# Interface to CFOUR by J. Stanton and J. Gauss

Code author: Lori A. Burns

Section author: Lori A. Burns

Module: Keywords, PSI Variables, Samples

Psi4 contains code to interface to the Cfour quantum chemistry suite of John F. Stanton (U. Texas, Austin) and Jürgen Gauss (U. Mainz), which is available after a license agreement from http://www.cfour.de/.

## Installation

Follow the instructions provided with the Cfour download to install the executable or to build the source. To by used by Psi4, the program binary (xcfour) must be found in your `PATH` or `PSIPATH`. The `GENBAS` file containing basis sets in Cfour format is not necessary for this interface, but if you prefer to access basis sets the “Cfour way” using a custom `GENBAS` file (the distributed one is included with the interface), it, too, must be in `PATH` or `PSIPATH`. If Psi4 is unable to execute the binary, an error will be reported.

Caution

The p4c4 interface hasn’t been fully adapted for the new March 2014 version.

## Cfour for Psi4 Users

- Set memory as usual
- Set molecule as usual
- Set basis set as usual (Cfour only cares about orbital basis, no fitting bases)
- Set the task as usual, indicating Cfour as the intended code by prepending “c4-” to the method argument. So `energy('scf')` becomes `energy('c4-scf')` and `optimize('ccsd(t)')` becomes `optimize('c4-ccsd(t)')`. Find available methods for `energy()` at Energy (CFOUR) and for `optimize()` at Gradient (CFOUR).
- Generally, the p4c4 interface will handle best practices for path of execution: `vcc`/`ecc`, derivative type, etc. The user is still responsible for setting convergence, frozen core, guess, diis, etc. For the moment, so-called “best-practices” keywords are summarized at Best Practices.
- For the type of computation intended, find appropriate options at Keywords. These keyword summaries contain the same information as the proper CFOUR options list plus notes on keyword relevance when run through Psi4. Information at the CFOUR manual may also be useful, as may the many samples at psi4/samples/cfour.
- Set Cfour keywords just like Psi4 keywords. The names of keywords are unchanged beyond a prepended “cfour_”. (Though be aware that common abbreviations like CALC and REF must be fully spelled out as CFOUR_CALC_LEVEL and CFOUR_REFERENCE when used in Psi4.)
- In limited trial cases, keywords nominally directed at non-Cfour modules are translated into their Cfour counterparts. For example, setting REFERENCE will appropriately set CFOUR_REFERENCE. For a list of applicable keywords, see source of `qcdb.cfour.muster_psi4options()`.
- Consult Functionality for information on what Cfour functionality is accessible through Psi4.

## Psi4 for Cfour Users

In the simplest use of the Psi4/Cfour interface, a Psi4 input file can simply “wrap” a `ZMAT` file and execute xcfour. This is illustrated in the following example:

    cfour {
    UHF-SCF energy calculation
    N
    H 1 R
    H 1 R 2 A

    R=1.008
    A=105.0

    *ACES2(CALC=HF,BASIS=qz2p
    MULT=2,REF=UHF
    OCCUPATION=3-1-1-0/3-0-1-0
    SCF_CONV=12
    MEMORY=20000000)
    }

    energy('cfour')

Here, the contents of the `cfour {...}` block are written directly to a `ZMAT` file. This is joined by a default `GENBAS` file (psi4/lib/basis/GENBAS). To preferentially use your own `GENBAS`, place it in `PATH` or `PSIPATH`. The line calling `energy()` with argument `'cfour'` invokes xcfour.

After execution of the `energy('cfour')` line completes, Cfour results are read back into Psi4 format and are thereafter accessible for further processing in the input file. See Output for details. This storage of results in variables and arrays in memory for the duration of the Psi4 instance (as opposed to solely in files) is the only advantage thus far incurred by the P4C4 interface. We’ll call this mode of basic utility the “sandwich” mode.

Molecule specification in Psi4 allows Cartesians, Z-matrices, mixed Cartesian/Z-matrix, negation of variables, delayed specification of variables, specification of fragments, etc., all in a whitespace-tolerant format. See Molecule and Geometry Specification for details and cfour/mints5 for examples. When a Psi4-style molecule is supplied, its geometry is written to `ZMAT` in Cartesian form and the CFOUR_COORDINATES=CARTESIAN, CFOUR_UNITS=ANGSTROM, CFOUR_CHARGE, and CFOUR_MULTIPLICITY keywords are set appropriately in the `*CFOUR(...)` directive.

Warning

There exist molecules (e.g., allene) where the inertial frame is not unique (planes along atoms or between atoms). The orientation reconciling machinery currently does not handle these cases and will fail with “Axis unreconcilable between QC programs”. I will get to this soon.

Whenever the molecule is supplied in Psi4 format, the job control keywords must be too. All Cfour keywords are the usual ones, prepended by `cfour_` to avoid any possible name conflicts. As detailed in Job Control Keywords, setting keywords is flexible in format. The previous example translates to:

    # UHF-SCF energy calculation

    molecule {
    0 2                                          # multiplicity from the MULT keyword
    N
    H 1 R
    H 1 R 2 A

    R=1.008
    A=105.0
    }

    set {
    cfour_CALC_level=HF                          # only full keyword names allowed
    cfour_BASIS=qz2p
    #MULT=2                                      # now in molecule {...} block
    cfour_REFerence=UHF
    cfour_OCCUPATION [[3, 1, 1, 0], [3,0,1,0] ]  # arrays in python notation
    cfour_SCF_CONV=12
    cfour_MEMORY=20000000
    }

    energy('cfour')

Here, note that none of capitalization, equals sign, or whitespace matter for the keyword commands. Specifcation of strings and integers requires no translation; booleans have extended freedom of format; arrays must be translated into Python-style (square-bracket bounded and comma delimited) of appropriate dimension. There are many sample inputs in psi4/tests/cfour/ starting with `sp-` that take examples from the Cfour manual and first run them in sandwich mode and then run them as translated into Psi4 format.

Note

Psi4 only recognizes keywords by their full name, so the common Cfour keyword abbreviations CALC, REF, etc. must be replaced by their proper names of CFOUR_CALC_LEVEL, CFOUR_REFERENCE, etc.

Whenever the molecule is supplied in Psi4 format, it is possible to perform geometry optimizations where Cfour supplies the gradient and the Psi4 module optking drives the structural changes. Because of the limitations on geometry specification for optimizations in Cfour, optking-driven optimizations are the only optimizations allowed in the P4C4 interface. (The exception is sandwich mode, which, of course, permits optimizations with the Cfour optimizer.) Below is an example of a geometry optimization:

    memory 200 mb

    molecule {
    O
    H 1 R
    H 1 R 2 A

    R=0.958
    A=104.5
    }

    set {

    cfour_CALC_level CCSD(T)
    cfour_BASIS      DZP
    cfour_CC_CONV    12
    cfour_LINEQ_CONV 12
    cfour_SCF_CONV   12
    g_convergence    cfour
    }

    optimize('cfour')

Note that the primary change is the exchange of `energy()` for `optimize()` to trigger an optimization. Setting G_CONVERGENCE=CFOUR provides a good imitation of Cfour default convergence criteria. Although Cfour produces gradients only in its standard orientation and atom ordering, these are transformed back to input orientation by the P4C4 interface. Several sample inputs in psi4/tests/cfour/ starting with `opt-` show basic geometry optimizations. cfour/mints5-grad shows optimizations from a variety of molecule input formats, and cfour/psi-ghost-grad shows an optimization with ghosted atoms. To obtain a single gradient sans optimization, call instead `gradient()`.

Note that it can be convenient to monitor the progress of a geometry optimization by grepping the tilde `~` character.

    Measures of convergence in internal coordinates in au.
    Criteria marked as inactive (o), active & met (*), and active & unmet ( ).
    --------------------------------------------------------------------------------------------- ~
     Step     Total Energy     Delta E     MAX Force     RMS Force      MAX Disp      RMS Disp    ~
    --------------------------------------------------------------------------------------------- ~
      Convergence Criteria    1.00e-06 *    3.00e-04 *    1.00e-06 *    1.20e-03 *             o  ~
    --------------------------------------------------------------------------------------------- ~
        1     -76.33224285   -7.63e+01      2.41e-03      1.60e-03      1.51e-02      8.82e-03 o  ~
        2     -76.33226097   -1.81e-05      4.84e-04      4.03e-04      7.71e-04 *    7.04e-04 o  ~
        3     -76.33226140   -4.39e-07 *    4.31e-05 *    3.58e-05      9.89e-05 *    8.93e-05 o  ~
        4     -76.33226141   -4.26e-09 *    9.76e-07 *    6.58e-07 *    6.22e-06 *    3.71e-06 o  ~
    --------------------------------------------------------------------------------------------------------------- ~
     Step         Total Energy             Delta E       MAX Force       RMS Force        MAX Disp        RMS Disp  ~
    --------------------------------------------------------------------------------------------------------------- ~
        1     -76.332242848098    -76.332242848098      0.00241281      0.00160359      0.01507630      0.00881949  ~
        2     -76.332260965382     -0.000018117284      0.00048446      0.00040256      0.00077146      0.00070447  ~
        3     -76.332261404452     -0.000000439070      0.00004307      0.00003577      0.00009889      0.00008926  ~
        4     -76.332261408714     -0.000000004262      0.00000098      0.00000066      0.00000622      0.00000371  ~
    --------------------------------------------------------------------------------------------------------------- ~

The above example also shows the total memory for the computation being set in Psi4 format. See Memory Specification for details. When specified, the memory value is passed on to Cfour by setting keywords CFOUR_MEMORY_SIZE and CFOUR_MEM_UNIT=MB.

Psi4 has an extensive basis set library in Gaussian94 format. See Basis Sets for details. Contrasts to Cfour basis handling include identifying basis sets by standard name (aug-cc-pVDZ instead of AUG-PVDZ), direct handles for diffuse-function-pruned sets (e.g., jun-cc-pVDZ), case insensitivity, appropriate setting of spherical/Cartesian depending on basis set design, and syntax to set different basis sets to different classes of atoms without listing each atom. All of these features are available to Cfour by using the BASIS keyword instead of CFOUR_BASIS (accompanied, of course, by specifying the molecule Psi4-style). Internally, Psi4 processes the basis set as usual, then translates the basis set format and writes out a `GENBAS` file with an entry for each atom. The P4C4 interface sets keyword CFOUR_BASIS=SPECIAL and CFOUR_SPHERICAL as appropriate, then writes the basis section necessary for SPECIAL below the `*CFOUR(...)` block. (I’m sorry that the name of the basis doesn’t appear in `ZMAT`, but the combination of the ~14 character basis name limit and the absence of a comment line marker rather precludes that helpful label.)

The input below employs a Psi4 library basis set and also introduces the final stage of conversion toward Psi4 format. Instead of the generic `'cfour'`, the computational method is specified as the first argument to the `optimize()` call. In the computational command below, the string argument `'c4-ccsd(t)'` directs that a CCSD(T) computation be run using Cfour (as opposed to `'ccsd(t)'` which would call Psi4 CC code). Specifying computational method in this manner sets CFOUR_CALC_LEVEL from the argument and CFOUR_DERIV_LEVEL as appropriate from the function call: `energy()`, `gradient()`, or `optimize()`. If those keywords are also set explicitly to contradictory values, the interface will complain.

    memory 2 gb

    molecule CH2F2  {
      units au
      C     0.0000000000  -0.0000000000   1.0890958457
      F     0.0000000000  -2.1223155812  -0.4598161475
      F    -0.0000000000   2.1223155812  -0.4598161475
      H     1.7084139850   0.0000000000   2.1841068002
      H    -1.7084139850  -0.0000000000   2.1841068002
    }

    set basis aug-cc-pvdz
    set rms_force_g_convergence 6
    set cfour_abcdtype aobasis
    set cfour_scf_conv 12
    set cfour_cc_conv 12
    set cfour_lineq_conv 12

    optimize('c4-ccsd(t)')

The utility of this method specification is that examination can be made of the reference, the derivative level, the excitation level, etc. and some options can be set according to best practices. Practically speaking, CFOUR_CC_PROGRAM (and eventually CFOUR_ABCDTYPE) will always be set to the fastest safe value. For example, the input above will run with CFOUR_CC_PROGRAM=ECC unless explicitly set to VCC.

An advantage of Psi4‘s Python driver is that any number of common work-up procedures can be automated and wrapped around the the conventional single-point and optimization procedures at the heart of all quantum chemistry codes. Three core “wrappers” available in Psi4 are `cp()`, `database()`, and `complete_basis_set()`; read their respective sections for details, but an overview is provided here. `cp()` computes the interaction energy of a bimolecular complex (counterpoise-corrected, not, or both).

    molecule dimer {
      Ne
    --
      Ne 1 R
      symmetry c1
    }

    Rvals=[2.5, 3.0, 4.0]
    set basis aug-cc-pVDZ

    for R in Rvals:
      dimer.R = R
      ecp = cp('c4-mp2')
      print_stdout('R [A] = %.1f  IE [kcal/mol] = %.3f\n' % (R, psi_hartree2kcalmol * ecp))

yields

    R [A] = 2.5  IE [kcal/mol] = 0.804
    R [A] = 3.0  IE [kcal/mol] = 0.030
    R [A] = 4.0  IE [kcal/mol] = -0.014

Next, the `database()` wrapper allows any computational model chemistry to be applied a predefined collection of molecules. Thus an input

    set {
        basis jun-cc-pvdz
        d_convergence 9
    }

    database('c4-mp2','nbc10',cp='on',subset='MeMe')

yields the counterpoise-corrected interaction energy for several points along the dissociation curve of methane dimer, which is a member of the NBC10 database:

    //>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>//
    //       Database nbc10 Results      //
    //<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<//

    For each VARIABLE requested by tabulate, a 'Reaction Value' will be formed from
    'Reagent' values according to weightings 'Wt', as for the REQUESTED ENERGY below.
    Depending on the nature of the variable, this may or may not make any physical sense.

    ==> Requested Energy <==

    ----------------------------------------------------------------------------------------------
                Reaction     Reaction Energy      Error           Reagent 1           Reagent 2
                                Ref     Calc [kcal/mol]              [H] Wt              [H] Wt
    ----------------------------------------------------------------------------------------------
           NBC1-MeMe-3.2     0.0690   1.1639     1.0949     -80.72700202  1     -40.36442840 -2
           NBC1-MeMe-3.3    -0.2390   0.6709     0.9099     -80.72764911  1     -40.36435916 -2
           NBC1-MeMe-3.4    -0.4170   0.3407     0.7577     -80.72806043  1     -40.36430165 -2
           NBC1-MeMe-3.5    -0.5080   0.1244     0.6324     -80.72831099  1     -40.36425461 -2
           NBC1-MeMe-3.6    -0.5410  -0.0129     0.5281     -80.72845373  1     -40.36421659 -2
           NBC1-MeMe-3.7    -0.5390  -0.0961     0.4429     -80.72852567  1     -40.36418623 -2
           NBC1-MeMe-3.8    -0.5150  -0.1430     0.3720     -80.72855247  1     -40.36416227 -2
           NBC1-MeMe-3.9    -0.4800  -0.1659     0.3141     -80.72855167  1     -40.36414365 -2
           NBC1-MeMe-4.0    -0.4390  -0.1733     0.2657     -80.72853498  1     -40.36412938 -2
           NBC1-MeMe-4.1    -0.3960  -0.1712     0.2248     -80.72850993  1     -40.36411859 -2
           NBC1-MeMe-4.2    -0.3540  -0.1633     0.1907     -80.72848118  1     -40.36411044 -2
           NBC1-MeMe-4.3    -0.3150  -0.1525     0.1625     -80.72845143  1     -40.36410422 -2
           NBC1-MeMe-4.4    -0.2790  -0.1403     0.1387     -80.72842215  1     -40.36409932 -2
           NBC1-MeMe-4.6    -0.2170  -0.1155     0.1015     -80.72836761  1     -40.36409177 -2
           NBC1-MeMe-4.8    -0.1680  -0.0933     0.0747     -80.72831991  1     -40.36408563 -2
           NBC1-MeMe-5.0    -0.1300  -0.0747     0.0553     -80.72827951  1     -40.36408021 -2
           NBC1-MeMe-5.4    -0.0800  -0.0479     0.0321     -80.72821875  1     -40.36407122 -2
           NBC1-MeMe-5.8    -0.0500  -0.0312     0.0188     -80.72817678  1     -40.36406353 -2
    ----------------------------------------------------------------------------------------------
             Minimal Dev                         0.0188
             Maximal Dev                         1.0949
         Mean Signed Dev                         0.3509
       Mean Absolute Dev                         0.3509
                 RMS Dev                         0.4676
    ----------------------------------------------------------------------------------------------

Thirdly, the `complete_basis_set()` wrapper allows any compound computational method that can be expressed through CBS to be applied to a molecule while employing the minimum number of calculations. For example, the job below computes a triple-quadruple-zeta Helgaker extrapolation of the mp2 correlation energy atop a quadruple zeta reference to which is appended a double-triple-zeta Helgaker extrapolated ccsd(t) - mp2 delta correction. Since the mp2 has been requested through Psi4 and the ccsd(t) through Cfour, the wrapper runs only MP2/cc-pVQZ (P4), CCSD(T)/cc-pVDZ (C4), and CCSD(T)/cc-pVTZ (C4) single-points.

    molecule {
    H 0.0 0.0 0.0
    H 1.0 0.0 0.0
    }

    set mp2_type conv

    cbs('mp2', corl_basis='cc-pV[TQ]Z', delta_wfn='c4-ccsd(t)', delta_basis='cc-pV[DT]Z')

This yields:

    ==> CBS <==

    ---------------------------------------------------------------------------------------------------------
        Stage               Method / Basis                                Energy [H]   Scheme
    ---------------------------------------------------------------------------------------------------------
          scf                  scf / cc-pvqz                             -1.10245974   highest_1
         corl                  mp2 / cc-pv[tq]z                          -0.03561890   corl_xtpl_helgaker_2
        delta     c4-ccsd(t) - mp2 / cc-pv[dt]z                           0.03507767   corl_xtpl_helgaker_2
        total                  CBS                                       -1.10300098
    ---------------------------------------------------------------------------------------------------------

Note that especially for `complete_basis_set()`, the basis set needs to be specified through BASIS, not CFOUR_BASIS. Many of the wrappers can be used in combination to, for example, apply a compound method to every molecule in a database or to optimize a molecule with an extrapolated basis set (findif only for the moment- analytics coming).

Finally, any number and combination of jobs can be run from a single Psi4 input file. Depending on the nature of preceeding or following jobs, it is prudent to separate them with the following:

    clean()            # removes Psi4 scratch files
    clean_variables()  # empties the PSI variables list
    cfour {}           # empties the cfour block

Warning

Because p4c4 does not inspect the contents of the `cfour {...}` block, once the user specifies a Psi4-style molecule, the interface cannot judge whether a sandwich mode (drop the Psi4 molecule and use the cfour block as the entirety of the `ZMAT`) or a standard mode (translate the Psi4 molecule and append additional input from the cfour block) is intended. The latter is what actually occurs. If there is both a Psi4 molecule and a molecule in the cfour block, `ZMAT` will end up with multiple molecules and multiple `*CFOUR(...)` blocks, and it will not run. Therefore, if mixing sandwich and standard or pure-Psi4 computations in an input file, place all the sandwich jobs at the beginning before declaring Psi4 molecules. If necessary, clear the cfour block with `cfour {}` before commencing standard P4C4 jobs.

## Output

The output of xcfour invoked from a Psi4 input file is written to the Psi4 output file as the computation progresses. If a Cfour module terminates with a non-zero error code, the value will show up in `CFOUR ERROR CODE`.

Energies & Scalars

After execution of xcfour has completed, the output string is extensively parsed and appropriate results are stored in PSI Variables. All gleaned variables are printed in the Cfour output section of the Psi4 output file, as shown below.

    //>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>//
    //  Cfour c4-ccsd(t) Energy Results  //
    //<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<//

    Variable Map:
    ----------------------------------------------------------------------------
    "(T) CORRECTION ENERGY"      =>      -0.007263598030
    "CCSD CORRELATION ENERGY"    =>      -0.275705492359
    "CCSD TOTAL ENERGY"          =>     -76.338453952539
    "CCSD(T) CORRELATION ENERGY" =>      -0.007263598030
    "CCSD(T) TOTAL ENERGY"       =>     -76.345717550569
    "CFOUR ERROR CODE"           =>       0.000000000000
    "CURRENT CORRELATION ENERGY" =>      -0.007263598030
    "CURRENT ENERGY"             =>     -76.345717550569
    "CURRENT REFERENCE ENERGY"   =>     -76.062748460180
    "MP2 CORRELATION ENERGY"     =>      -0.270191667755
    "MP2 OPPOSITE-SPIN ENERGY"   =>      -0.204890356651
    "MP2 SAME-SPIN ENERGY"       =>      -0.065301311104
    "MP2 TOTAL ENERGY"           =>     -76.332940127935
    "NUCLEAR REPULSION ENERGY"   =>       9.187331653300
    "SCF TOTAL ENERGY"           =>     -76.062748460180

The PSI Variables are also available from the input file for manipulation. For instance, to compute the MBPT 2 3/4 energy from MBPT 3 results, the following could be used.

    energy('c4-mp3')
    mp2p75_corl = 0.75 * get_variable('mp3 correlation energy') + \
                  0.25 * get_variable('MP2 correlation energy')
    print mp2p75_corl + get_variable('scf total energy')

Caution

Some features are not yet implemented. Buy a developer a coffee.

- No PSI Variables for properties: e.g., `SCF DIPOLE X`
- No PSI Variables for excited state energies

The formation of further regexes for properties, excited states, etc. is one of the primary areas in which this interface requires further work.

Gradients and Arrays

In addition to parsing the output stream, results are collected from files written to the scratch directory. Presently, the `GRD` file is parsed and printed to the output file, as shown below. Also printed is the Cfour gradient after manipulation by the P4C4 interface and used by Psi4 going forward. Manipulation is necessary because Cfour determinedly uses its own internal orientation and atom ordering while Psi4 naturally expects the gradient to be aligned with the active molecule. The geometry in `GRD` and the geometry of Psi4‘s active molecule are shifted, rotated, flipped, and otherwise badgered into coincidence, then the same manipulations are applied to the gradient in `GRD`, the result of which is printed below and passed on to Optking.

    //>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>//
    //   Cfour c4-scf Gradient Results   //
    //<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<//

    ...

    Irrep: 1 Size: 4 x 3

                   1            2            3

      1    0.0000000   -0.0122978    0.0000000
      2   -0.0051192    0.0040993   -0.0088667
      3   -0.0051192    0.0040993    0.0088667
      4    0.0102384    0.0040993    0.0000000

    CFOUR scratch file GRD has been read
      4        0.0000000000
          7.0000000000       -0.0880964705        0.0000000000        0.0000000000
          1.0000000000        0.4080144050       -0.9178691296       -1.5897959670
          1.0000000000        0.4080144050       -0.9178691296        1.5897959670
          1.0000000000        0.4080144050        1.8357382590        0.0000000001
          7.0000000000       -0.0122978407        0.0000000000        0.0000000000
          1.0000000000        0.0040992802       -0.0051191833       -0.0088666856
          1.0000000000        0.0040992802       -0.0051191833        0.0088666856
          1.0000000000        0.0040992802        0.0102383666        0.0000000000

The gradient can also be accessed from the input file as a psi4.Matrix object through `psi4.get_gradient()`.

Cfour Files

The contents of all files associated with Cfour are accessible from the input file through the Python dictionary `P4C4_INFO`. That is, `P4C4_INFO['zmat']` returns a string of the input file sent to Cfour. Accessible arguments are `zmat`, `output`, and any that have been produced of `grd`. For example, to print to the screen if CC convergence is reached, the following could be placed in the Psi4 input file.

    energy('c4-ccsd')
    print 'miracle?', 'miracle' in P4C4_INFO['output']

Scratch Files

By default, a separate subdirectory for each Cfour call is created within the job’s scratch directory. To explicitly specify the location of the the Cfour scratch, execute with, for example, `energy('cfour', path='/full/path/to/cfour/scratch')`. Regardless of whether the location is specified or default, whether to preserve the scratch directory after the computation can be specified with `energy('cfour', keep=True)` or (the default) `energy('cfour', keep=False)`. path and keep are keyword arguments that get interpreted by the `run_cfour()` function documented below.

`run_cfour`(name[, keep, path])

  Function that prepares environment and input files for a calculation calling Stanton and Gauss’s CFOUR code. Also processes results back into Psi4 format.

  This function is not called directly but is instead called by `energy()` or `optimize()` when a Cfour method is requested (through name argument). In order to function correctly, the Cfour executable `xcfour` must be present in `PATH` or `PSIPATH`.

  - Many PSI Variables extracted from the Cfour output
  - Python dictionary of associated file constants accessible as `P4C4_INFO['zmat']`, `P4C4_INFO['output']`, `P4C4_INFO['grd']`, etc.

  Parameters:

  - name (string) –

    `'c4-scf'` || `'c4-ccsd(t)'` || `'cfour'` || etc.

    First argument, usually unlabeled. Indicates the computational method to be applied to the system.

  - keep (boolean) –

    `'on'` || `'off'`

    Indicates whether to delete the Cfour scratch directory upon completion of the Cfour job.

  - path (string) –

    Indicates path to Cfour scratch directory (with respect to Psi4 scratch directory). Otherwise, the default is a subdirectory within the Psi4 scratch directory.

    If specified, GENBAS and/or ZMAT within will be used.

  - genbas (string) – Indicates that contents should be used for GENBAS file.

  GENBAS is a complicated topic. It is quite unnecessary if the molecule is from a molecule {...} block and basis is set through Psi4‘s BASIS keyword. In that case, a GENBAS is written from LibMints and all is well. Otherwise, a GENBAS is looked for in the usual places: PSIPATH, PATH, PSIDATADIR/basis. If path kwarg is specified, also looks there preferentially for a GENBAS. Can also specify GENBAS within an input file through a string and setting the genbas kwarg. Note that due to the input parser’s aggression, blank lines need to be replaced by the text blankline.

## Functionality

Through clever use of the `cfour {...}` block, one could run most any Cfour computation through the P4C4 interface. In contrast, enumerated below are tested functionalities where results from Cfour are collected into Psi4 data objects.

Implemented

- Single-point `energy()` commands for ground state methods. Examples: cfour/sp-rhf-ccsd_t_-ao-ecc, cfour/scf4, cfour/mints5.
- Analytic `gradient()` and `optimize()` commands for ground state methods. Real and Ghost atoms permitted (though the latter will naturally collapse after several cycles). Examples: cfour/opt-rhf-ccsd_t_, cfour/mp2-1, and cfour/mints5-grad.

Warning

There exist molecules (e.g., allene) where the inertial frame is not unique (planes along atoms or between atoms). The orientation reconciling machinery currently does not handle these cases and will fail with “Axis unreconcilable between QC programs”. I will get to this soon.

- Finite difference of energy `gradient()` and `optimize()` for methods. Force with `gradient('name', dertype=0)`, etc..
- `cp()` for computation of interaction energies with or without counterpoise correction. Example: cfour/dfmp2-1.
- `database()` for computation of a collection of molecules in a single input, with summarization of results. Examples: cfour/pywrap-db1 and cfour/psi-a24-grad.
- `complete_basis_set()` for computation of compound methods involving basis set extrapolations and/or delta corrections with any combination of Psi4 and Cfour computational methods and Psi4 basis sets. Example: cfour/pywrap-cbs1.

Not Yet Implemented

- Ground state CI energies and optimizations
- Excited state energies and optimizations
- Properties are not yet regex-ed, transformed into input frame, and stowed in PSI Variables.
- Property calls that required extra computation not yet translated into `property()` computation command
- Frequencies

Energy methods available through P4C4 interface

> name | calls method in Stanton and Gauss’s CFOUR program [manual]
> --- | ---
> c4-scf | Hartree–Fock (HF)
> c4-mp2 | 2nd-order Moller-Plesset perturbation theory (non-density-fitting) (MP2)
> c4-mp3 | 3rd-order Moller-Plesset perturbation theory (MP3)
> c4-mp4(sdq) | 4th-order MP perturbation theory (MP4) less triples
> c4-mp4 | full MP4
> c4-cc2 | approximate coupled cluster singles and doubles (CC2)
> c4-ccsd | coupled cluster singles and doubles (CCSD)
> c4-cc3 | approximate CC singles, doubles, and triples (CC3)
> c4-ccsd(t) | CCSD with perturbative triples (CCSD(T))
> c4-ccsdt | coupled cluster singles, doubles, and triples (CCSDT)
> cfour | expert full control over cfour program

Gradient methods available through P4C4 interface

> name | calls method in Stanton and Gauss’s CFOUR program [manual]
> --- | ---
> c4-scf | Hartree–Fock (HF)
> c4-mp2 | 2nd-order Moller-Plesset perturbation theory (non-density-fitting) (MP2)
> c4-mp3 | 3rd-order Moller-Plesset perturbation theory (MP3)
> c4-mp4(sdq) | 4th-order MP perturbation theory (MP4) less triples
> c4-mp4 | full MP4
> c4-cc2 | approximate coupled cluster singles and doubles (CC2)
> c4-ccsd | coupled cluster singles and doubles (CCSD)
> c4-cc3 | approximate CC singles, doubles, and triples (CC3)
> c4-ccsd(t) | CCSD with perturbative triples (CCSD(T))
> c4-ccsdt | coupled cluster singles, doubles, and triples (CCSDT)
> cfour | expert full control over cfour program

## Specification Details

The above narrative introduction to the P4C4 interface should be sufficient to get started. Issues of competition between Psi4 and Cfour specification format are generally resolved behind the scenes: not according to a simple rule but according to sensible, sometimes intricate, rules governed by user intent (and integration of Cfour to behave like a Psi4 module). Much can be gleaned by just running inputs and inspecting the `ZMAT` passed to Cfour, but when questions arise, here are the specifics, the governing laws.

- Specifying a piece of input in Psi4 format is entering into a contract that you mean it. In particular this applies to molecule (including charge/multiplicity through `molecule optional_molecule_name {...}`), memory (through `memory value unit`), computational method (through . If Cfour keywords are specified with values that contradict the Psi4 input, execution is halted.

  As an example, the input below is set up to fail in four ways: contradictory specification of memory, multiplicity, computational method, and derivative level. Note, though, that the `cfour_units angstrom` setting is permissible, since it concurs with the value implied in the molecule block.

      memory 300 mb

      molecule {
      H
      H 1 0.7
      }

      set basis 6-31g
      set cfour_multiplicity 3         # clash with implicit singlet in molecule {} above
      set cfour_units angstrom         # no problem, consistent with molecule {} above
      set cfour_memory_size 100000000  # clash with 300 mb above
      set cfour_calc_level ccsd        # clash with 'c4-scf' below
      set cfour_deriv_level first      # clash with energy() below (use gradient('c4-scf') to achieve this)

      energy('c4-scf')

- Specifying anything in Psi4 format (molecule, basis, options, method call) starts building a `*CFOUR(...)` directive for the `ZMAT` file. Since the contents of the `cfour {...}` block are blindly appended to any input interpreted from Psi4 format, mixing of Psi4 and Cfour input formats likely will give rise to multiple `*CFOUR(...)` directives in the prospective `ZMAT`, execution of which will be trapped and halted. Proper uses for the `cfour {...}` block are for the sandwich mode, where the entire `ZMAT` is enclosed, or for extra directives like `%excite*`, which presently have no other specification route.

- Specifying the basis is perhaps the regulated piece of input. Since basis set names differ between Psi4 and Cfour and it’s not practical to compare exponent-to-exponent, any input file with both BASIS and CFOUR_BASIS keywords present will halt. Once a basis set has been requested through BASIS, overriding the default spherical/Cartesian setting must be done through PUREAM (as opposed to CFOUR_SPHERICAL).

- Specifying keywords that control geometry optimization is straightforward. Unless the optimization is invoked in sandwich mode, all Cfour optimization keywords (e.g., CFOUR_GEO_MAXCYC) are ineffective, as the Cfour optimizer is never invoked. Psi4 optimization keywords (e.g., GEOM_MAXITER) instead fill these roles.

- Specifying the computational method (through, for instance, `energy('c4-ccsd')` instead of `energy('cfour')`) often sets additional keywords consistent with best practices (e.g., CFOUR_CC_PROGRAM). Since those settings are implicit, any explicit setting of those those keywords, whether contradicting or concurring, takes priority (halts never generated). The following are some concrete examples. For the moment, click the source button at `qcdb.cfour.muster_modelchem()` for details of what keywords get set.

  - runs in vcc since that’s Cfour’s default for cc_program

        set cfour_calc_level ccsd
        energy('cfour')

  - runs in ecc since Cfour’s default overwritten by keyword

        set cfour_calc_level ccsd
        set cfour_cc_program ecc
        energy('cfour')

  - runs in ecc since that’s best practice for the requested ccsd

        energy('c4-ccsd')

  - runs in vcc since hidden default overwritten by keyword

        set cfour_cc_program vcc
        energy('c4-ccsd')

- Specifying certain keywords that are nominally applicable for pure-Psi4 modules directs them to fulfil analogous roles in the Cfour program (e.g., MAXITER is used to set CFOUR_SCF_MAXCYC). This keyword translation only takes place if the keywords are explicitly set in the input file (part of that contract that you mean it), meaning that Psi4‘s defaults don’t get imposed on Cfour. Also, in the case where a translatable pure-Psi4 keyword and its translation Cfour keyword are both set, the value attached to the latter is always used. Below are a few clarifying examples.

  - uses SCF conv crit since that’s Cfour’s default for CFOUR_SCF_CONV

        energy('c4-scf')

  - uses SCF conv crit since default overwritten by keyword

        set cfour_scf_conv 6
        energy('c4-scf')

  - uses SCF conv crit since default overwritten by SCF module keyword

        set d_convergence 5
        energy('c4-scf')

  - uses SCF conv crit since default overwritten by SCF module keyword (local scope works, too) where the Psi4‘s more flexible float input has been rounded down to the integer required by Cfour

        set scf d_convergence 5e-6
        energy('c4-scf')

  - uses SCF conv crit since default overwritten and Cfour module keyword trumps Psi4 SCF module keyword

        set cfour_scf_conv 6
        set d_convergence 8
        energy('c4-scf')

  The keyword translation feature is still in the proof-of-principle stage, so only a handful (found here) of keywords participate.

Note

Longtime Cfour users who may consider this keyword translation a flaw rather than a feature can avoid it entirely by confining keywords to the Cfour module along with BASIS and PUREAM (opt, too?)

## Misc. Running

Naturally, in Psi4 multiple jobs can be run in succession from the input file.

Control optimizations with optking keywords HERE. Cfour `GRD` file is written to Psi4 output file. Gradient transformed back into the frame in which it was shipped off to Cfour is also written to the Psi4 output file and is available from input as `get_gradient()`.

sandwich mode := molecule and cfour list within Naturally, additional jobs can follow in the input file. Depending on the nature of preceeding or following jobs, it is prudent to separate them with the following:

    clean()            # removes Psi4 scratch files
    clean_variables()  # empties the PSI variables list
    cfour {}           # empties

In this scheme, the contents of the `cfour {...}` block are tacked onto the end of the `ZMAT` file that is otherwise written from psi style format. It is by this route that, for example `%excite*` sections can at present be spcified.

The execution of xcfour can be modified by a few parameters. Setting the option CFOUR_OMP_NUM_THREADS sets the environment variable `OMP_NUM_THREADS` for only the duration of the Cfour computation. That is, portions of an input file that run Psi4 modules are unaffected. Additionally, there are a few arguments to the function `run_cfour()` that control the Cfour scratch directory.