BondOrderParameter.cpp

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 *
 * [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
 * [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
 * [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008).
 * [4] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
 * [5] Kuang & Gezelter, Mol. Phys., 110, 691-701 (2012).
 * [6] Lamichhane, Gezelter & Newman, J. Chem. Phys. 141, 134109 (2014).
 * [7] Lamichhane, Newman & Gezelter, J. Chem. Phys. 141, 134110 (2014).
 * [8] Bhattarai, Newman & Gezelter, Phys. Rev. B 99, 094106 (2019).
 */
 
#include "applications/staticProps/BondOrderParameter.hpp"
 
#include <sstream>
 
#include "io/DumpReader.hpp"
#include "math/Wigner3jm.hpp"
#include "primitives/Molecule.hpp"
#include "utils/Constants.hpp"
#include "utils/Revision.hpp"
#include "utils/simError.h"
 
using namespace MATPACK;
namespace OpenMD {
 
  BondOrderParameter::BondOrderParameter(SimInfo* info,
                                         const std::string& filename,
                                         const std::string& sele, double rCut,
                                         int nbins) :
      StaticAnalyser(info, filename, nbins),
      selectionScript_(sele), seleMan_(info), evaluator_(info) {
    setAnalysisType("Bond Order Parameters");
    setOutputName(getPrefix(filename) + ".bo");
 
    evaluator_.loadScriptString(sele);
    if (!evaluator_.isDynamic()) {
      seleMan_.setSelectionSet(evaluator_.evaluate());
    }
 
    // Set up cutoff radius and order of the Legendre Polynomial:
 
    rCut_ = rCut;
 
    std::stringstream params;
    params << " rcut = " << rCut_ << ", nbins = " << nBins_;
    const std::string paramString = params.str();
    setParameterString(paramString);
 
    Qcount_.resize(lMax_ + 1);
    Wcount_.resize(lMax_ + 1);
 
    // Q can take values from 0 to 1
 
    MinQ_   = 0.0;
    MaxQ_   = 1.1;
    deltaQ_ = (MaxQ_ - MinQ_) / nbins;
 
    // W_6 for icosahedral clusters is 11 / sqrt(4199) = 0.169754, so we'll
    // use values for MinW_ and MaxW_ that are slightly larger than this:
 
    MinW_   = -1.1;
    MaxW_   = 1.1;
    deltaW_ = (MaxW_ - MinW_) / nbins;
 
    // Make arrays for Wigner3jm
    RealType* THRCOF = new RealType[2 * lMax_ + 1];
    // Variables for Wigner routine
    RealType lPass, m1Pass, m2m, m2M;
    int error, mSize;
    mSize = 2 * lMax_ + 1;
 
    for (int l = 0; l <= lMax_; l++) {
      lPass = (RealType)l;
      for (int m1 = -l; m1 <= l; m1++) {
        m1Pass = (RealType)m1;
 
        std::pair<int, int> lm = std::make_pair(l, m1);
 
        // Zero work array
        for (int ii = 0; ii < 2 * l + 1; ii++) {
          THRCOF[ii] = 0.0;
        }
 
        // Get Wigner coefficients
        Wigner3jm(lPass, lPass, lPass, m1Pass, m2m, m2M, THRCOF, mSize, error);
 
        m2Min[lm] = (int)floor(m2m);
        m2Max[lm] = (int)floor(m2M);
 
        for (int mmm = 0; mmm <= (int)(m2M - m2m); mmm++) {
          w3j[lm].push_back(THRCOF[mmm]);
        }
      }
    }
    delete[] THRCOF;
    THRCOF = NULL;
  }
 
  void BondOrderParameter::initializeHistogram() {
    for (int bin = 0; bin < nBins_; bin++) {
      for (int l = 0; l <= lMax_; l++) {
        Q_histogram_[std::make_pair(bin, l)] = 0;
        W_histogram_[std::make_pair(bin, l)] = 0;
      }
    }
  }
 
  void BondOrderParameter::process() {
    Molecule* mol;
    Atom* atom;
    int myIndex;
    SimInfo::MoleculeIterator mi;
    Molecule::AtomIterator ai;
    StuntDouble* sd;
    Vector3d vec;
    RealType costheta;
    RealType phi;
    RealType r;
    std::map<std::pair<int, int>, ComplexType> q;
    std::vector<RealType> q_l;
    std::vector<RealType> q2;
    std::vector<ComplexType> w;
    std::vector<ComplexType> w_hat;
    std::map<std::pair<int, int>, ComplexType> QBar;
    std::vector<RealType> Q2;
    std::vector<RealType> Q;
    std::vector<ComplexType> W;
    std::vector<ComplexType> W_hat;
    int nBonds, Nbonds;
    SphericalHarmonic sphericalHarmonic;
    int i;
    bool usePeriodicBoundaryConditions_ =
        info_->getSimParams()->getUsePeriodicBoundaryConditions();
 
    DumpReader reader(info_, dumpFilename_);
    int nFrames   = reader.getNFrames();
    frameCounter_ = 0;
 
    q_l.resize(lMax_ + 1);
    q2.resize(lMax_ + 1);
    w.resize(lMax_ + 1);
    w_hat.resize(lMax_ + 1);
 
    Q2.resize(lMax_ + 1);
    Q.resize(lMax_ + 1);
    W.resize(lMax_ + 1);
    W_hat.resize(lMax_ + 1);
    Nbonds = 0;
 
    for (int istep = 0; istep < nFrames; istep += step_) {
      reader.readFrame(istep);
      frameCounter_++;
      currentSnapshot_ = info_->getSnapshotManager()->getCurrentSnapshot();
 
      if (evaluator_.isDynamic()) {
        seleMan_.setSelectionSet(evaluator_.evaluate());
      }
 
      // outer loop is over the selected StuntDoubles:
 
      for (sd = seleMan_.beginSelected(i); sd != NULL;
           sd = seleMan_.nextSelected(i)) {
        myIndex = sd->getGlobalIndex();
        nBonds  = 0;
 
        for (int l = 0; l <= lMax_; l++) {
          for (int m = -l; m <= l; m++) {
            q[std::make_pair(l, m)] = 0.0;
          }
        }
 
        // inner loop is over all other atoms in the system:
 
        for (mol = info_->beginMolecule(mi); mol != NULL;
             mol = info_->nextMolecule(mi)) {
          for (atom = mol->beginAtom(ai); atom != NULL;
               atom = mol->nextAtom(ai)) {
            if (atom->getGlobalIndex() != myIndex) {
              vec = sd->getPos() - atom->getPos();
 
              if (usePeriodicBoundaryConditions_)
                currentSnapshot_->wrapVector(vec);
 
              // Calculate "bonds" and build Q_lm(r) where
              //      Q_lm = Y_lm(theta(r),phi(r))
              // The spherical harmonics are wrt any arbitrary coordinate
              // system, we choose standard spherical coordinates
 
              r = vec.length();
 
              // Check to see if neighbor is in bond cutoff
 
              if (r < rCut_) {
                costheta = vec.z() / r;
                phi      = atan2(vec.y(), vec.x());
 
                for (int l = 0; l <= lMax_; l++) {
                  sphericalHarmonic.setL(l);
                  for (int m = -l; m <= l; m++) {
                    sphericalHarmonic.setM(m);
                    q[std::make_pair(l, m)] +=
                        sphericalHarmonic.getValueAt(costheta, phi);
                  }
                }
                nBonds++;
              }
            }
          }
        }
 
        for (int l = 0; l <= lMax_; l++) {
          q2[l] = 0.0;
          for (int m = -l; m <= l; m++) {
            q[std::make_pair(l, m)] /= (RealType)nBonds;
 
            q2[l] += norm(q[std::make_pair(l, m)]);
          }
          q_l[l] = sqrt(q2[l] * 4.0 * Constants::PI / (RealType)(2 * l + 1));
        }
 
        // Find Third Order Invariant W_l
 
        for (int l = 0; l <= lMax_; l++) {
          w[l] = 0.0;
          for (int m1 = -l; m1 <= l; m1++) {
            std::pair<int, int> lm = std::make_pair(l, m1);
            for (int mmm = 0; mmm <= (m2Max[lm] - m2Min[lm]); mmm++) {
              int m2 = m2Min[lm] + mmm;
              int m3 = -m1 - m2;
              w[l] += w3j[lm][mmm] * q[lm] * q[std::make_pair(l, m2)] *
                      q[std::make_pair(l, m3)];
            }
          }
 
          w_hat[l] = w[l] / pow(q2[l], RealType(1.5));
        }
 
        collectHistogram(q_l, w_hat);
 
        Nbonds += nBonds;
        for (int l = 0; l <= lMax_; l++) {
          for (int m = -l; m <= l; m++) {
            QBar[std::make_pair(l, m)] +=
                (RealType)nBonds * q[std::make_pair(l, m)];
          }
        }
      }
    }
 
    // Normalize Qbar2
    for (int l = 0; l <= lMax_; l++) {
      for (int m = -l; m <= l; m++) {
        QBar[std::make_pair(l, m)] /= Nbonds;
      }
    }
 
    // Find second order invariant Q_l
 
    for (int l = 0; l <= lMax_; l++) {
      Q2[l] = 0.0;
      for (int m = -l; m <= l; m++) {
        Q2[l] += norm(QBar[std::make_pair(l, m)]);
      }
      Q[l] = sqrt(Q2[l] * 4.0 * Constants::PI / (RealType)(2 * l + 1));
    }
 
    // Find Third Order Invariant W_l
 
    for (int l = 0; l <= lMax_; l++) {
      W[l] = 0.0;
      for (int m1 = -l; m1 <= l; m1++) {
        std::pair<int, int> lm = std::make_pair(l, m1);
        for (int mmm = 0; mmm <= (m2Max[lm] - m2Min[lm]); mmm++) {
          int m2 = m2Min[lm] + mmm;
          int m3 = -m1 - m2;
          W[l] += w3j[lm][mmm] * QBar[lm] * QBar[std::make_pair(l, m2)] *
                  QBar[std::make_pair(l, m3)];
        }
      }
 
      W_hat[l] = W[l] / pow(Q2[l], RealType(1.5));
    }
 
    writeOrderParameter(Q, W_hat);
  }
 
  void BondOrderParameter::collectHistogram(std::vector<RealType> q,
                                            std::vector<ComplexType> what) {
    for (int l = 0; l <= lMax_; l++) {
      if (q[l] >= MinQ_ && q[l] < MaxQ_) {
        int qbin = int((q[l] - MinQ_) / deltaQ_);
        Q_histogram_[std::make_pair(qbin, l)] += 1;
        Qcount_[l]++;
      } else {
        snprintf(painCave.errMsg, MAX_SIM_ERROR_MSG_LENGTH,
                 "q_l value outside reasonable range\n");
        painCave.severity = OPENMD_ERROR;
        painCave.isFatal  = 1;
        simError();
      }
    }
 
    for (int l = 0; l <= lMax_; l++) {
      if (real(what[l]) >= MinW_ && real(what[l]) < MaxW_) {
        int wbin = int((real(what[l]) - MinW_) / deltaW_);
        W_histogram_[std::make_pair(wbin, l)] += 1;
        Wcount_[l]++;
      } else {
        snprintf(painCave.errMsg, MAX_SIM_ERROR_MSG_LENGTH,
                 "Re[w_hat] value (%lf) outside reasonable range\n",
                 real(what[l]));
        painCave.severity = OPENMD_ERROR;
        painCave.isFatal  = 1;
        simError();
      }
    }
  }
 
  void BondOrderParameter::writeOrderParameter(std::vector<RealType> Q,
                                               std::vector<ComplexType> What) {
    Revision rev;
    std::ofstream osq((getOutputFileName() + "q").c_str());
 
    if (osq.is_open()) {
      osq << "# " << getAnalysisType() << "\n";
      osq << "# OpenMD " << rev.getFullRevision() << "\n";
      osq << "# " << rev.getBuildDate() << "\n";
      osq << "# selection script: \"" << selectionScript_ << "\"\n";
      if (!paramString_.empty())
        osq << "# parameters: " << paramString_ << "\n";
 
      for (int l = 0; l <= lMax_; l++) {
        osq << "# <Q_" << l << ">: " << Q[l] << "\n";
      }
      // Normalize by number of frames and write it out:
      for (int i = 0; i < nBins_; ++i) {
        RealType Qval = MinQ_ + (i + 0.5) * deltaQ_;
        osq << Qval;
        for (int l = 0; l <= lMax_; l++) {
          osq << "\t"
              << (RealType)Q_histogram_[std::make_pair(i, l)] /
                     (RealType)Qcount_[l] / deltaQ_;
        }
        osq << "\n";
      }
 
      osq.close();
 
    } else {
      snprintf(painCave.errMsg, MAX_SIM_ERROR_MSG_LENGTH,
               "BondOrderParameter: unable to open %s\n",
               (getOutputFileName() + "q").c_str());
      painCave.isFatal = 1;
      simError();
    }
 
    std::ofstream osw((getOutputFileName() + "w").c_str());
 
    if (osw.is_open()) {
      osq << "# " << getAnalysisType() << "\n";
      osq << "# OpenMD " << rev.getFullRevision() << "\n";
      osq << "# " << rev.getBuildDate() << "\n";
      osq << "# selection script: \"" << selectionScript_ << "\"\n";
      if (!paramString_.empty())
        osq << "# parameters: " << paramString_ << "\n";
 
      for (int l = 0; l <= lMax_; l++) {
        osw << "# <W_" << l << ">: " << real(What[l]) << "\t" << imag(What[l])
            << "\n";
      }
      // Normalize by number of frames and write it out:
      for (int i = 0; i < nBins_; ++i) {
        RealType Wval = MinW_ + (i + 0.5) * deltaW_;
        osw << Wval;
        for (int l = 0; l <= lMax_; l++) {
          osw << "\t"
              << (RealType)W_histogram_[std::make_pair(i, l)] /
                     (RealType)Wcount_[l] / deltaW_;
        }
        osw << "\n";
      }
 
      osw.close();
    } else {
      snprintf(painCave.errMsg, MAX_SIM_ERROR_MSG_LENGTH,
               "BondOrderParameter: unable to open %s\n",
               (getOutputFileName() + "w").c_str());
      painCave.isFatal = 1;
      simError();
    }
  }
}  // namespace OpenMD