# Binary result files¶

## ams.rkf¶

The main ams.rkf file is written by the AMS driver. It contains high level information about the trajectory that the AMS driver took over the potential energy surface. Part of what used to be on TAPE21 is since the AMSification of ADF in ams.rkf.

This file contains information on geometry optimization, transition state search, linear transit, PES scan, NEB, or IRC, if that was requested in the calculation. For a geometry optimization or transition state search, for example, it contains the history of how the systems geometry changed during the optimization as well as the final optimized geometry. The format in which this information is written is independent from which engine was used for a calculation.

If a property, like vibrational modes, is tied to a special point on the potential energy surface, it is stored in the engine main output file adf.rkf.

## adf.rkf (TAPE21)¶

adf.rkf is the general result file of an ADF calculation. In ADF<=2019 it was known as TAPE21. It is a KF file: Direct-Access, binary, and keyword driven. It contains information about the calculation. You can use it as a fragment file in a subsequent calculation on a bigger molecule, where the current one may be a part, or in an analysis program. Part of what used to be on TAPE21 is since the AMSification of ADF in ams.rkf.

A description of the various utilities that can be used to process adf.rkf can be found in other parts of this ADF manual.

### adf.rkf: Added notes¶

#### Section Multipole matrix elements¶

Information about a response calculation

`dipole elements`

The matrix elements of the 3 dipole operator components between occupied and virtual orbitals: outer loop over the operators (in order: y, z, x), loop over virtual MOs, inner loop over occupied MOs

`quadrupole elements`

Similar as for dipole. Order of operators: \(\sqrt{3}\) *xy \(\sqrt{3}\) *yz z2-(x2+y2)/2 \(\sqrt{3}\) *xz \(\sqrt{3}\) *(x2-y2)/2

`octupole elements`

Similar as for dipole and quadrupole. Order of operators: \(\sqrt{10}\) *y*(3*x2-y2)/4 \(\sqrt{15}\) *xyz \(\sqrt{6}\) *y*(4*z2-x2-y2)/4 z*(z2-3(x2-y2)/2) \(\sqrt{6}\) *x*(4*z2-x2-y2)/4 \(\sqrt{15}\) *z*(x2-y2)/2 \(\sqrt{10}\) *x*(x2-3y2)/4

`hexadecapole elements`

Similar as for dipole and quadrupole. Order of operators: \(\sqrt{35}\) *xy*(x2-y2)/2 \(\sqrt{70}\) *z*(3x2y-y3)/4 \(\sqrt{5}\) *xy*(6z2-x2-y2)/2 \(\sqrt{10}\) *(4yz3-3yz*(x2+y2))/4 (8z4-24*z2*(x2+y2)+3(x4+2x2y2+y4))/8 \(\sqrt{10}\) *(4xz3-3xz*(x2+y2))/4 \(\sqrt{5}\) *(x2-y2)*(6z2-x2-y2)/4 \(\sqrt{70}\) *z*(x3-3xy2)/4 \(\sqrt{35}\) (x4-6x2y2+y4)/8

#### Representation of functions and frozen cores¶

ADF uses the cartesian representation for the spherical harmonics part in functions:

The angular momentum quantum number *l* is then given by *l*=a+b+c, and the main quantum number *n* = *l* +d+1.

There are (*l* + 1)(*l* + 2)/2 different combinations of (a, b, c) for a given *l* - value, rather than (2 *l* +1). The excess is caused by the presence of spurious non-*l* Functions in the set; a Cartesian d-set for instance consists of six functions, five of which are true d-functions while one linear combination is in fact an s-type function (x2+y2+z2). Only the five true d-combinations are actually used as degrees of freedom in the basis set, but lists of primitive basis functions (bas) for instance run over all Cartesian functions including the improper ones.

A function *set* in ADF is characterized by the quantum numbers *l* and *n*, and by the exponential decay factor a. A set thus represents (*l* +1)(*l* +2)/2 Cartesian functions and (2 *l*+1) degrees of freedom.

The atomic frozen core orbitals are described as expansions in Slater-type functions; these are not the functions of the normal basis set but another set of functions, defined on the data files you use in Create mode.

Orthogonality of the valence space to the frozen core states is enforced as follows: for each frozen core shell (characterized by the quantum numbers *l* and *n*: all orbitals with *m* = - *l* … + *l* are identical apart from rotation in space) the set of valence basis functions is augmented with a so-called core orthogonalization function set. You may conceptually interpret the core orthogonalization functions as single zeta expansions of the true frozen core states. Each of the normal valence basis functions is now transformed into a linear combination of that valence function with all core orthogonalization functions, where the coefficients are uniquely defined by the requirement that the resulting function is orthogonal to all true core functions.

So the list of all Cartesian basis functions is much larger than the degree of freedom of the basis: it contains the spurious *non-l* combinations and it contains also the core orthogonalization functions.

#### Evaluation of the charge density and molecular orbitals¶

adf.rkf contains all the information you need to evaluate the charge density or a Molecular Orbital (MO) in any point in space. Most of the information is located in section Basis:

A list of function characteristics (kx,ky,kz,kr,alf), including the core orthogonalization functions. This list does *not* run over *all* bas functions used in the molecule: if a particular function is used on the atoms of a given atomtype, the function occurs only once in the list, but in the molecule it occurs as many times as there are atoms of that type.

With array nbptr you locate the subsections in the function list that correspond to the different types of atoms: for atom type i the functions nbptr(i)…nbptr(i+1)-1. The distinct atom types are listed in an early section of the standard output file.

Array nqptr gives the number of atoms for type i: nqptr(i+1)-nqptr(i). With this information you construct the complete list of all functions. Repeat the subsection of type i as many times as there are atoms of that type: the complete list can be considered to be constructed as a double loop, the outer being over the atom types, the inner over the atoms that belong to that type. The total ‘overall’ list of functions you obtain in this way contains naos functions. Note that in this way we have implicitly also defined a list of all atoms, where all atoms that belong to a particular atom type are contiguous. This list is the so-called ‘internal’ atom ordering, which may not be identical to the order in which atoms were specified in input, under atoms.

For a given symmetry representation (Sections S) the array npart gives the indices of the basis functions in the overall list that are used to describe orbitals in this representation. In case of an unrestricted run the array npart applies for either spin: the same basis functions are used; the expansion coefficients for the molecular orbitals are different of course.

In the symmetry-representation sections Eigen_bas gives the expansion coefficients that describe the MOs. The expansion refer to the functions indicated by npart, and the function characteristics are given by the arrays kx,ky,kz,kr,alf, *and* bnorm, i.e. the expansion is in* normalized*functions.

The value of an MO is now obtained as a summation of values of primitive basis functions. For the evaluation of any such basis function you have to take into account that its characteristics are defined in the local coordinate system of its atom.

To obtain the charge density you sum all MOs, squared and multiplied by the respective occupation numbers (array froc in the appropriate irrep section).

Note that the auxiliary program densf, which is provided with the ADF package, generates orbital and density values on a user-specified grid.

## TAPE10¶

TAPE10 is a binary KF file. By default TAPE10 is a scratch file. TAPE10 contains data related to the numerical integration: points and weights, values of functions (depends on direct-SCF options) and core densities and potentials.

Use the keywords ‘SAVE TAPE10’ in the ADF calculation such that TAPE10 is saved. NMR requires a TAPE10 file, see also documentation on NMR chemical shifts and NMR spin-spin couplings.

## TAPE13¶

TAPE13 is a binary KF file. TAPE13 is the checkpoint file for restarts after a crash. It is a concise version of adf.rkf, containing only the data the program uses for restarting the calculation. See the restart keyword. Note that since the AMSification of ADF in most case this TAPE13 has lost it usefulness. Instead one should use the file ams.rkf, which is produced by the AMS driver, for restarting a geometry optimization, for example.

Like adf.rkf, TAPE13 is a binary, keyword driven KF file.

The calculation that produces TAPE13 determines which section are written on it. The actual values of the variables should be identical to the corresponding variables on adf.rkf. Also they should have the same names and be located in the same sections. In some cases, TAPE13 contains the complete corresponding section of adf.rkf.

## TAPE15¶

TAPE15 is a binary KF file. By default TAPE15 is a scratch file. TAPE15 contains data related to matrices like the density matrix, the Fock matrix, and the overlap matrix.

Use the keywords ‘SAVE TAPE15’ in the ADF calculation such that TAPE15 is saved. Some external programs may need data that is stored on TAPE15. See, for example, the documentation on adf2nbo to produce an input for NBO and adf2damqt to produce an input for DAMQT.

## TAPE41¶

TAPE41 is a binary KF file. It is produced by the *densf* program to generate values of molecular orbitals, charge densities and potentials in a user-specified grid, to be used typically for plotting or graphical display, see the documentation on densf.

## Other binary files¶

In the results directory that ams creates one may find other binary KF files. There may be binary adf.rkf-like output files for some points on the potential energy surface that was visited during the calculation. One may find t21.*.elementname files which are atomic adf.rkf-like files, that were created during an ADF calculation. One may find the binary t12.rel file that is not a KF file, which is an auxiliary binary file for relativistic calculations. Depending on the kind of ADF calculation more binary KF (scratch) files may be used.