for numerical calculation of
second derivatives, which is automatically invoked when Drude particles
are present in the system. Note, Drude coordinates are reset to atomic
centers upon leaving the MOLVIB analysis.
```

This data is processed by subroutine MOLINP. As the CHARMM command parser is not used, this input does not conform to CHARMM standards, e.g.

- parameter substitution will not work
- the STREAM command will not work, all commands will be read
- from the current input stream
- OPEN, READ, WRITE, etc. commands will not work
- most entries are not free format

The MOLVIB input consists of a series of blocks; each block consists of a command and an (optional) data structure; i.e. it has the form:

```
command-spec
[data-struc]
command-spec ::== keyword [<int1>] [<int2>] [<int3>] [<int4>]
format: A4,6X,4I5
data-struc ::== one of the MOLVIB input data structures; defined by the
keyword.
```

The list of currently supported keywords folows. One of the first group of keywords must be used first in order to define type of calculation.

Keyword | Interpretation |
---|---|

G | perform redundancy analysis |

GF | solve standard Wilson GF problem |

GAUS | choose GAUSSIAN analysis option |

GFX | vibrational problem in cartesian coordinates |

KANO | determine canonical force field |

CRYS | crystal vibrations for k=0; |

STEP | generate cartesian displacements in a given |

For the remaining keywords, the order is arbitrary:

Keyword | Interpretation |
---|---|

CART | read in cartesian coordinates |

MASA | interpret fourth column of cartesian coord input as A numbers |

MASZ | interpret the above column as Z numbers |

UMAT | read in U Matrix for similarity transformation |

FMAT | read in F matrix |

LX | read in cartesian eigenvectors |

IC | read in internal/external coordinate definitions |

PRNT | set print level |

TEST | set print level |

NULL | control card for ‘G ‘ option with IGLEV=2 |

PED | read in PED data structure |

SCAL | read in scale factor for F matrix |

TRRM | remove translational and rotational contributions to LX |

MNAT | read in the numbers of atoms for each molecule in unit cell |

IFTR | specifies the dimension (and type) of F matrix |

SYMM | read in symmetry blocking data |

EXPF | read in reference frequencies for the system |

FINI | step size for numerical icalculation of second derivatives (applicable to classical Drude oscillator polarizable model only) Note, Drude coordinates are reset to atomic centers upon leaving the MOLVIB analysis. |

END | end input section, perform MOLVIB calculations and |

This section gives a more detailed explanation of the keywords and the associated data structures.

```
keyword Interpretation
G - perform redundancy analysis
<int1> == IGLEV
IGLEV=1 - diagonalize G and write out eigenvalues
and eigenvectors
IGLEV=2 - additionally generate a set of null and
independent coordinates orthogonal to the
initially specified ones
GF - solve standard Wilson GF problem
GAUS - choose GAUSSIAN analysis option
GFX - vibrational problem in cartesian coordinates
KANO - determine canonical force field
<int1> == ICANO
ICANO=1 - preliminary run, just to output the FR
matrix; one of the other keywords must follow
GF, GFX or GAUS - so that FR is evaluated
or just read in as part of those processes.
ICANO=2 - evaluation of the canonic force field FR*
N.B. No U matrix allowed here.
Give: DIMensions, CARTesian coords, IC's and FMAT.
CRYS - crystal vibrations for k=0;
<int1> == IZMOL, <int2> == IFCRYS
IZMOL - no. of molecules in unit cell
IFCRYS=0 (default) - calculation analogous to GFX
STEP - generate cartesian displacements in a given
direction.
<int1> == IFSTEP
<int2> == ISTCOR
<int3> == IFFMAT
<int4> == IFLMAT
Additionally, the card following the 'STEP'
card contains the value of STPSIZ (real,free format)
IFSTEP=1 - cartesian eigenvector no. ISTCOR
(IFSTEP=2 - internal eigenvector no. ISTCOR, not implemented)
(IFSTEP=3 - internal coordinate no. ISTCOR, not implemented)
STPSIZ - step size, e.g. the transformation is
X(I)=X(I)+STPSIZ*LX(I,ISTCOR) for cart. eigenvectors
where LX the columns of LX are normalized.
IFFMAT,IFLMAT - determine the starting point of the
calculation:
IFFMAT=0 and IFLMAT
=1 - start from LX
=2 - start from LS
IFLMAT=0 and IFFMAT
=1 - start from FX
=2 - start from FS
CART - cartesian coordinates for NAT atoms will follow
<int1> == unused
<int2> == IFC
In MOLVIB <int1> usually used to define the number of
atoms NAT. In the CHARMM version, NAT is specified
on the MOLVIB command line (if NOTO flag is used) or
is read from the PSF (if NOTO is absent).
IFC - specifies format for cart. coords:
IFC=0 free format, four real numbers per line
X, Y, Z, and MASS (see below).
IFC=1 CHARMM format; only atom entry lines, no titles
or NATOM field, mass information in WMAIN field.
N.B.
For the 'GAUS' option use GAUSSIANxx CMS coordinates.
FOR THE 'GFX ' option use GAUSSIANxx coordinates in the
Z-matrix orientation.
Mass specification : (1) enter mass in amu as fourth real
number in entry line for each atom. (2) instead of mass
place atomic number Z or mass number A as fourth real
number and subsequently use a 'MASZ' or 'MASA'
control cards. NB. For 'CRYS' NAT should be equal to
no. of atoms in unit cell.
MASA - interpret fourth column of cartesian coord input
as atomic mass numbers (A) ; useful for isotopes, e.g.
a mass of 2.0 will designate D, mass of 15.0 - 15N etc.
MASZ - interpret the above column as atomic numbers (Z)
UMAT - read in U Matrix for similarity transformation
<int1> == IFU
<int2> == INU
<int3> == IUU
<int4> == IZU
IFU - defines format
=0 Schachtschneider/Snyder format only supported
INU = 1/0 - normalize/dont normalize rows of U
IUU - defines FORTRAN unit for U read
if left blank, unit input stream will be used
if >0 then the data should be provided in the correct
FORTRAN file
IZU - multiplicity; usually IZU=(no. of molecules in unit
cell). IZU.GT.1 turns on autogeneration of U for
whole unit cell from the provided values for the first
asymmetric unit.
(see SUBROUTINE RDMAT in MOLVIO)
Details:
Two, one or none U matrices may be supplied on input. These are
(generally) rectangular matrices which perform linear transformations
on internal coordinate sets, of the type
S=U*R ( or S(i) = {sum over j} U(i,j)*R(j) ),
with S - final, and R initial coordinate sets. The function of the
U matrix is e.g. to transform from primitive IC' s (of which there
are NIC0>NQ) to a set of independent IC's NQ in number, or to scale
the IC's by a factor (useful when trying to reproduce vibrations
reported in the literature, as different research groups use different
definitons of angle or dihedral IC's).
If two U matrices are given, then the IC's (and the B and G matrices)
are sequentially transformed using first U1, then U2. The F matrix is
assumed to be expressed in the final IC's on input, and is not
transformed (except for the 'KANO' option - see 'IFTR').
FMAT - read in F matrix, (the second derivatives of energy wrt
coordinates)
<int1> == IFF
<int2> == ISF
<int3> == IUF
IFF - specifies format
= 0 - Schatschneider/Snyder format
= 1 - GAUSSIANxx format
N.B. remember to use 'Z matrix' oriented cartesian
coords.
= 2 - CHARMM formatted SECO file format
IFS = 1/0 - symmetrize/dont symmetrize (upper triangle
assumed on input)
IUF - FORTAN unit no., as for 'UMAT'
(see RDMAT, RFORC, RDSECO in MOLVIO)
LX - read in cartesian eigenvectors
<int1> == IFL
<int2> == unused
<int3> == IUL
IFL - specifies format
= 0 - GAUSSIANxx format (see SUBROUTINE REIGEN)
all 3*NAT eigenvectors read in
N.B. remember to use 'standard' (or 'CMS') oriented
cartesian coordinates
= 1 - CHARMM binary format (see SUBROUTINE REIGCH)
only the NQ=3*NAT-6 "vibrational" eigenvectors
are expected by REIGCH; use "WRITE NORM 7 THRU ..."
command to achieve this.
NB. Binary files are machine specific.
IUL - FORTAN unit no. from which to read , aas in 'UMAT'
IC - read in internal/external coordinate definitions;
<int1> == IZIC
Five integers will be read from NIC0 lines in free
format; each line contains:
ITYP,I,J,K,L - specify type and four atom numbers
as defined in cartesian coordinates
Note: it is necessary to add zeros in unused fields.
IZIC - multiplicity, usually = no. of molecules in unit
cell. IZIC.GT.1 turns on autogeneration of
internal/external coordinates for unit cell from
the ones provided for the first asymmetric unit.
ITYP=1,2,3,4,5,6 - internal coordinates
ITYP = 1 - I-J bond stretch
I --- J
ITYP = 2 - I-J-K angle bend
J
/ \
/ \
I K
ITYP = 3 - I-L bond angle with J-K-L plane (Wilson wag)
K
/
/
I --- L
\
\
J
ITYP = 4 - angle between IJK abd JKL planes
I
\
\
J --- K
\
\
L
ITYP = 5 - I-J-K linear bend in IJL plane
ITYP = 6 - I-J-K linear bend perpendicular to IJL plane
I --- J --- K
. .
. .
L
Note: For ITYP = 5 and 6, atom L can be omitted, in which
case the reference plane will be defined arbitrarily
based on the cartesian basis.
For details : a) see SUBROUTINE BMAT
b) see Wilson,Decius,Cross section 4.1,
substituting their atom numbers with:
ITYP=1 (12) -> (IJ)
2 (123) -> (IKJ) ! that's right !
3 (1234) -> (IJKL)
4 (1234) -> (IJKL)
A good reference for standard definitions of independent
internal coordinates for a wide selection of chemical
groups is:
P.Pulay,G.Fogarasi,F.Pang & J.E.Boggs, JACS 101, 2550 (1979)
For the 'CRYS' option, the external coordinates are defined
here; their codes:
ITYP=11 - x translation
ITYP=12 - y translation
ITYP=13 - z translation
ITYP=14 - x rotation
ITYP=15 - y rotation
ITYP=16 - z rotation
In this case the I field should hold the consecutive number
of the molecule in the unit cell (consistent with MNAT data).
PRNT - set print level
<int1> == IPRNT
IPRNT=0 - minimal printout
IPRNT=5 - maximum printout [default is 2]
TEST - equivalent to 'PRNT' with IPRNT=4
NULL - control card for 'G ' option with IGLEV=2
<int1> == NULL
<int2> == NSTRT
NULL = the number of orthonormal vectors for the null
space to be read from the U2 matrix
NSTRT = the number of starting vectors for the Gram-Schmidt
procedure in the vibrational space
Note: If any null coordinates are known, they should be orthonormalized
and placed in the first NULL rows of U2. The program will then write out
the complete set of orthonormal coordinates spanning the null space,
starting with the ones provided. If NSTRT.GT.0 a completely independent
calculation will be performed in the vibrational space. In that case,
the NULL+1,...NULL+NSTRT rows of U2 should contain the known coordinates
of the vibrational space orthogonal to each other and the redundancies
(null space vectors). The program will construct an orthonormal basis of
the vibrational space which is orthogonal to the redundancies, starting
with the provided vectors.
PED - symbolic PED analysis will be performed
<int1> == NGRUP
<int2> == NCUTP
NGRUP - number of coordinate groups to be defined
NCUTP - cutoff level; PED contributions below NCUTP % will
not be printed, for clarity (default is 3%).
The following cards must contain:
1. for each group I=1,NGRUP: LGRUP(I),IGRUP(I,J), J=1,LGRUP(I)
- the number of coords in group and their consecutive numbers
(these are the final numbers, i.e. after all U matrix
operations) (20I3)
2. for each coordinate : IS,SS - its consecutive number (after
all U matrix operations) and the assigned symbol.
4(I3,2X,A8,2X) - zero to four entries per line; blank fields
skipped, negative IS value to end this input section.
Only the first coord of each group needs a symbol defnition,
the rest are set to this string; contributions from the whole
group are added up and printed beside the group symbol.
SCAL - scale the F matrix Fij' = FACT*Fij;
the real value of FACT will be read from next line (F10.6).
TRRM - remove translational and rotational contributions from cartesian
coordinate vibrational eigenvectors. (currently used only
for GAUS)
MNAT - lines following this card will contain the numbers of atoms
of the individual molecules comprising the unit cell (or
molecular aggregate) in 20I3 format.
Application - makes possible external coordinate use in
vibrational analysis of mixed crystals or molecular
aggregates (use CRYS option in both cases).
The value of IZMOL should already be defined for this card
IFTR - specifies the dimension (and type) of F matrix
<int1> == IFTRAN
= 0 - F is in primitive ICs R, NIC0xNIC0
= 1 - F is in S1=U1*R, NICxNIC
= 2 - F is in S2=U2*U1*R coords, NQxNQ
If card is not given, default IFTRAN=NUMAT is assumed
(works only for 'KANO' option)
SYMM - use symmetry (in symbolic PED analysis only)
<int1> == NBLOCK
It is assumed that by use of similarity transformations (the U
matrices), the vibrational problem has been transformed to
such coordinates that the Hamiltonian (G and F) is
block-diagonal. This usually happens if the coordinates form
a basis for the irreducible representations of the molecular
point group.
The following cards should contain the data:
IBLOCK(I),I=1,NBLOCK - sizes of consecutive blocks (coordinate
numbering is as for PED analysis, i.e. after all U matrix
transformations)
SBLOCK(I),I=1,NBLOCK - block symbols (e.g. representation names)
EXPF - read in reference frequencies for the system
Frequencies should be in ascending order (if 'SYMM' is
present, the ordering should be separate within each block).
The frequencies from MOLVIB will be printed out side-by-side
with the reference set, differences and an rms deviation will
computed. (If 'SYMM' is present, a separate analysis will be
performed for each block).
Format: free, 1 real value per line.
FINI - a finite difference step size can be specified (default is 0.01
Angstrom). Applicable to classical Drude oscillator systems only.
MOLVIB supports such systems by automatic switching to numerical
second derivatives when coordinates of Drude particles are
self-consistently adjusted to positions of real atoms. Note,
Drude coordinates are reset to atomic centers upon leaving the
MOLVIB analysis.
END - end input section, perform MOLVIB calculations and
return to CHARMM.
```

Note

the Schactschneider/Snyder format

This format is very useful for i/o of sparse matrices (or small and not so sparse ones). The basic format is: 4(2I3,F12.6) The two integer fields specify the row and column number, the real field - the value of the array element. Any elements not explicitly specified are set to zero. Each line of input may contain 0-4 entries, blank lines are ignored, a negative value for the column number terminates input. See subroutine RDMAT in MOLVIO.