# PES generators

{XSURF,options}

The XSURF program allows for the calculation of the potential energy surface around a reference structure as required for the calculation of anharmonic frequencies (see the VSCF, VCI or VPT2 programs). The reference structure is supposed to be a (local) minimum or a transition state of a double-minimum potential. The potential is represented by energy grid points rather than an analytical representation. Within the XSURF program the potential energy surface is expanded in terms of normal coordinates, linear combination of normal coordinates or localized normal coordinates. XSURF can handle $n$-mode and Taylor expansions of the PES of arbitrary order, e.g.
$$V(q_1,\dots,q_{3N-6}) = \sum_i V_i(q_i) + \sum_{i<j} V_{ij}(q_i,q_j) + \sum_{i<j<k} V_{ijk}(q_i,q_j,q_k) + \dots$$ with $$\begin{eqnarray*} V_i(q_i) & = & V_i^0(q_i) - V(0) \\ V_{ij}(q_i,q_j) & = & V_{ij}^0(q_i,q_j) - \sum_{r\in\{i,j\}} V_r(q_r) - V(0) \\ V_{ijk}(q_i,q_j,q_k) & = & V_{ijk}^0(q_i,q_j,q_k) - \sum_{\stackrel{r,s\in\{i,j,k\}}{r>s}} V_{rs}(q_r,q_s) - \sum_{r\in\{i,j,k\}} V_r(q_r) - V(0)\\ V_{ijkl}(q_i,q_j,q_k,q_l) & = & \dots \label{diff4}\end{eqnarray*}$$ where $q_i$ denotes the coordinates. This expansion needs to be terminated after an $n$-body contribution as controlled by the keyword NDIM. Moreover, it can handle any kind of symmetry, e.g. non-Abelian point groups or permutational symmetry. A harmonic frequency calculation needs to be performed first. This can be done by the FREQ program or the VFREQ directive of the XSURF program. For technical reasons the XSURF program always requires curly brackets around its call. The XSURF program is fully parallelized in a sense that the calculation of different grid points is send to different processors (embarassingly parallel MPPX scheme). For example, the input for the calculation of a CCSD surface looks like:

label1
hf
ccsd
{xsurf,sym=auto}

The XSURF program is based on an iterative algorithm, i.e. grid points will be added automatically to the grid representation of the potential until a convergence threshold will be met. This guarantees a well-balanced description of the different terms in the expansion of the potential and simultaneously minimizes the number of ab initio calculations for a representation of the potential. For further details see:

G. Rauhut, Efficient Calculation of Potential Energy Surfaces for the Generation of Vibrational Wave Functions, J. Chem. Phys. 121, 9313 (2004).
B. Ziegler, G. Rauhut, Rigorous use of symmetry within the construction of multidimensional potential energy surfaces, J. Chem. Phys. 149, 164110 (2018).
B. Ziegler, G. Rauhut, Localized Normal Coordinates in Accurate Vibrational Structure Calculations: Benchmarks for Small Molecules, J. Chem. Theory Comput. 15, 4187 (2019)

#### Options

The following options are available:

• CORRECT=n (=1 (on) Default) If a certain subsurface does not converge despite increasing the number of ab initio calculations, symmetry in this subsurface (if any) will be neglected in order to avoid any errors due to inaccuracies in the displacement vectors and the subsurface will be recalculated accordingly. This option is automatically switched off in any Taylor expansions of the PES.
• DELAUTO=variable(=off Default) If DELAUTO=on, all not converged surfaces of the highest considered dimension are deleted. It only works after a restart from an external file.
• INFO=n (=1 Default) INFO=0 suppresses any information about the program parameters and symmetry information. INFO=1 refers to the standard output, while INFO=2 provides additional information about the symmetry recognition.
• LOWERDIM=n (=2 Default) In order to determine energy differences for the subsurfaces, contributions of subsurfaces of lower order need to be substracted from those of current order. The lower order energy contribution can be determined in three different ways: LOWERDIM=1 uses Kronecker product fitting of the lower order terms and LOWERDIM=2 retrieves this information from the intermediate fine grid representation of the underlying subsurfaces.
• MAXxD=n The maximum number of coarse grid points can be controlled by the keywords MAX1D, MAX2D, MAX3D, MAX4D. These 4 keywords determine the maximum number of ab initio calculations in one dimension for each 1D, 2D, 3D and 4D surface. The defaults are currently MAX1D=14, MAX2D=14, MAX3D=12, MAX4D=10. Presently, values larger than 24 are not supported.
• MINxD=n The minimum number of coarse grid points can be controlled by the keywords MIN1D, MIN2D, MIN3D, MIN4D. These 4 keywords determine the minimum number of ab initio calculations in one dimension for each 1D, 2D, 3D and 4D surface. The defaults are currently MIN1D=4, MIN2D=4, MIN3D=4, MIN4D=4. Presently, values larger than 24 are not supported.
• MINxD_CRIT1=n Minimum number of ab initio calculations per dimension, which are needed before a subsurfaces can be declared to be converged according to criterion 1. For dimension 1-3 the default is 6, while it is reduced to 4 for all higher order subsurfaces.
• MPG=n Symmetry of the normal modes is recognized by the program automatically. Only Abelian point groups can be handled at the moment. Symmetry of the modes will be determined even if the NOSYM keyword is used in the electronic structure calculations. In certain cases numerical noise can be very high and thus prohibits a correct determination of the symmetry labels. Symmetry can be switched off by using MPG=1.
• NDIM=n The keyword NDIM=n terminates the expansion of the PES after the $n$-body term. The default is set to 3. Please note, when you use NDIM=4 as a keyword for the XSURF program, you need to pass this information to the VSCF and VCI programs also. Otherwise these programs will neglect the 4-body terms.
• NGRID=n Based on a coarse grid of ab initio points a fine grid will be generated from automated interpolation techniques. The keyword NGRID=n determines the number of equidistant grid points in one dimension. NGRID=n has to be an even number. The default is currently set to 16.
• NSA=n (=1 Default) This option prints out some information about the progress of the XSURF calculation. NSA=1 prints this information is an additional file, which will be deleted once the XSURF calculation is completed, NSA=2 prints this information to the console.
• ONLYHEAD=n (=0 (off) Default) If set to 1, the XSURF calculation will be terminated after writing the header of the external restart file, i.e. prior to the calculation of the 1D terms.
• ORIENT Allows to specify a certain orientation of the molecule. With ORIENT=yes (Default) the orientation is choosed automatically according to the asymmetric parameter of the molecule. To choose a certain orientation, ORIENT=XC need to be set. X represents a number from 1 to 3 (in arabic or roman letters), and C need to be set to r or l. For example, ORIENT=IIl orientates the molecule according to the IIl convention. ORIENT=old does not rotate the molecule at all.
• RDM=n (=0 (off) Default) Degenerate modes can be rotated in a manner, that the corresponding 1D potentials will be identical. By default, this feature is switched off, but can be activated by RDM=1. Typically this results in rotational angles of 45 or 135 degrees.
• RDM_THR=n (=1.0d-10 Default) This threshold controls, if the potentials of two degenerate modes are identical or not. See the keyword RDM=n.
• SKIP=n (=1 (on) Default) By default, (pre)screening of any terms higher than 2D of the PES expansion is switched on. It can be deactivated by SKIP=0.
• SKIPCRIT=n (=1 Default) SKIPCRIT defines the method and thus the criterion for (pre)screening of the high-order terms of the PES expansion. SKIPCRIT=1 activates prescreening and SKIPCRIT=2 screening. In the latter case a label must be defined (see SKIPLABEL).
• SKIPLAB=variable The name of the label in the input stream must be defined, which determines the electronic structure level to be used for screening the high-order terms of a PES expansion.
• SKIP_THRx(i)=value ($x$=1,2 $i$=1,2,…) Definition of thresholds used for prescreening (SKIP_THR1) and screening SKIP_THR2 (see option SKIPCRIT). $i$ specifies the individual orders of the $n$-mode expansion of the PES. The defaults are SKIP_THR1(1)=0.0d0, SKIP_THR1(2)=0.0d0, SKIP_THR1(3)=1.0d-18, SKIP_THR1(4)=1.0d-27 and SKIP_THR2(1)=0.0d0, SKIP_THR2(2)=0.0d0, SKIP_THR2(3)=1.0d-2, SKIP_THR2(4)=1.0d-1. All other thresholds are not yet defined and need to be entered explicitly.
• START1D=label (=LABEL1 default) Sets the label to start the calculations for the 1D terms of the potential.
• STOP=i (=1000 Default) The calculation of an $n$-mode expansion of a PES can be terminated at lower orders, specified by STOP, while all information for the high-order terms is already provided in the header of the external restart file and the potential information once a multi-level scheme has been used.
• SYM=variable Symmetry within electronic structure calculations can be exploited by the keyword SYM=Auto (which is the default). Usually this leads to significant time savings. The symmetry recognition can be switched off by SYM=NOSYM as certain calculations may cause some trouble (e.g. local correlation methods). Symmetry in electronic structure calculations may not be mistaken by the symmetry of the mode-coupling terms (see keyword MPG). Once SYM=Auto is used, it is advisable to insert an INT card prior to the call of the Hartree-Fock program.
• THRDEGx=value ($x$=1,2,…) Threshold used for recognizing degeneracies within the individual orders of the PES expansion. The defaults are THRDEG1=5.0d-5, THRDEG2=1.0d-5,THRDEG3=5.0d-6,THRDEG4=1.0d-6.
• THRFITx=value ($x$=1,2,…) Threshold used for testing on convergence of a subsurface according to criterion 1 for the individual orders of the PES expansion. The defaults are THRFIT1=2.0d-3, THRFIT2=5.0d-3,THRFIT3=5.0d-3,THRFIT4=2.0d-2. Criterion 1 controls the convergence of the intermediate fine grid.
• THRLOWx=value ($x$=1,2,…) Threshold used for testing on convergence of a subsurface according to criterion 2 for the individual orders of the PES expansion. The defaults are THRLOW1=0.0d0, THRLOW2=5.0d-7,THRLOW3=1.0d-6,THRLOW4=2.0d-6. Criterion 2 controls the convergence with respect to the ab initio single points.
• THRSED=value (=1.0d-6 Default) Threshold for determining symmetry elements of the molecule.
• THRSYMx=value ($x$=1,2,…) Threshold used for recognizing symmetry within a subsurface of the PES expansion - in dependence on the order of the expansion term. The defaults are THRSYM1=5.0d-5, THRSYM2=1.0d-5,THRSYM3=5.0d-6,THRSYM4=5.0d-6,THRSYM5=1.0d-7.
• USEMRCC=n Once the MRCC program of M. Kallay or the Gecco program of A. Köhn is used for determining individual grid points, the option USEMRCC=1 needs to be set, which is needed to ensure proper communication between Molpro and Mrcc. Default: USEMRCC=0.
• VAR1D=variable The XSURF program reads the energy of electronic structure calculations from the internal Molpro variables, e.g. ENERGY, EMP2, $\dots$. The internal variable is specified by the keyword VAR1D. The default for the VAR1D keyword is the internal variable ENERGY.
• VIBIRREP=variable The irreps of the vibrations within the XSURF, VSCF and VCI programs may differ from those within the FREQ program as the molecules will be be reoriented according to the conventions (see keyword ORIENT). In order to use the same irreps as in the FREQ program, one may use VIBIRREP=Sort.

The following example shows the input of a calculation which computes energy and dipole surfaces at the MP2/cc-pVTZ level and subsequently determines the anharmonic frequencies at the VSCF and VCI levels. Hartree-Fock calculations will not be restarted and the .log-file is directed to the scratch directory as defined by the $TMPDIR variable. !options: --logfile-scratch memory,20,m orient,mass geometry={ 3 Water O 0.0675762564 0.0000000000 -1.3259214590 H -0.4362118830 -0.7612267436 -1.7014971211 H -0.4362118830 0.7612267436 -1.7014971211 } mass,iso basis=vdz hf mp2 optg frequencies,symm=auto label1 int {hf start,atden} {mp2 cphf,1} vibstate,combi=1 {xsurf,sym=auto intensity,dipole=2} poly vscf,pot=poly vci,pot=poly INTENSITY,options The INTENSITY directive of the SURF program provides the option to alter the electronic structure methods for calculating the dipole surfaces. It also allows to define the VARDIPnD[X,Y,Z] variables separately.$n$describes the dimension of the coupling surface and can be chosen to be 1 - 4. Dipole surfaces can be computed for all those methods for which analytical gradients are available in Molpro. For all methods except Hartree-Fock this requires the keyword CPHF,1 after the keyword for the electronic structure method. In multi-level schemes for which the variables VAR1D, VAR2D and VAR3D are set individually, the VARDIPnD[X,Y,Z] variables have to be set accordingly. Symmetry is currently only implemented for the 1D, 2D and 3D dipole surfaces. For 4D terms symmetry will automatically switched off at the moment. The determination of dipole surfaces beyond Hartree-Fock quality effectively doubles the computation time for surface calculations. #### Options • DIPOLE=n Allows to switch between the different dipole surface calculations. DIPOLE=0 switches off all dipole calculations. DIPOLE=1 (this is the default) computes the dipole surfaces at the Hartree Fock level of theory, and therefore does not increase the computation time of electronic structure theory. DIPOLE=2 switches on the dipole surfaces at the full level of theory, therefore CPHF,1 is required. This effectively doubles the computation time for surface calculations. • NDIMDIP=n This denotes the term after which the$n$-body expansion of the dipole surfaces is truncated. The default is set to 3. Note that NDIMDIP has to be lower or equal to NDIM. • NDIMPOL=n This variable denotes the term after which the$n$-body expansion of the polarizability tensor surfaces is truncated. The default is set to 0. Note that NDIMPOL has to be lower or equal to NDIM and must be smaller than 4. Note that currently only Hartree-Fock and MP2 polarizabilities are supported, which requires the POLARI keyword in the respective programs. Besides that, the frozen core approximation cannot yet be employed within the calculation of MP2 polarizabilities. • POLYSYM=variable (=ON Default). Symmetry in the polarizability surfaces differs from symmetry in energy or dipole surfaces and its recognition can be switched on or off. Symmetry is only detected based on geometrical parameters. • VARDIPxDX=variable (x=1..4) Variable which is used for the$x$direction of the dipole moment for 1D surfaces. • VARDIPxDY=variable (x=1..4) Variable which is used for the$y$direction of the dipole moment for 1D surfaces. • VARDIPxDZ=variable (x=1..4) Variable which is used for the$z$direction of the dipole moment for 1D surfaces. • VARPOLxDXX=variable (x=1..4) Variable which is used for the$xx$component of the polarizability tensor for 1D surfaces. • VARPOLxDYY=variable (x=1..4) Variable which is used for the$yy$component of the polarizability tensor for 1D surfaces. • VARPOLxDZZ=variable (x=1..4) Variable which is used for the$zz$component of the polarizability tensor for 1D surfaces. • VARPOLxDXY=variable (x=1..4) Variable which is used for the$xy$component of the polarizability tensor for 1D surfaces. • VARPOLxDXZ=variable (x=1..4) Variable which is used for the$xz$component of the polarizability tensor for 1D surfaces. • VARPOLxDYZ=variable (x=1..4) Variable which is used for the$yz$component of the polarizability tensor for 1D surfaces. An example for a calculation, which provides both, infrared and Raman intensities, is given below. label1 {hf start,atden} {mp2 core,0 polari} {xsurf,info=1 intensity,ndimpol=3 scalnm,auto=on } poly,ndimpol=3 vscf,pot=poly,ndimpol=3,info=1 vci,pot=poly,version=4,ndimpol=3,info=1 DISK,options As XSURF calculations are very demanding it is highly recommended to dump the grid representation of the potential to disk. This allows for convenient restarts for subsequent vibrational structure calculations. Note, that restarts can also be performed for incomplete potentials. #### Options • AUTO=n For Franck-Condon calculations this allows to specify the number of the two potential energy surfaces. • DUMP=file name The potential can be dumped into an external ASCII-file which can be used for restarting. Its name must be provided as the argument of the DUMP keyword, e.g. DUMP=’formaldehyde.pot’. The ASCII-file provides the interface to other programs and offers the possibility for controlled storage and modification of the computed potentials. Dipole and polarizability surfaces will also be dumped if available. • EXTERN=file name XSURF calculations are restartable at any point of a truncated calculation as long as the automatically generated file *.pot_RESTART is available. • SAVE=record Once a complete surface has been generated, a record can be specified, where to dump the potential in the temporary binary files. Once this keyword is not provided explicitly, the potential will be dumped in record 5600.2 • TIME=value (=3600.00 Default) Time given in seconds for the next dumping of the restart file. For long lasting electronic structure single point calculations it is useful to increase this value. • WHERE=variable In combination with the keywords DUMP and EXTERN for an external restart file, the keyword WHERE specifies the path for the external ASCII file. Two options are available, WHERE=home and WHERE=scr. As the external files can be huge for XSURF calculations, they will be stored on the scratch disk given by the Molpro variable $TMPDIR by default.

VTAYLOR,options

By default, the XSURF program generates an $n$-mode expansion. However, the program structure allows also to retrieve a Taylor expansion of the potential, which is identical with a Taylor expansion obtained by differentiation. In principal Taylor expansions of arbitrary order can be generated, but of course it must be guaranteed that the order of coupling terms is sufficiently high, e.g. a sextic force field cannot be obtained from a NDIM=4 calculation, because this calculation generates coupling terms with at most 4 different indices. In such a case, the missing terms will simply be neglected.

#### Options

• ORDER=n (=5 Default) Number of basis functions within the Taylor expansion.
• POINTS=n (=5 Default) Number of ab initio points controlling the accuracy of the derivatives (e.g. 5-point formula).
• SCALE=value (=1.0d-1 Default) This keyword controls the step width.
• TYPE=variable
• TYPE=QFF (corresponds to POINTS=5 and ORDER=5) specifies a full quartic force field.
• TYPE=SQFF specifies a semi-quartic force field (as used in VPT2 calculations).
• TYPE=SEXTIC (corresponds to POINTS=7 and ORDER=7) is the shortcut for a sextic force field.

VMULT,options

The level of the electronic structure calculations can be changed for the different $i$-body terms in the expansion of the potential. As a consequence, the keywords START2D, START3D, VAR2D and VAR3D exist in full analogy to the keywords START1D and VAR1D in standard calculations (see above). The number always represents the level of the expansion term. Such calculations are termed multi-level calculations. There does not exist a corresponding set of keywords for the 4-body terms. 4-body terms will always use the variables specified for the 3-body terms (this restriction is lifted in the XSURF program.

#### Options

• MULTI=n The keywords START1D, START2D, START3D in combination with the commands VAR1D, VAR2D and VAR3D allow for the calculation of multi-level potential energy surfaces. This would imply in principle that the 1D term of the potential needs to be computed at all three levels and the 2D term at two computational levels. As certain low level results are byproducts of more sophisticated methods (e.g. the HF energy is a byproduct of an MP2 calculation or the MP2 energy is a byproduct of a CCSD(T) calculation) the computational overhead can be avoided by the MULTI option.
• MULTI=1: This is the default and most expensive choice. The 1D potential will be computed at all 3 levels of theory. Likewise, the 2D potential will be calculated at 2 levels explicitly. An example would be:
1D: CCSD(T)/cc-pVTZ
2D: MP4(SDQ)/cc-pVTZ
3D: MP2/cc-pVDZ

{XSURF,Sym=auto
VMULT,Start2D=label2,Start3D=label3,Multi=1}
• MULTI=2: All information is provided by the preceding calculations and thus no part of the potential has to be computed twice. Examples:
1D: CCSD(T)/cc-pVTZ
2D: CCSD(T)/cc-pVTZ
3D: MP2/cc-pVTZ

{XSURF,Sym=auto
VMULT,Start2D=label1,Start3D=label2
VMULT,Var3D=EMP2,Multi=2}
1D: CCSD(T)/cc-pVTZ
2D: MP2/cc-pVTZ
3D: MP2/cc-pVTZ

{XSURF,Sym=auto
VMULT,Start2D=label2,Start3D=label2
VMULT,Var2D=EMP2,Var3D=EMP2,Multi=2}
• MULTI=3: The 2D potential provides all information for the 3D part while there is no connection between 1D and 2D. Consequently, the 1D contributions need to be computed twice (at the 1D and 2D levels) while all other terms will be computed just once. Examples:
1D: CCSD(T)/cc-pVTZ
2D: MP4(SDQ)/cc-pVTZ
3D: MP2/cc-pVTZ

{XSURF,Sym=auto
VMULT,Start2D=label2,Start3D=label3
VMULT,Var3D=EMP2,Multi=3}
1D: CCSD(T)/cc-pVTZ
2D: MP4(SDQ)/cc-pVTZ
3D: MP4(SDQ)/cc-pVTZ

{XSURF,Sym=auto
VMULT,Start2D=label2,Start3D=label2,Multi=3}
• MULTI=4: The 1D calculation provides all information for the 2D potential but does not so for the 3D part. Hence, the 1D contribution and the 2D contributions need to be computed twice. Examples
1D: CCSD(T)/cc-pVTZ
2D: CCSD(T)/cc-pVTZ
3D: MP4(SDQ)/cc-pVTZ

{XSURF,Sym=auto
VMULT,Start2D=label1,Start3D=label2,Multi=4}
1D: CCSD(T)/cc-pVTZ
2D: MP2/cc-pVTZ
3D: MP2/cc-pVDZ

{XSURF,Sym=auto
VMULT,Start2D=label2,Start3D=label3
VMULT,Var2D=EMP2,Multi=4}
• STARTxD=label (x=2..4) Definition of the label in the input stream specifiying the 2nd, 3rd and 4th electronic structure method of the multi-level scheme.
• VARxD=variable Molpro variable to be read for the higher levels of the multi-level scheme.

In 2D and 4D calculations (i.e. NDIM=2,4) the VMULT command can be used as well. In 4D calculations the last level must always be identical to the 3D level. In 2D the meaning of MULTI=1 and MULTI=3 is the same. Likewise, MULTI=2 and MULTI=4 are the same in case of 2D calculations. START2D and START3D define labels in the input stream in order to compute the 2D and 3D terms at different levels of electronic structure theory than the 1D terms. The use of the START2D and START3D commands usually requests the use of GOTO commands in the input. The keywords VAR2D and VAR3D are defined in full analogy to the VAR1D option. They specify the internal variable (e.g. ENERGY, EMP2, CCSD, …) to be read out for a given grid point.

The following example shows a 1D:CCSD(T)/cc-pVTZ; 2D:MP4(SDQ)/cc-pVTZ and 3D:MP2/cc-pVTZ multi-level calculation. As the MP2 energy is a byproduct of the CCSD(T) and MP4(SDQ) calculations only the 1D grid points will be computed twice (at the CCSD(T) and MP4(SDQ) levels). The 1D and 2D energies will be obtained from the internal variable ENERGY while the 3D energies make use of the EMP2 variable.

!options: --logfile-scratch
memory,50,m
orient,mass
geometry={
6
Ethene
C          0.0000000000        0.0000000000       -0.6685890718
C          0.0000000000        0.0000000000        0.6685890718
H          0.0000000000       -0.9240027061       -1.2338497710
H          0.0000000000        0.9240027061       -1.2338497710
H          0.0000000000        0.9240027061        1.2338497710
H          0.0000000000       -0.9240027061        1.2338497710
}

mass,iso
basis=vtz

hf
ccsd(t)
optg
freq,symm=auto

label1
int
{hf
start,atden}
ccsd(t)
goto,label4

label2
int
{hf
start,atden}
{mp4
notripl}
goto,label4

label3
int
{hf
start,atden}
mp2

label4
{xsurf,sym=auto
vmult,start2D=label2,start3D=label3,Var3D=EMP2,Multi=3}
poly
vscf,pot=poly
vci,pot=poly

However, if you need a more specialized multi-level scheme, XSURF provides an expert mode. Within this you can for example change the method for 3D and 4D terms. When calculating an ab initio point for an $n$ dimensional body term, two aspects need to be considered. First, you may check whether information for higher-order terms can be retrieved from low-order terms, e.g. the MP2 energy is a byproduct of a CCSD calculation. Second, if the information cannot be retrieved, single-point calculations at different electronic structure levels may be repeated for the low-order terms. All this information is internally stored in a matrix. \begin{aligned} M&=&\left(\begin{array}{cccc} 1&0&-1&1\\ 0&1&-2&1\\ 0&0&1&1\\ 0&0&0&1 \end{array}\right)\end{aligned} The columns of the matrix belong to the method and the lines to the dimension. The only important numbers are therefore the upper diagonals. A $1$ means calculate something and a number smaller than one, that the information is somewhere available. This matrix is an example for the following set of methods:

1D: CCSD(T)/cc-pVTZ
2D: CCSD(T)/cc-pVTZ
3D: MP2/cc-pVTZ
4D: HF/minao

For the other multi cases (see above) the matrix elements look like:

• MULTI=1: $$M=\left(\begin{array}{ccc} 1&1&1\\ 0&1&1\\ 0&0&1 \end{array}\right)$$
• MULTI=2: $$M_1=\left(\begin{array}{ccc} 1&0&-1\\ 0&1&-2\\ 0&0&1 \end{array}\right); \qquad M_2=\left(\begin{array}{ccc} 1&-1&0\\ 0&1&0\\ 0&0&1 \end{array}\right)$$
• MULTI=3: $$M_1=\left(\begin{array}{ccc} 1&1&-2\\ 0&1&-2\\ 0&0&1 \end{array}\right); \qquad M_2=\left(\begin{array}{ccc} 1&1&0\\ 0&1&0\\ 0&0&1 \end{array}\right)$$
• MULTI=4: $$M_1=\left(\begin{array}{ccc} 1&0&1\\ 0&1&1\\ 0&0&1 \end{array}\right); \qquad M_2=\left(\begin{array}{ccc} 1&-1&1\\ 0&1&1\\ 0&0&1 \end{array}\right)$$

These expert multi level matrices can be set by MMAT(x,y)=n. Only non-zero elements need to be set.

LINCOMB,options

The LINCOMB directive allows for the calculation of linear combinations of normal coordinates for the expansion of the potential. This is realized by 2×2 Jacobi rotations. At most 3N-6/2 rotations can be provided in the input.

#### Options

• ANGLE=value Rotation angle in degree.
• BLx=n This option assigns mode $n$ to block $x$. For example, the line LINCOMB,BL1=1,BL1=2,BL2=5,BL2=6 for a 4-atomic molecule assigns modes 1 and 2 to a 1st block and thus these two modes will be localized afterwards. Modes 3 and 4 will not be affected and thus refer to standard normal coordinates, while modes 5 and 6 constitute a 2nd block
• LOCAL=n LOCAL=1 localizes the normal coordinates of the CH-stretchings. Note that this destroys symmetry of these modes. Usually localization has strong impact on subsequent VSCF calculations. LOCAL=2 localizes the normal coordinates of a molecular cluster to the contributing entities. This localization scheme localizes within the individual irreps, which usually leads to a very faint localization. Switching symmetry off by MPG=1 in the XSURF program leads to a much stronger localization.
• NM1=n, NM2=m Denotes the normal coordinates to be rotated.
• THRLOC=value (=1.0d-6 Default) Threshold within the localization procedure.

SCALNM,options

The SCALNM directive allows for the scaling with respect to the individual normal coordinates or an automated scaling of all of them. This is the recommended choice for potentials dominated by quartic rather than quadratic terms. At most 3N-6 individual scale factors and shift parameters can be provided. In particular the AUTO option was found to be very helpful in practical applications.

#### Options

• AUTO=on / off AUTO=on (default) switches on an automatic scaling procedure of the potential in order to determine meaningful elongations and SHIFT values with respect to all coordinates, i.e. for each normal mode an optimized scaling parameter SFAC and SHIFT parameter will be determined. Usually this results in an increased number of 1D grid points. The AUTO keyword intrinsically depends on the thresholds and parameters, which can be controlled by the keywords THRSHIFT, ITMAX, LEVMAX, DENSMAX, and DENSMIN.
• DENSMAX=value (=1.d-2 default) Threshold for the maximum vibrational density on the edges of the potential needed for the automated upscaling of the potentials (see keyword AUTO).
• DENSMIN=value (=1.d-4 default) Threshold for the minimum vibrational density on the edges of the potential needed for the automated downscaling of the potentials (see keyword AUTO).
• ITMAX=n (=10 default) Specifies the maximum number of iterations within the automatic scaling of the potentials (see Keyword AUTO).
• LEVMAX=n Maximum number of vibrational states to be included for controlling the automated scaling and shifting procedure. The default is set to 5. This value should support subsequent VCI calculations.
• MODE=n Denotes the normal coordinate to be scaled or shifted.
• SFAC=value Scaling factor for mode MODE. The default is 1.0.
• SHIFT=n Allows to shift the potential with respect to the specified coordinate by n or -n grid points, respectively. Default: SHIFT=0.
• SHOW=n (=0 default) Addition printing within the scaling procedure is switched on by SHOW=1.
• THRSHIFT=value Threshold controlling the automated shifting of potentials as obtained from the state densities on the lhs and rhs of the potentials. The default is given as THRSHIFT=0.05.

FIT,options

A fit function has to be defined for each coordinate. These fit functions are used as an intermediate fit to generate a fine grid representation of the potential energy surface. The fit functions can be defined either by the user or automatically via cross-validation. If no electronic structure level for the cross-validation is provided by the user, polynomials are used as a default. This directive also exists in the POLY program. If no fit functions are defined within the XSURF program, but in the POLY program, the fit functions of the POLY program are also used in the XSURF program.

#### Options

• COORD(x)=variable Defines the fit function for coordinate $x$. The possible fit functions are B-splines (bspline), Gaussian functions (gauss), Morse functions (morse), polynomials (poly) and trigonometric functions (trigo).
• FITLABEL=variable The name of the label defined in the input stream. The label contains the electronic structure level which should be used for the cross-validation.
• FITMETHOD=n (=1 Default) Within the iterative build-up of the individual subsurfaces, intermediate fitting will be used. This can be based on true multidimensional Kronecker product fitting (FITMETHOD=1) or on fitting along one-dimensional cuts (FITMETHOD=2).
• FITxD=n The maximum order of the polynomials used for fitting within the iterative interpolation scheme can be controlled by the keywords FIT1D, FIT2D, FIT3D, FIT4D. The default is given by 9. However in certain cases higher values may be necessary, but require an appropriate number of coarse grid points, which can be controlled by MIN1D etc. (See XSURF options)
• ONLY=variable Sets one fit function for all coordinates. The possible fit functons are the same as for the option COORD.

POINTS,options

The positioning of the ab initio single points along a coordinate can be controlled by this directive. The default is currently an empirically fixed distribution. Alternatively one can use a positioning based on Gaussian process regression.

#### Options

• GPRDERIV=n (=2 Default) Up to the dimension n, the derivatives obtained by a Gaussian process regression are used to weight the variance.
• GPRGRIDxD=n. The number n of grid points for which the variance is computed for the dimension x. Only odd values are possible. As a default, the maximum number of ab initio points is used. (See keyword MAXxD)
• GPRPRExD=n. For higher dimensions, it is recommended that the variance is not computed for all desired points. Instead a pre-selection, also based on gaussain process regression is used. With this keyword, n points are used for the pre-selection of the dimension x. Negative values will switch the pre-selection off. For the 1D and 2D, no pre-selection is done by default. The default for higher dimensions is set to 4. Not, that this value has to be considered adequately with respect to the keyword GPRGRIDxD.
• POINT_SCHEME=variable (=NOSHIFT Default) The distribution of ab initio points along a coordinate is determined by a fixed point scheme. This distribution has been generated for potentials, which have not been shifted. For strongly shifted potentials, improved point schemes can be used by the option POINT_SCHEME=SHIFT.
• TYPE=variable (=fix Default) In the case TYPE=gpr, the variance obtained by a Gaussian process regression is used to determine new points were the energy as to be computed.

VFREQ,options

Usually, the diplacements vectors of the normal coordinates are retrieved from a preceding harmonic frequency calculation called by the FREQ program. Alternatively, these vectors can be obtained from the XSURF program and the VFREQ directive. However, this alternative is solely based on a twofold numerical differentiation and does not take advantage out of analytical derivatives. However it offers a couple of options, which are not available in the FREQ program.

#### Options

• COORD=n (=2 Default) Symmetry adapted coordinates, COORD=1, or Cartesian coordinates, COORD=2, may be used within the numerical differentiation.
• METHOD=n (=1 Default) This option specifies the number of points within the numerical differentiation, i.e. METHOD=1 refers to the standard 3-point formula (central differences), METHOD=2 denotes the more accurate 5-point formula and METHOD=3 the 7-point formula.
• PRINT=n (=1 Default) Printout control.
• START=label This sets the label in the input stream to determine the electronic structure level to be used.
• STEP=value (=1.0d-2 Default) This option specifies the step width within the numerical differentiation.

GRAPH,options

The GRAPH directive is the interface to programs for visualizing potential terms and to provide potential information for any other programs in a most simple manner.

#### Options

• DIRECTORY=path (=./plots1 Default) Path or name of the directory to be specified for dumping the files for visualisation. See the keyword NDIM.
• MOLDEN=file name This allows to dump a file, which can directly read in by the Molden or Wxmacmolplot programs. This allows for the visualisation of the geometry and the harmonic frequencies of the molecule.
• NDIM=n (=0 Default) This keyword writes all nD surfaces and a corresponding Gnuplot script in a separate subdirectory (plots1) in the home-directory in order to allow for visualization of the computed nD surfaces. E.g. the command “gnuplot plotV1D.gnu” in the plots1 directory produces .eps files for all 1D surfaces.

REPAR,options

Within the framework of multi-level calculations (see the directive VMULT), 3D and 4D terms can be modeled. The modeling scheme is based on a reparametrization of the semiempirical AM1 method. Consequently, in the input stream the energy variable to be read in must refer to a semiempirical calculation. After the 2D terms the program optimizes the semiempirical parameters in order to represent the 1D and 2D surfaces best.

#### Options

• ITMAX1D=n The maximum number of iterations in the local optimization of the semiempirical parameters can be controlled by ITMAX1D and ITMAX2D. The defaults are ITMAX1D=100 and ITMAX2D=150.
• RMS1D=value The keywords RMS1D and RMS2D specify the threshold for terminating the 1D and 2D iterations in the local optimization of the semiempirical parameters. The defaults are given by RMS1D=1.d-6 and RMS2D=1.d-6.

The following example shows the input for a surface calculation in which the 3D terms will be modeled.

memory,20,m
orient,mass
geometry={
3
Water
O          0.0675762564        0.0000000000       -1.3259214590
H         -0.4362118830       -0.7612267436       -1.7014971211
H         -0.4362118830        0.7612267436       -1.7014971211
}

hf
mp2
optg
freq

label1
abinitio
basis=vdz
int
rhf
mp2
goto,label4

label2
semi,am1
int
rhf

label4
{xsurf
vmult,start2D=label1,start3D=label2,multi=4
repar}
poly
vscf,pot=poly
vci,pot=poly

ALTER,options

The ALTER directive of the XSURF program allows to apply error correction schemes for individual single point calculations. For example, in case that the Hartree Fock calculation for a certain grid point did not converge and the ORBITAL directive in the subsequent electron correlation calculation uses the IGNORE_ERROR option, an alternative calculation scheme can be provided, e.g. MCSCF in contrast to RHF. It allows to apply error correction schemes for individual single point calculations. For example, in case that the Hartree Fock calculation for a certain grid point did not converge and the ORBITAL directive in the subsequent electron correlation calculation uses the IGNORE_ERROR option, an alternative calculation scheme can be provided, e.g. MCSCF in contrast to RHF. The ALTER directive always requests to specify a new label, which replaces the old one. If more than one label shall be replaced, the ALTER directive needs to be called repeatedly.

#### Options

• NEW=label Specification of the new label.
• OLD=label Specification of the old label.

Note that DFT calculations often still converge when RHF calculations already fail to do so. The following example demonstrates the use of the ALTER directive within a multi-level PES calculation. In case that the RHF calculation for the 1D or 2D terms does not converge, this will be recognized by the UCCSD(T)-F12a calculations. The option orbital,ignore_error=2 prevents a termination of Molpro and the programs tries to enforce convergence by the recipe specified below label5.

!options: --logfile-scratch
memory,500,m
geometry={
O   ,,     -0.4187902305    ,   -2.0024156961    ,    0.0000000000
N   ,,      0.9293931761    ,   -0.1403574221    ,    0.0000000000
N   ,,     -0.3385150234    ,    2.0246339597    ,    0.0000000000
H   ,,     -2.2504006895    ,    1.9819452952    ,    0.0000000000
H   ,,      0.6869538492    ,    3.6185403577    ,    0.0000000000
}

basis=vtz-f12
mass,iso

charge=1
{rhf
start,atden}
uccsd(t)-f12a
optg
freq,symm=auto

{rhf
start,atden}
{uccsd(t)-f12a,freeze_save=1891.2}

label1
symmetry,auto
charge=1
{rhf
start,atden}
{uccsd(t)-f12a,freeze_start=1891.2;orbital,ignore_error=2}
goto,label4

label2
symmetry,nosym
charge=1
{uks,b3lyp
start,atden}
goto,label4

label5
symmetry,nosym
basis=vtz-f12
int
{rhf
start,atden
save,2111.2}
{multi
occ,13
closed,11
wf,23,1,1
canonical,3111.2
start,2111.2}
{rhf
start,3111.2}
{uccsd(t)-f12a,freeze_start=1891.2}

label4
{xsurf,sym=auto
alter,old=label1,new=label5
vmult,start2D=label1,start3D=label2,multi=4
disk,where=home,dump='N2H2O.pot'}


DELETE,surface labels

The DELETE directive allows to eliminate individual surfaces within the multi-mode expansion of the potential. Unlike the SKIP keyword, this directive can only be used once a calculation is restarted from a completed potential energy surface calculation. This directive is meant for studying the impact of individual surfaces or to eleminate troublesome surfaces, which failed to converge in the iterative fitting procedure.

 DELETE,i,j deletes the 2D surface $ij$ DELETE,i,j,k deletes the 3D surface $ijk$ DELETE,i,j,k,l deletes the 4D surface $ijkl$

VIBMODE,options

The VIBMODE directive allows to span the PES only with predefined modes. The following options can be combined in various ways.

#### Options

• ENERGHIGH=value Modes with a frequency lower than value are used to span the surface (according to the harmonic frequencies)
• ENERGLOW=value Modes with a frequency higher than value are used to span the surface (according to the harmonic frequencies)
• HIGH=n the highest n modes are used to span the surface
• LOW=n the lowest n modes are used to span the surface
• MODE=n Mode which is used to span the surface (can be used multiple times)

INTERFACE,options

The INTERFACE directive allows for the communication with other programs. It writes information about the individual grid points of a PES to an external ASCII file, which can be processed by other software. Likewise, files in the same structure with additional information from external programs can be read in. After reading in all data points, the date points will be transformed into a fine grid and fitted to polynomials.

#### Options

• COPY=n (=0 Default) Once new data have been generated in the external ASCII file, the coefficients of the corresponding polynomials can be displayed in the POLY program using the option COEF_INTERFACEx with (x=1,2…). It is also possible to replace the energy or dipole surfaces generated by Molpro by these new quantities by COPY=ENE or COPY=DIP.
• DATA=n (=1 Default) DATA=1 provides detailed information about each single point of the PES in a formatted output. DATA=2 provides the geometry and energy of a given point in a single line. New information about this point needs to be added at the end of the line. DATA=2 prints the displacements along the coordinates and the energy in a single line. Again, new information needs to be added at the end of this line.
• FILE=file name Specifies the name of the external file.
• NDIM=n (=0 Default) Dimension of the $n$-mode expansion to which the geometry information shall be dumped.
• NRES=n (=1 Default) Number of columns being added to the external file by an external program.
• SURFACE=n (=0 Default) Information about the energy values printed in the external file. SURFACE=0 refers to absolute energies (minus the reference energy), while SURFACE=1 refers to energy differences belonging to the individual increments of the subsurfaces.
• TYPE=variable (=OUT Default) This option controls, if the file shall be written TYPE=OUT or read in TYPE=IN.
• ZERO=n (=1 Default) If set to 1, geometries of lower orders of the $n$-mode representation will be printed, i.e. the external file contains redundand data. ZERO=0 neglects all redundancies and prints only unique points. As a consequence, an external file generated this way cannot be read in again for technical reasons.

XGRIDCOMP,options

The GRIDCOMP directive of the XSURF program allows to interface Molpro with a grid computing client such as Segl. It is also possible to use the grid computing interface without any grid computing client by using scripts, which will automatically been generated within the individual calls of XGRIDCOMP. The charge of the molecule as well as some other general commands are transferred to the individual grid point command files, which are printed out in the subdirectory points. If there are any doubts whether the specified command is transferred to the single point or not, the command should be given within the definition of the electronic structure calculations. Note, grid computing is needed is very special cases, when the standard “XSURF” procedure shall be bypassed.

#### Options

• CORES=n Number of cores to be used within the grid computing.
• FILE=n (n=1..2) specifies the file number of the Molpro *.wfu file (see the FILE command of Molpro).
• LOOP=n When processing the batches of single point calculations, the grid coumputing interface needs to know, if it is the very first batch (LOOP=0), in which just input files for Molpro will be generated or if it is one of the subsequent batches (LOOP=1), in which also the outputs of processed single point calculations need to be read in.
• MEMORY=n Denotes the amount of memory (in MW) which is needed in each single point calculation. The default is given by 100 MW.
• WFU=file name If additional information need to be read in from a .wfu file, this can be specified here.
!options: --logfile-scratch
memory,50,m
orient,mass
geometry={
6
Ethene
C          0.0000000000        0.0000000000       -0.6685890718
C          0.0000000000        0.0000000000        0.6685890718
H          0.0000000000       -0.9240027061       -1.2338497710
H          0.0000000000        0.9240027061       -1.2338497710
H          0.0000000000        0.9240027061        1.2338497710
H          0.0000000000       -0.9240027061        1.2338497710
}

mass,iso
basis=vtz

hf
ccsd(t)
optg
freq,symm=auto

label1
int
{hf
start,atden}
ccsd(t)
goto,label4

label2
int
{hf
start,atden}
{mp4
notripl}
goto,label4

label3
int
{hf
start,atden}
mp2

label4
{xsurf,sym=auto
xgridcomp,memory=10,loop=0
vmult,start2D=label2,start3D=label3,Var3D=EMP2,Multi=3
disk,where=home,dump='ethene.pot'}
vscf
vci

To generate a potential energy surface with the grid computing interface, follow these steps:

• Run a Molpro calculation on the master control file (see the example above) to generate the control files for the individual single points.
• Use the generated xgridcomp.sh to run the individual single point calculations.
• Increase the loop option to 1, read in the generated *.pot file (using the EXTERN command) and dump to a new *.pot file, e.g. ethene_2.pot.
• Repeat the last steps until all single point calculations have been performed.

VADD,options

In practice one may come to the conclusion that the $n$-mode expansion of an existing potential has been truncated too early and one needs to extend the order. Once the level of the electronic structure calculations shall not be changed between the highest existing order and the one to be added, one can simply restart the calculation from the exisiting restart file by increasing the option NDIM in the input stream. However, if one needs to alter the electronic structure level, the VADD directive needs to be used.

#### Options

• START=label Specification of the label for the order to be added.
• QCOORD=variable (=POT Default) This option specifies from where to take the displacement vectors for the normal coordinates. By default they are taken from the external restart file, but QCOORD=FREQ allows to take them from a new harmonic frequency calculation.

CHECK,options

The CHECK directive of the XSURF program allows for a quality check of a completed surface. This routine simply computes the exact ab initio energies at randomly selected grid points and compares these values with the interpolated ones, which will be used subsequently for the determination of the wavefunction. This program is fully parallelized.

#### Options

• LEVEL=n Denotes the level to be checked, i.e. 1 corresponds to 1D, etc. Note, levels below $n$ will not be checked automatically.
• POINTS=value Determines the number of grid points in one dimension to be checked. The default is set to 4.

EXTRADATA,options

The XSURF programs allows to compute energy surfaces, dipole surfaces and polarizability surfaces. In addition to that, arbitrary property surfaces can be generated and dumped into an external restart file.

#### Options

• NDIM=n Dimension of the $n$-mode expansion to be used for the new property.
• NEL=n Number of data to be read in for one point.
• VARx=variable (x=number) Name of the variable, which shall be read from the input file.

It is recommended to

• use the ORIENT,MASS keyword in order to rotate the molecule into standard orientation. This is necessary for a full exploitation of symmetry within the generation of the potential energy surface.
• use the MASS,ISO keyword to use the most available isotopes.
• use multi-level schemes in combination with symmetry and run Molpro in parallel in order to speed up the calculations. Explicitly correlated methods are preferable over conventional approaches.
• always dump the potential energy surface to an external file.

SURF,options

The old SURF program for generating potential energy surfaces is still implemented, but will no longer be supported in the future. The new and much improved XSURF code follows the same philosophy and many options are the same as in the old SURF code, but XSURF cannot read any potential files being generated by SURF. If you need to use the old SURF program, see older versions of the manual for the corresponding keywords.