5.2.1. Tuning the range separation

In this example we optimize the value of gamma parameter for long-range corrected XC functional (in our case: LCY-PBE) in ADF. Long-range corrected XC functionals can be used in ADF with XCfun (see ADF manual).

The optimal range separation parameter gamma yields the HOMO energy equal to the ionization potential (IP). Given a molecular system, we simultaneously minimize the difference between HOMO and IP for that system (N) and its anion (A) (system with one more electron). We define the J function as:

\[J = \sqrt{N^2+A^2}\]

and find the value of gamma (within a certain range) which minimizes J.

We define a new job type GammaJob by extending MultiJob. The goal of GammaJob is to calculate the J function for one fixed value of gamma To do that we need to perform 3 different single point calculations: 1 for the given system (let’s call it S0), 1 for the system with one more electron (S-) and 1 for the system with one less electron (S+). S+ calculation is needed to find the ionization potential of S0.

The constructor (__init__) of GammaJob accepts several new arguments and simply stores them. These new arguments define: the value of gamma, the Molecule together with its initial charge, and the values of spin for S-, S0 and S+ (as a tuple of length 3). Then the prerun() method is used to create three children jobs with different values of total charge and spin multiplicity. A dedicated Results subclass features a simple method for extracting the value of J based on results on three children jobs:

class GammaResults(Results):

    def get_difference(job, jobplus):
        """Calculate the difference between HOMO and IP.
        *jobplus* should be the counterpart of *job* with one less electron."""
        homo = job.results.get_properties()['HOMO']
        IP = jobplus.results.get_energy() - job.results.get_energy()
        return IP + homo

    def get_J(self):
        N = GammaResults.get_difference(self.job.children[1], self.job.children[2])
        A = GammaResults.get_difference(self.job.children[0], self.job.children[1])
        return (N*N + A*A)**0.5

class GammaJob(MultiJob):
    _result_type = GammaResults

    def __init__(self, molecule, gamma, charge, spins, **kwargs):
        MultiJob.__init__(self, **kwargs)
        self.molecule = molecule
        self.charge = charge
        self.spins = spins
        self.gamma = gamma

    def prerun(self):
        charges = [self.charge-1, self.charge, self.charge+1]
        for charge, spin in zip(charges, self.spins):
            name = '{}_{}'.format(self.name, charge)
            newjob = ADFJob(name=name, molecule=self.molecule, settings=self.settings)
            newjob.settings.input.charge = '{} {}'.format(charge, spin)
            newjob.settings.input.xc.rangesep = "gamma={:f}".format(self.gamma)
            if spin != 0:
                newjob.settings.input.unrestricted = True

Now we can treat our newly defined GammaJob as a blackbox with simple interface: input gamma -> run -> extract J. The next step is to create multiple instances of GammaJob for a range of different gammas. That task can be conveniently wrapped in a simple function:

def gamma_scan(gammas, settings, molecule, name='gammascan', charge=0, spins=(1,0,1)):
    """Calculate values of J function for given range of gammas.

    gammas   - list of gamma values to calculate the J function for
    settings - Settings object compatible with ADFJob
    molecule - Molecule object with the system of interest
    name     - base name of all the jobs
    charge   - base charge of the system of interest. The J function is going to be
               calculated based on two systems: with charge, and charge-1
    spins    - values of spin polarization (see keyword CHARGE of ADF) for jobs with,
               respectively, charge-1, charge and charge +1

    In other words, if charge=X and spins=(a,b,c) the three resulting jobs
    are going to have the following values of CHARGE keyword:

    CHARGE X-1  a
    CHARGE   X  b
    CHARGE X+1  c

    Returns a list of pairs (gamma, J) of the same length as the parameter *gammas*
    jobs = [GammaJob(molecule=molecule, settings=settings, gamma=g,
            charge=charge, spins=spins, name=name+str(g)) for g in gammas]
    results = [j.run() for j in jobs]
    js = [r.get_J() for r in results]
    return list(zip(gammas, js))

(Alternatively, instead of a function, we could define a new type of MultiJob with the same functionality. Such a job would create a list of GammaJob instances as its children. The difference in that case is rather cosmetic: in case of a new job type all GammaJob data would be stored inside new job’s folder, whereas with the function defined above that data ends up directly in the main working folder. When running the gamma scan for a lot of different molecules in one script, the function approach can lead to the main working folder being somehow messy and hard to navigate. The new job type approach would keep the data for different molecules in different subfolders of the main working folder.)

An example usage of our newly defined function:

from numpy import arange
config.default_jobrunner = JobRunner(parallel=True, maxjobs=8)

s = Settings()
s.input.basis.type = 'TZP'
s.input.basis.core = 'None'
s.input.xc.gga = 'PBE'
s.input.xc.xcfun = True
s.runscript.nproc = 1

mol = Molecule('somemolecule.xyz')
gammas = arange(0.4, 0.8, 0.02)

results = gamma_scan(gammas, s, mol)

log('gamma \t J')
for g,j in results:
    log('{:.4f} \t {:.8f}'.format(g,j))
log('Optimal gamma value: {:.4f}'.format(min(results,key=lambda x:x[1])[0]))

All the code presented in above snippets can be put into a single file and executed with plams onebigfile.py (or $ADFBIN/plams onebigfile.py if $ADFBIN is not in your $PATH). Alternatively, one can place the definitions (of GammaJob and gamma_scan ) in one file gammajob.py and the execution in a separate small script rungamma.py and call it with plams gammajob.py rungamma.py.