# 4.2.52. SLAPAF¶

Provided with the first order derivative with respect to nuclear displacements
the program is capable to optimize molecular structures with or
without constraints for minima or
transition states. This will be achieved with a quasi-Newton approach
in combination with 2nd ranks updates of the approximate Hessian or
with the use of a computed (analytic or numerical) Hessian.
Note that *if* a computed Hessian is available on the
RUNFILE then it will be used rather than the approximate Hessian generated by SLAPAF.
On completion of an optimization SLAPAF will automatically execute a single energy evaluation,
this can be disabled with the NOLAst keyword.

## 4.2.52.1. Description¶

SLAPAF has three different ways in selecting the basis for the displacements during the optimization. The first format require user input (not recommended), whereas the two other options are totally black-boxed. The formats are:

the old format as in Molcas-3, which is user specified. The internal coordinates are here represented as linear combination of internal coordinates (such as bonds, angles, torsions, out of plane angles, Cartesian coordinates and separation of centers of mass) and the linear combinations are totally defined by user input. This format does also require the user to specify the Hessian (default a diagonal matrix). This option

*allows*for frozen internal coordinates.the second format is an automatic option which employs the Cartesian eigenvectors of the approximative Hessian (generated by the Hessian model functional [190]).

the third format (this is the recommend and default) is an automatic option which utilizes linear combinations of some curvilinear coordinates (stretches, bends, and torsions). This implementation has two variations. The first can be viewed as the conventional use of non-redundant internal coordinates [191][192][193]. The second variation is a force constant weighted (FCW) redundant space (the HWRS option) version of the former implementation [194].

All three formats of internal coordinates can be used in combinations with constraints on the molecular parameters or other type of constraints as for example energy differences.

The displacements are symmetry adapted and any rotation and translation if present is deleted. The relaxation is symmetry preserving.

## 4.2.52.2. Dependencies¶

SLAPAF depends on the results of ALASKA and also possibly on MCKINLEY and MCLR.

## 4.2.52.3. Files¶

### 4.2.52.3.1. Input files¶

Apart from the standard input file SLAPAF will use the following input files.

- RUNFILE
File for communication of auxiliary information. If a computed Hessian is available on this file it will be used rather than the approximate Hessian generated by SLAPAF.

- RUNFILE2
File for communication of auxiliary information of the “ground state” in case of minimum energy cross point optimizations.

- RUNOLD
File for communication of auxiliary information for reading an old Hessian matrix from a previous geometry optimization.

### 4.2.52.3.2. Output files¶

In addition to the standard output file SLAPAF will use the following output files.

- RUNFILE
File for communication of auxiliary information.

- RUNFILE2
File for communication of auxiliary information of the “ground state” in case of minimum energy cross point optimizations.

- MD_GEO
Molden input file for geometry optimization analysis.

- MD_MEP
Molden input file for minimum energy path (MEP).

- MD_SADDLE
Molden input file for energy path (MEP) of a Saddle TS optimization.

- MD_IRC
Molden input file for intrinsic reaction coordinate analysis of a TS.

- MD_FREQ
Molden input file for harmonic frequency analysis.

- UNSYM
ASCII file where all essential information, like geometry, Hessian normal modes and dipole derivatives are stored.

- STRUCTURE
Output file with a statistics of geometry optimization convergence.

## 4.2.52.4. Input¶

SLAPAF will as standard provided with an energy and a corresponding gradient update the geometry (optimize). Possible update methods include different quasi-Newton methods. The program will also provide for updates of the Hessian. The program has a number of different variable metric methods available for the Hessian update. This section describes the input to the SLAPAF program.

This section describes the input to the SLAPAF program in the Molcas program system. The input starts with the program name

```
&SLAPAF
```

There are no compulsory keywords

Optional convergence control keywords

- ITERations
Maximum number of iterations which will be allowed in the relaxation procedure. Default is 500 iterations, however, if environment variable MOLCAS_MAXITER has been exported by the user this is the assumed default value.

- THRShld
Enter two real numbers which specifies the convergence criterion with respect to the energy change and the norm of the gradient. The defaults are 0.0 and 3.0D-4 au for Gaussian convergence criteria (which normally do not consider the energy change), and 1.0D-6 and 3.0D-4 for Baker criteria (see the BAKER keyword).

- BAKEr
Activate convergence criteria according to Baker [195]. Default is to use the convergence criteria as in the Gaussian program [196].

- MAXStep
This keyword is followed by the value which defines the seed of largest change of the internal coordinates which will be accepted. A change which is larger is reduced to the max value. The value is dynamically modified each iterations. The default value is 0.3 au or rad.

- CNWEight
Sets the maximum weight assigned to the fulfillment of the constraints, relative to the step taken in the complementary space for energy minimization. The step in the constraint space is truncated to be at most as large as the step in the minimization space, or half the maximum total step, whichever is larger, multiplied by this value. Default is 1.0.

- TOLErance
Controls how strictly the constraints (if any) must be satisfied at convergence. The default value is very large, such that this criterion is always met, and only the gradient and maximum step (or energy difference) control convergence. If you set this keyword to some value, a constrained optimization will only converge if the maximum error in any constraint is lower than this number (in atomic units, and radians).

Optional coordinate selection keywords

- CARTesian
Activate SLAPAF to use the eigenvectors of the approximative Hessian expressed in Cartesian as the definition of the internal coordinates. The default is to use the FCW non-redundant internal coordinates. The Hessian will be modeled by the Hessian Model Functional.

- INTErnal
This marks the start of the definition of the internal coordinates. This section is always ended by the keyword End of Internal. For a complete description of this keyword see Section 4.2.52.4.1. This option will also use a diagonal matrix as default for the Hessian matrix. The default is to use the FCW non-redundant internal coordinates.

- HWRS
Use the force constant weighted (FCW) redundant space version of the nonredundant internal coordinates. This is the default. The Hessian will be modeled by the Hessian Model Functional.

- NOHWrs
Disable the use of the force constant weighted redundant space version of the nonredundant internal coordinates. The default is to use the HWRS option. The Hessian will be modeled by the Hessian Model Functional.

- FUZZ
When automatically generating the primitive internal coordinates, the system may end up in disconnected fragments, in which case additional bonds are defined between the fragments. This keyword controls how many inter-fragment bonds are added. Bonds are generated between the closest atoms of two fragments, and all pairs of atoms in separate fragments at a distance up to the specified value longer. The value can be followed with the unit BOHR or ANGSTROM. The default is 0.5 a.u.

Optional Hessian update keywords

- HUPDate
Method used for updating the Hessian matrix. It must be one of:

`None`

— No update is applied.`BFGS`

— Activate update according to Broyden–Fletcher–Goldfarb–Shanno. This is the default.`MSP`

— Activate the Murtagh–Sargent–Powell update according to Bofill [197]. This update is preferred for the location of transition states.`EU`

— Activate the EU update according to Bofill [198]. This update can be used for the location of transition states.`TS-BFGS`

— Activate the TS-BFGS update according to Bofill [198]. This update can be used for the location of minima or transition states.

- UORDer
Order the gradients and displacements vectors according to Schlegel prior to the update of the Hessian. Default is no reorder.

- WINDow
Maximum number of previous iterations to include in the Hessian update. When using RVO (see KRIGing keyword), the maximum number of sample points used is twice this value. Default is 5.

Optional optimization procedure keywords

- NOLIne
Disable line search. Default is to use line search for minima.

- RATIonal
Activate geometry optimization using the restricted step Rational Functional optimization [199][200], this is the default.

- C1-Diis
Activate geometry optimization using the C1-GDIIS method [201][202][203]. The default is to use the Rational Functional approach.

- C2-Diis
Activate geometry optimization using the C2-GDIIS method [131]. The default is to use the Rational Functional approach.

- DXDX
This option is associated to the use of the C1- and C2-GDIIS procedures. This option will activate the computation of the so-called error matrix elements as \(e=\delta x^{\text{T}}\delta x\), where \(\delta x\) is the displacement vector.

- DXG
This option is associated to the use of the C1- and C2-GDIIS procedures. This option will activate the computation of the so-called error matrix elements as \(e=\delta x^{\text{T}}g\), where \(\delta x\) is the displacement vector and \(g\) is the gradient vector.

- GDX
See above.

- GG
This option is associated to the use of the C1- and C2-GDIIS procedures. This option will activate the computation of the so-called error matrix elements as \(e=g^{\text{T}}g\), where \(g\) is the gradient vector. This is the default.

- NEWTon
Activate geometry optimization using the standard quasi-Newton approach. The default is to use the Rational Functional approach.

- RS-P-rfo
Activate RS-P-RFO [200] as default for TS-search. Default is RS-I-RFO.

- TS
Keyword for optimization of transition states. This flag will activate the use of the mode following rational functional approach [204]. The mode to follow can either be the one with the lowest eigenvalue (if positive it will be changed to a negative value) or by the eigenvector which index is specified by the MODE keyword (see below). The keyword will also activate the Murtagh–Sargent–Powell update of the Hessian and inactivate line search. This keyword will also enforce that the Hessian has the right index (i.e. one negative eigenvalue).

- MODE
Specification of the Hessian eigenvector index, this mode will be followed by the mode following RF method for optimization of transition states. The keyword card is followed by a single card specifying the eigenvector index.

- FINDTS
Enable a constrained optimization to release the constraints and locate a transition state if negative curvature is encountered and the gradient norm is below a specific threshold (see the GNRM option). Keyword TSCOnstraints should be used in combination with FINDTS.

- TSCOnstraints
Specify constraints that will be active during the initial stage of an optimization with FINDTS. When negative curvature and low gradient are encountered, these constraints will be released and other constraints will remain active. If this block is not given in the input, all constraints will be released. The syntax of this keyword is exactly like normal constraints, and it must be ended with End of TSConstraints (see Section 4.2.52.4.1 below).

- GNRM
Modify the gradient norm threshold associated with the FINDTS option. The actual threshold is specified on the subsequent line. The default value is 0.2.

- MEP-search or MEP
Enable a minimum energy path (MEP) search.

- rMEP-search
Enable a reverse minimum energy path (MEP) search.

- IRC
The keyword is used to perform an intrinsic reaction coordinate (IRC) analysis of a transition state structure. The analysis will follow the reaction path forward and backward until the energy increases. The keyword requires that the starting structure be that of a transition state and that the reaction vector be specified explicitly (check the keyword REACtion vector) or implicitly if it can be found on RUNOLD. Note that the user should not specify any explicit constraints!

- NMEP or NIRC
Maximum number of points to find in a minimum energy path search or intrinsic reaction coordinate analysis.

- MEPStep or IRCStep
The keyword is used to specify the step length done in the MEP search or IRC analysis. The step length can be followed with the unit BOHR or ANGSTROM. The default is 0.1 a.u. (in normalized mass-weighted coordinates).

- MEPType or IRCType
Specifies what kind of constraint will be used for optimizing the points during the MEP search or IRC analysis. The possibilities are SPHERE, the default, which uses the Sphere constraint (each structure is at a given distance in coordinate space from the reference), or PLANE which uses the Transverse constraint (each structure is at a given distance from the hyperplane defined by the reference and the path direction). The reference structure changes at each step, according to the MEPAlgorithm keyword.

- MEPAlgorithm or IRCAlgorithm
Selects the algorithm for a MEP search or IRC analysis. The possibilities are GS for the González–Schlegel algorithm, the default, or MB for the Müller–Brown algorithm.

- MEPConvergence or IRCConvergence
Sets the gradient convergence for a MEP search or IRC analysis. The path will be terminated when the gradient norm at an optimized point is below this threshold. By default it is the same as the gradient threshold for the normal iterations, specified with THRShld, it may be necessary to reduce it to follow a path on a very flat surface.

- REFErence
The keyword is followed by a list of the symmetry unique coordinates (in au) of the origin of the hyper sphere. The default origin is the structure of the first iteration.

- GRADient of reference
The keyword is followed by a list of the gradient vector components. This keyword is compulsory when using the Transverse kind of constraint. The optimization is performed in a space orthogonal to the given vector.

- REACtion vector
The keyword is followed by the reaction vector specified as the Cartesian vector components on each of the symmetry unique atoms.

Optional force constant keywords

- OLDForce
The Hessian matrix is read from the file RUNOLD. This Hessian is either an analytic or approximative Hessian updated by Slapaf. Note that for this option to work properly the type of internal coordinates must be the same!

- FCONstant
Input of Hessian in internal coordinates. There are two different syntaxes.

The keyword is followed by an entry with the number of elements which will be set (observe that the update will preserve that the elements \(H_{ij}\) and \(H_{ji}\) are equal). The next entries will contain the value and the indices of the elements to be replaced.

The keyword if followed by the label Square or Triangular. The subsequent line specifies the rank of the Hessian. This is then followed by entries specifying the Hessian in square or lower triangular order.

- XFCOnstant
Input of an external Hessian matrix in cartesian coordinates. The syntax is the same as for the FCONSTANT keyword.

- NUMErical
This invokes as calculation of the force constant matrix by a two-point finite difference formula. The resulting force constant matrix is used for an analysis of the harmonic frequencies.

**Observe**that in case of the use of internal coordinates defined as Cartesian coordinates that these has to be linear combinations which are free from translational and rotational components for the harmonic frequency analysis to be valid.**Alternative:**see keyword RowH in the section about Internal coordinates.- CUBIc
This invokes a calculation of the 2nd and the 3rd order force constant matrix by finite difference formula.

- DELTa
This keyword is followed by a real number which defines the step length used in the finite differentiation. Default: 1.0D-2.

- PRFC
The eigenvalues and eigenvectors of the Hessian matrix are printed. The internal coordinates definitions are also printed.

- RHIDden
Define the hidden atoms selection radius in order to improve a QM/MM Hessian. It can be followed by Angstrom.

Optional miscellaneous keywords

- CTOF
Coordinates TO Follow defines an internal coordinate whose values will be printed in the output during the optimization. Both the original and the new values will be printed. The keyword must be followed by the definition on the primitive coordinate.

- RTRN
Maximum number of atoms for which bond lengths, angles and dihedral angles are listed, and the radius defining the maximum length of a bond follows. The latter is used as a threshold when printing out angles and dihedral angles. The length can be followed by Bohr or Angstrom which indicates the unit in which the length was specified, the default is Bohr. The default values are 15 and 3.0 au.

- THERmochemistry
Request frequencies to be computed followed by an user specified thermochemical analysis. The keyword must be followed by different entries containing the Rotational Symmetry Number, the Pressure (in atm), and one entry per Temperature (in K) for which the thermochemistry will be calculated. The section is ended by the keyword End of PT.

- DISOtope
Calculates frequencies modified for double isotopic substitution.

- TRACk
Tries to follow electronic states during an optimization, by computing state overlaps with RASSI at each step. Root numbers selected with RlxRoot in RASSCF or with the “EDiff” constraint are only fixed in the first iteration, then the best-matching states are chosen.

- LASTenergy
Specifies the quantum chemical method requested for the Last_Energy module (e.g., SCF, CASSCF, CASPT2, etc.) The keyword must be followed by the name of the module. Moreover, the EMIL command COPY needs to be used in the global input to provide a file named LASTEN, containing the input for the specified module.

- NOLAst energy
Disables the call to the LAST_ENERGY module when convergence is achieved.

Optional restricted variance optimization (RVO) [205][206] keywords

- KRIGing
Activate RVO using gradient-enhanced Kriging (GEK) to describe the surrogate model. The maximum number of sample points (energies and gradients) is twice the value indicated by the WINDow keyword (i.e. 10 by default).

- TFOFfset
Trend function or baseline offset for the GEK surrogate model. The surrogate model will tend to the maximum energy among the sample points plus this value (in au). The default value is 10.0 au.

- MAXDisp
Maximum energy dispersion allowed during each macro iteration of the RVO procedure. A real value is read from the input, the maximum dispersion is this value times the maximum Cartesian gradient. The default value is 0.3 au. During the constrained phase of an optimization with FindTS, the default is 0.1 au.

- MXMI
Maximum number of micro iterations in each macro iteration of the RVO procedure. The default value is 50.

- NDELta
Activate partial gradient enhanced Kriging, PGEK. This integer number determines for how many fewer iterations the gradients will be included in the PGEK procedure. The default value is 0, that is standard GEK.

Example: A complete set of input decks for a CASSCF geometry optimization. These are the input decks for the optimization of the enediyne molecule.

```
&GATEWAY
Title= Enediyne
Coord= $MOLCAS/Coord/enediyne.xyz
Basis= ANO-L-VQZP
Group= x z
> DoWhile
&SEWARD
&SCF
ITERATIONS= 30; Occupied= 9 8 2 1; Thresholds= 1.0d-8 1.0d-3 1.5d-3 0.2d-3; IVO
&RASSCF
Symmetry= 1; Spin= 1
NactEl= 12 0 0; Inactive= 7 7 0 0; Ras2= 3 3 3 3
Iterations= 50 50; CiRoot= 1 1; 1; Thrs= 1.0e-08 1.0e-05 1.0e-05
Lumorb
&SLAPAF; Iterations= 20
> EndDo
```

Example: Thermochemistry for an asymmetric top (Rotational Symmetry Number = 1), at 1.0 atm and 273.15, 298.15, 398.15 and 498.15 K.

```
&SLAPAF; THERmochemistry= 1; 1.0; 273.15; 298.15; 398.15; 498.15; End of PT
End of input
```

### 4.2.52.4.1. Definition of internal coordinates or constraints¶

The input section defining the internal coordinates always start with the keyword Internal coordinates and the definition of the constraints starts with the keyword Constraints. Note that the latter is an input section for the GATEWAY module.

The input is always sectioned into two parts where the first section defines a set of primitive internal coordinates and the second part defines the actual internal coordinates as any arbitrary linear combination of the primitive internal coordinates that was defined in the first section. In case of constraints the second part does also assign values to the constraints.

In the first section we will refer to the atoms by their atom label (SEWARD will make sure that there is no redundancy). In case of symmetry one will have to augment the atom label with a symmetry operation in parenthesis in order to specify a symmetry related center. Note that the user only have to specify distinct internal coordinates (ALASKA will make the symmetry adaptation).

In the specification below *rLabel* is a user defined label with no more
than 8 (eight) characters. The specifications atom1, atom2, atom3, and atom4
are the unique atom labels as specified in the input to SEWARD.

**The primitive internal coordinates** are defined as

*rLabel*= Bond atom1 atom2a primitive internal coordinate

*rLabel*is defined as the bond between center atom1 and atom2.*rLabel*= Angle atom1 atom2 atom3a primitive internal coordinate

*rLabel*is defined as the angle between the bonds formed from connecting atom1 to atom2 and connecting atom2 to atom3.*rLabel*= LAngle(1) atom1 atom2 atom3a primitive internal coordinate

*rLabel*is defined as the linear angle between the bonds formed from connecting atom1 to atom2 and connecting atom2 to atom3. To define the direction of the angle the following procedure is followed.—

*the three centers are linear*,

form a reference axis, \(R_1\), connecting atom1 and atom3,

compute the number of zero elements,

*nR*, in the reference vector,

—

*nR=0*, a first perpendicular direction to the reference axis is formed by\[R=(R_{1x},R_{1y},-R_{1z})\]followed by the projection

\[R_2=R-\frac{R \cdot R_1}{R_1 \cdot R_1} R_1.\]The second perpendicular direction completes the right-handed system.

—

*nR=1*, a first perpendicular direction to the reference axis is defined by setting the element in \(R_2\) corresponding to the zero entry in \(R_1\) to unity. The second perpendicular direction completes the right-handed system.—

*nR=2*, a first perpendicular direction to the reference axis is defined by setting the element corresponding to the first zero entry in \(R_1\) to unity. The second perpendicular direction completes the right-handed system.

—

*the three centers are nonlinear*, the first perpendicular direction is the one which is in the plane formed by atoms atom1, atom2, and atom3. The second perpendicular direction is taken as the direction perpendicular to the same plane.

The direction of the bend for

**LAngle(1)**is taken in the direction of the first perpendicular direction, etc.*rLabel*= LAngle(2) atom1 atom2 atom3a primitive internal coordinate

*rLabel*is defined as the linear angle between the bonds formed from connecting atom1 to atom2 and connecting atom2 to atom3. The definition of the perpendicular directions is as described above. The direction of the bend for**LAngle(2)**is taken in the direction of the second perpendicular direction.*rLabel*= Dihedral atom1 atom2 atom3 atom4a primitive internal coordinate

*rLabel*is defined as the angle between the planes formed of atom1, atom2 and atom3, and atom2, atom3 and atom4, respectively.*rLabel*= OutOfP atom1 atom2 atom3 atom4a primitive internal coordinate

*rLabel*is defined as the angle between the plane formed by atom2, atom3, and atom4 and the bond formed by connecting atom1 and atom4.*rLabel*= Dissoc (n1+n2) atom1 atom2 atom3 … atomNa primitive internal coordinate

*rLabel*is defined as the distance between the center of masses of two sets of centers. The first center has n1 members and the second has n2. The input contains the labels of the atoms of the first group followed immediately by the labels of the second group. This option is not available for constraints.*rLabel*= Cartesian i atom1a primitive internal coordinate

*rLabel*is defined as the pure Cartesian displacement of the center labeled atom1. The label i is selected to x, y, or z to give the appropriate component.*rLabel*= Ediff [i j]the energy difference between states i and j (if provided, the brackets indicate they are optional, do not include the brackets). If i and j are not provided, the difference is between the “current” state and the state provided on RUNFILE2. This is only used in constrained optimization in which crossings or conical intersections are located. If this constraint is used, the average energy of the two states will be optimized, subject to the constraint. If the value is 0.0 and the spin and spatial symmetry of both states is the same, a conical intersection will be searched. In this case, SLAPAF will request an analytical calculation of the nonadiabatic coupling vector, if available. If it is not available, or if RUNFILE2 is being used (i and j not provided), the branching space update method of Maeda et al. will be used [207].

*rLabel*= Spherethe radius of the hypersphere defined by two different molecular structures (the origin is the first structure) in relative mass-weighted coordinates. This is only used in constrained optimization in which minimum reaction paths (MEP) or intrinsic reaction coordinate (IRC) paths are followed. The units of the radius is in mass-weighted coordinates divided with the square root of the total mass of the molecule.

*rLabel*= Transversea level of “orthogonality”. This is used to perform an optimization in a space orthogonal to a given vector. Recommended value 0.0. Requires usage of GRAD keyword.

*rLabel*= Fragment atom1 atom2 atom3 … atomNa dummy internal coordinate

*rLabel*is defined. This translates to that a set of internal coordinates are generated automatically according to a standard Z-matrix format to define all degrees of freedom of the fragment defined by the list of atoms on the same line. These internal coordinates will be automatically fixed in the geometry optimizations to the values of starting structure. Note, the values of these do not need to be explicitly defined and set in the Values section. Note, too, that the generation of the internal coordinates is done according to the order in which atom1, atom2, etc. are given; for some systems, especially with linear angles, it may be preferable to define the coordinates manually.

The second section starts with the label Vary or in the case of constraints with the label Values.

In case of a definition of **internal coordinates** in this section the user
specifies all symmetric internal coordinates excluding translation and rotation
using a list of expressions like

label= f1rLabel1+ f2rLabel2+ …

which defines an internal coordinate *label* as the linear combination of the
primitive internal coordinates *rLabel1*, *rLabel2*, … with the coefficients
f1, f2, …, respectively. If the internal coordinate just corresponds to
the primitive internal coordinate, the same label can be used

label

If some internal coordinates are chosen to be fixed they should be defined after the label Fix. The fixed internal coordinate are defined with expressions as in the section Vary. Observe: using expression can introduce linear dependence and/or undefined nuclear coordinates, so use with care.

For the internal coordinates defined after Vary (and Fix, if present)
a numerical estimation of rows and columns of the Hessian matrix can be performed. The
*label* of internal coordinates (max 10) must be specified after keyword RowH.
Keywords NUMErical and RowH are mutually exclusive.

In case of a definition of **constraints** the sections contains either a
direct reference to a *rLabel* as in

rLabel=rValue[Angstrom,Degrees] [Soft,Hard] [Phantom]

or one can also use expressions like

f1

rLabel1± f2rLabel2± … =Value[Angstrom,Degrees] [Soft,Hard] [Phantom]

where *rValue* is the desired value of the constraint in au or rad, or in
angstrom or degrees if the corresponding keyword is added. The “Hard” and “Soft”
keywords are only meaningful for numerical differentiation: the coordinates corresponding
to soft constraints are differentiated, those of hard constraints are not [29].
By default almost all constraints are hard, only constraints of the type “Sphere”, “Transverse”
and “Ediff” default to soft. The “Hard” and “Soft” keywords override the default.
When using constraints in combination with the FINDTS keyword, one should use
soft constraints, at least for the constraint most similar to the expected reaction vector.
Constraints defined in TSCOnstraints (recommended) are automatically considered
soft.

The “Phantom” modifier can be used to ignore a constraint in the optimization. A phantom constraint will only be considered for numerical differentiation. Phantom constraints are useful in combination with the KEEPOldGradient keyword of ALASKA. Using NGEXclude in GATEWAY is equivalent to phantom constraints, and it is the preferred way to set up composite gradients [29].

Alternatively, if the current value of an internal coordinate is to be used, i.e. no change is to be allowed (frozen), this is expressed as

rLabel= Fix [Soft,Hard] [Phantom]

Note that a coordinate of type “Fragment” does not need to appear in the Values section, but if it does it must be assigned the value “Fix”.

Example: A definition of user specified internal coordinates of benzene. The molecule is
in \(D_{6h}\) and since Molcas only uses up to \(D_{2h}\) the
Fix option is used to
constrain the relaxation to the higher point group. **Observe** that this will
only restrict the nuclear coordinates to \(D_{6h}\). The electronic wavefunction,
however, can have lower symmetry.

```
Internal coordinates
r1 = Bond C1 C2
r2 = Bond C1 H1
r3 = Bond C2 H2
r4 = Bond C2 C2(x)
f1 = Angle H1 C1 C2
f2 = Angle H2 C2 C1
Vary
a = 1.0 r1 + 1.0 r4
b = 1.0 r2 + 1.0 r3
c = 1.0 f1 + 1.0 f2
Fix
a = 1.0 r1 + -1.0 r4
b = 1.0 r2 + -1.0 r3
c = 1.0 f1 + -1.0 f2
End of Internal
```

Example: A input for the optimization of water constraining the structure to be linear at convergence.

```
&GATEWAY
Title= H2O geom optim, using the ANO-S basis set.
Coord=$MOLCAS/Coord/Water.xyz
Basis=ANO-S-VDZ
Group= c1
Constraints
a1 = langle(1) H2 O1 H3
Values
a1 = 179.99 degrees
End of Constraints
>>> DO WHILE <<<
&SEWARD; &SCF
&SLAPAF
>>> END DO <<<
```

Example: A complete set of input decks for a UHF transition structure geometry optimization of an identity hydrogen transfer reaction (\(\ce{HO + H_2O -> H_2O + OH}\)).

```
&GATEWAY
ZMAT
O.STO-3G....
H.STO-3G....
H1
Z2 1 1.0
O3 1 1.15 2 92.
O4 1 1.15 2 92. 3 180.
H5 3 0.98 4 105.4 2 120.
H6 4 0.98 3 105.4 2 120.
>>> DO WHILE <<<
&SEWARD;
&SCF; UHF
&SLAPAF; TS; PRFC
Internal
bOO4 = Bond O3 O4
bOH5 = Bond H5 O3
bOH6 = Bond H6 O4
bOH1 = Bond O3 H1
aOOH5 = Angle O4 O3 H5
aOOH6 = Angle O3 O4 H6
aHOH1 = Angle H5 O3 H1
dH6 = Dihedral H6 O4 O3 H5
dH1 = Dihedral O4 H5 O3 H1
Vary; bOO4; bOH5; bOH6; bOH1; aOOH5; aOOH6; aHOH1; dH6; dH1
RowH; bOH1
End of Internal
>>> ENDDO <<<
```

Example: Optimization of a minimum energy conical intersection point, using automatic calculation of analytical gradients and nonadiabatic coupling.

```
&GATEWAY
Coord = acrolein.xyz
Basis = cc-pVDZ
Group = NoSymm
Constraints
a = Ediff 1 2
Values
a = 0.0
End of constraints
>>> DoWhile
&SEWARD
>>> If (iter = 1)
&SCF
&MBPT2
PrPt
>>> EndIf
&RASSCF
FileOrb = $Project.MP2Orb
Charge = 0
NActEl = 6 0 0
RAS2 = 5
CIRoot = 4 4 1
&SLAPAF
>>> EndDo
```