src/gromacs/gmxana/gmx_dos.cpp

   1 /*
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  35 #include "gmxpre.h"
  36
  37 #include <cmath>
  38 #include <cstdio>
  39 #include <cstdlib>
  40 #include <cstring>
  41
  42 #include "gromacs/commandline/pargs.h"
  43 #include "gromacs/commandline/viewit.h"
  44 #include "gromacs/correlationfunctions/autocorr.h"
  45 #include "gromacs/correlationfunctions/integrate.h"
  46 #include "gromacs/fft/fft.h"
  47 #include "gromacs/fileio/confio.h"
  48 #include "gromacs/fileio/gmxfio.h"
  49 #include "gromacs/fileio/trxio.h"
  50 #include "gromacs/fileio/xvgr.h"
  51 #include "gromacs/gmxana/gmx_ana.h"
  52 #include "gromacs/math/functions.h"
  53 #include "gromacs/math/units.h"
  54 #include "gromacs/math/utilities.h"
  55 #include "gromacs/math/vec.h"
  56 #include "gromacs/topology/index.h"
  57 #include "gromacs/topology/topology.h"
  58 #include "gromacs/trajectory/trajectoryframe.h"
  59 #include "gromacs/utility/arraysize.h"
  60 #include "gromacs/utility/fatalerror.h"
  61 #include "gromacs/utility/futil.h"
  62 #include "gromacs/utility/pleasecite.h"
  63 #include "gromacs/utility/smalloc.h"
  64
  65 enum {
  66     VACF, MVACF, DOS, DOS_SOLID, DOS_DIFF, DOS_CP, DOS_S, DOS_A, DOS_E, DOS_NR
  67 };
  68
  69 static int calcMoleculesInIndexGroup(const t_block *mols, int natoms, const int *index, int nindex)
  70 {
  71     int   i    = 0;
  72     int   mol  = 0;
  73     int   nMol = 0;
  74     int   j;
  75
  76     while (i < nindex)
  77     {
  78         while (index[i] > mols->index[mol])
  79         {
  80             mol++;
  81             if (mol >= mols->nr)
  82             {
  83                 gmx_fatal(FARGS, "Atom index out of range: %d", index[i]+1);
  84             }
  85         }
  86         for (j = mols->index[mol]; j < mols->index[mol+1]; j++)
  87         {
  88             if (index[i] != j)
  89             {
  90                 gmx_fatal(FARGS, "The index group does not consist of whole molecules");
  91             }
  92             i++;
  93             if (i > natoms)
  94             {
  95                 gmx_fatal(FARGS, "Index contains atom numbers larger than the topology");
  96             }
  97         }
  98         nMol++;
  99     }
 100     return nMol;
 101 }
 102
 103 static double FD(double Delta, double f)
 104 {
 105     return (2*std::pow(Delta, -4.5)*std::pow(f, 7.5) -
 106             6*std::pow(Delta, -3.0)*std::pow(f, 5.0) -
 107             std::pow(Delta, -1.5)*std::pow(f, 3.5) +
 108             6*std::pow(Delta, -1.5)*std::pow(f, 2.5) +
 109             2*f - 2);
 110 }
 111
 112 static double YYY(double f, double y)
 113 {
 114     return (2*gmx::power3(y*f) - gmx::square(f)*y*(1+6*y) +
 115             (2+6*y)*f - 2);
 116 }
 117
 118 static double calc_compress(double y)
 119 {
 120     if (y == 1)
 121     {
 122         return 0;
 123     }
 124     return ((1+y+gmx::square(y)-gmx::power3(y))/(gmx::power3(1-y)));
 125 }
 126
 127 static double bisector(double Delta, double tol,
 128                        double ff0, double ff1,
 129                        double ff(double, double))
 130 {
 131     double fd, f, f0, f1;
 132     double tolmin = 1e-8;
 133
 134     f0 = ff0;
 135     f1 = ff1;
 136     if (tol < tolmin)
 137     {
 138         fprintf(stderr, "Unrealistic tolerance %g for bisector. Setting it to %g\n", tol, tolmin);
 139         tol = tolmin;
 140     }
 141
 142     do
 143     {
 144         f   = (f0+f1)*0.5;
 145         fd  = ff(Delta, f);
 146         if (fd < 0)
 147         {
 148             f0 = f;
 149         }
 150         else if (fd > 0)
 151         {
 152             f1 = f;
 153         }
 154         else
 155         {
 156             return f;
 157         }
 158     }
 159     while ((f1-f0) > tol);
 160
 161     return f;
 162 }
 163
 164 static double calc_fluidicity(double Delta, double tol)
 165 {
 166     return bisector(Delta, tol, 0, 1, FD);
 167 }
 168
 169 static double calc_y(double f, double Delta, double toler)
 170 {
 171     double y1, y2;
 172
 173     y1 = std::pow(f/Delta, 1.5);
 174     y2 = bisector(f, toler, 0, 10000, YYY);
 175     if (std::abs((y1-y2)/(y1+y2)) > 100*toler)
 176     {
 177         fprintf(stderr, "Inconsistency computing y: y1 = %f, y2 = %f, using y1.\n",
 178                 y1, y2);
 179     }
 180
 181     return y1;
 182 }
 183
 184 static double calc_Shs(double f, double y)
 185 {
 186     double fy  = f*y;
 187
 188     return BOLTZ*(std::log(calc_compress(fy)) + fy*(3*fy-4)/gmx::square(1-fy));
 189 }
 190
 191 static real wCsolid(real nu, real beta)
 192 {
 193     real bhn = beta*PLANCK*nu;
 194     real ebn, koko;
 195
 196     if (bhn == 0)
 197     {
 198         return 1.0;
 199     }
 200     else
 201     {
 202         ebn  = std::exp(bhn);
 203         koko = gmx::square(1-ebn);
 204         return gmx::square(bhn)*ebn/koko;
 205     }
 206 }
 207
 208 static real wSsolid(real nu, real beta)
 209 {
 210     real bhn = beta*PLANCK*nu;
 211
 212     if (bhn == 0)
 213     {
 214         return 1;
 215     }
 216     else
 217     {
 218         return bhn/std::expm1(bhn) - std::log1p(-std::exp(-bhn));
 219     }
 220 }
 221
 222 static real wAsolid(real nu, real beta)
 223 {
 224     real bhn = beta*PLANCK*nu;
 225
 226     if (bhn == 0)
 227     {
 228         return 0;
 229     }
 230     else
 231     {
 232         return std::log((1-std::exp(-bhn))/(std::exp(-bhn/2))) - std::log(bhn);
 233     }
 234 }
 235
 236 static real wEsolid(real nu, real beta)
 237 {
 238     real bhn = beta*PLANCK*nu;
 239
 240     if (bhn == 0)
 241     {
 242         return 1;
 243     }
 244     else
 245     {
 246         return bhn/2 + bhn/std::expm1(bhn)-1;
 247     }
 248 }
 249
 250 int gmx_dos(int argc, char *argv[])
 251 {
 252     const char         *desc[] = {
 253         "[THISMODULE] computes the Density of States from a simulations.",
 254         "In order for this to be meaningful the velocities must be saved",
 255         "in the trajecotry with sufficiently high frequency such as to cover",
 256         "all vibrations. For flexible systems that would be around a few fs",
 257         "between saving. Properties based on the DoS are printed on the",
 258         "standard output."
 259         "Note that the density of states is calculated from the mass-weighted",
 260         "autocorrelation, and by default only from the square of the real",
 261         "component rather than absolute value. This means the shape can differ",
 262         "substantially from the plain vibrational power spectrum you can",
 263         "calculate with gmx velacc."
 264     };
 265     const char         *bugs[] = {
 266         "This program needs a lot of memory: total usage equals the number of atoms times 3 times number of frames times 4 (or 8 when run in double precision)."
 267     };
 268     FILE               *fp, *fplog;
 269     t_topology          top;
 270     int                 ePBC = -1;
 271     t_trxframe          fr;
 272     matrix              box;
 273     int                 gnx;
 274     real                t0, t1;
 275     t_trxstatus        *status;
 276     int                 nV, nframes, n_alloc, i, j, fftcode, Nmol, Natom;
 277     double              rho, dt, Vsum, V, tmass, dostot, dos2;
 278     real              **c1, **dos, mi, beta, bfac, *nu, *tt, stddev, c1j;
 279     gmx_output_env_t   *oenv;
 280     gmx_fft_t           fft;
 281     double              cP, DiffCoeff, Delta, f, y, z, sigHS, Shs, Sig, DoS0, recip_fac;
 282     double              wCdiff, wSdiff, wAdiff, wEdiff;
 283     int                 grpNatoms;
 284     int                *index;
 285     char               *grpname;
 286     double              invNormalize;
 287     gmx_bool            normalizeAutocorrelation;
 288
 289     static     gmx_bool bVerbose   = TRUE, bAbsolute = FALSE, bNormalizeDos = FALSE;
 290     static     gmx_bool bRecip     = FALSE;
 291     static     real     Temp       = 298.15, toler = 1e-6;
 292     int                 min_frames = 100;
 293
 294     t_pargs             pa[]     = {
 295         { "-v", FALSE, etBOOL, {&bVerbose},
 296           "Be loud and noisy." },
 297         { "-recip", FALSE, etBOOL, {&bRecip},
 298           "Use cm^-1 on X-axis instead of 1/ps for DoS plots." },
 299         { "-abs", FALSE, etBOOL, {&bAbsolute},
 300           "Use the absolute value of the Fourier transform of the VACF as the Density of States. Default is to use the real component only" },
 301         { "-normdos", FALSE, etBOOL, {&bNormalizeDos},
 302           "Normalize the DoS such that it adds up to 3N. This should usually not be necessary." },
 303         { "-T", FALSE, etREAL, {&Temp},
 304           "Temperature in the simulation" },
 305         { "-toler", FALSE, etREAL, {&toler},
 306           "[HIDDEN]Tolerance when computing the fluidicity using bisection algorithm" }
 307     };
 308
 309     t_filenm            fnm[] = {
 310         { efTRN, "-f",    NULL,    ffREAD  },
 311         { efTPR, "-s",    NULL,    ffREAD  },
 312         { efNDX, NULL,    NULL,    ffOPTRD },
 313         { efXVG, "-vacf", "vacf",  ffWRITE },
 314         { efXVG, "-mvacf", "mvacf", ffWRITE },
 315         { efXVG, "-dos",  "dos",   ffWRITE },
 316         { efLOG, "-g",    "dos",   ffWRITE },
 317     };
 318 #define NFILE asize(fnm)
 319     int                 npargs;
 320     t_pargs            *ppa;
 321     const char         *DoSlegend[] = {
 322         "DoS(v)", "DoS(v)[Solid]", "DoS(v)[Diff]"
 323     };
 324
 325     npargs = asize(pa);
 326     ppa    = add_acf_pargs(&npargs, pa);
 327     if (!parse_common_args(&argc, argv, PCA_CAN_VIEW | PCA_CAN_TIME,
 328                            NFILE, fnm, npargs, ppa, asize(desc), desc,
 329                            asize(bugs), bugs, &oenv))
 330     {
 331         return 0;
 332     }
 333
 334     beta = 1/(Temp*BOLTZ);
 335
 336     fplog = gmx_fio_fopen(ftp2fn(efLOG, NFILE, fnm), "w");
 337     fprintf(fplog, "Doing density of states analysis based on trajectory.\n");
 338     please_cite(fplog, "Pascal2011a");
 339     please_cite(fplog, "Caleman2011b");
 340
 341     read_tps_conf(ftp2fn(efTPR, NFILE, fnm), &top, &ePBC, NULL, NULL, box, TRUE);
 342
 343     /* Handle index groups */
 344     get_index(&top.atoms, ftp2fn_null(efNDX, NFILE, fnm), 1, &grpNatoms, &index, &grpname);
 345
 346     V     = det(box);
 347     tmass = 0;
 348     for (i = 0; i < grpNatoms; i++)
 349     {
 350         tmass += top.atoms.atom[index[i]].m;
 351     }
 352
 353     Natom = grpNatoms;
 354     Nmol  = calcMoleculesInIndexGroup(&top.mols, top.atoms.nr, index, grpNatoms);
 355     gnx   = Natom*DIM;
 356
 357     /* Correlation stuff */
 358     snew(c1, gnx);
 359     for (i = 0; (i < gnx); i++)
 360     {
 361         c1[i] = NULL;
 362     }
 363
 364     read_first_frame(oenv, &status, ftp2fn(efTRN, NFILE, fnm), &fr, TRX_NEED_V);
 365     t0 = fr.time;
 366
 367     n_alloc = 0;
 368     nframes = 0;
 369     Vsum    = 0;
 370     nV      = 0;
 371     do
 372     {
 373         if (fr.bBox)
 374         {
 375             V      = det(fr.box);
 376             Vsum  += V;
 377             nV++;
 378         }
 379         if (nframes >= n_alloc)
 380         {
 381             n_alloc += 100;
 382             for (i = 0; i < gnx; i++)
 383             {
 384                 srenew(c1[i], n_alloc);
 385             }
 386         }
 387         for (i = 0; i < gnx; i += DIM)
 388         {
 389             c1[i+XX][nframes] = fr.v[index[i/DIM]][XX];
 390             c1[i+YY][nframes] = fr.v[index[i/DIM]][YY];
 391             c1[i+ZZ][nframes] = fr.v[index[i/DIM]][ZZ];
 392         }
 393
 394         t1 = fr.time;
 395
 396         nframes++;
 397     }
 398     while (read_next_frame(oenv, status, &fr));
 399
 400     close_trj(status);
 401
 402     if (nframes < min_frames)
 403     {
 404         gmx_fatal(FARGS, "You need at least %d frames in the trajectory and you only have %d.", min_frames, nframes);
 405     }
 406     dt = (t1-t0)/(nframes-1);
 407     if (nV > 0)
 408     {
 409         V = Vsum/nV;
 410     }
 411     if (bVerbose)
 412     {
 413         printf("Going to do %d fourier transforms of length %d. Hang on.\n",
 414                gnx, nframes);
 415     }
 416     /* Unfortunately the -normalize program option for the autocorrelation
 417      * function calculation is added as a hack with a static variable in the
 418      * autocorrelation.c source. That would work if we called the normal
 419      * do_autocorr(), but this routine overrides that by directly calling
 420      * the low-level functionality. That unfortunately leads to ignoring the
 421      * default value for the option (which is to normalize).
 422      * Since the absolute value seems to be important for the subsequent
 423      * analysis below, we detect the value directly from the option, calculate
 424      * the autocorrelation without normalization, and then apply the
 425      * normalization just to the autocorrelation output
 426      * (or not, if the user asked for a non-normalized autocorrelation).
 427      */
 428     normalizeAutocorrelation = opt2parg_bool("-normalize", npargs, ppa);
 429
 430     /* Note that we always disable normalization here, regardless of user settings */
 431     low_do_autocorr(NULL, oenv, NULL, nframes, gnx, nframes, c1, dt, eacNormal, 0, FALSE,
 432                     FALSE, FALSE, -1, -1, 0);
 433     snew(dos, DOS_NR);
 434     for (j = 0; (j < DOS_NR); j++)
 435     {
 436         snew(dos[j], nframes+4);
 437     }
 438
 439     if (bVerbose)
 440     {
 441         printf("Going to merge the ACFs into the mass-weighted and plain ACF\n");
 442     }
 443     for (i = 0; (i < gnx); i += DIM)
 444     {
 445         mi = top.atoms.atom[index[i/DIM]].m;
 446         for (j = 0; (j < nframes/2); j++)
 447         {
 448             c1j            = (c1[i+XX][j] + c1[i+YY][j] + c1[i+ZZ][j]);
 449             dos[VACF][j]  += c1j/Natom;
 450             dos[MVACF][j] += mi*c1j;
 451         }
 452     }
 453
 454     fp = xvgropen(opt2fn("-vacf", NFILE, fnm), "Velocity autocorrelation function",
 455                   "Time (ps)", "C(t)", oenv);
 456     snew(tt, nframes/2);
 457
 458     invNormalize = normalizeAutocorrelation ? 1.0/dos[VACF][0] : 1.0;
 459
 460     for (j = 0; (j < nframes/2); j++)
 461     {
 462         tt[j] = j*dt;
 463         fprintf(fp, "%10g  %10g\n", tt[j], dos[VACF][j] * invNormalize);
 464     }
 465     xvgrclose(fp);
 466
 467     fp = xvgropen(opt2fn("-mvacf", NFILE, fnm), "Mass-weighted velocity autocorrelation function",
 468                   "Time (ps)", "C(t)", oenv);
 469
 470     invNormalize = normalizeAutocorrelation ? 1.0/dos[VACF][0] : 1.0;
 471
 472     for (j = 0; (j < nframes/2); j++)
 473     {
 474         fprintf(fp, "%10g  %10g\n", tt[j], dos[MVACF][j] * invNormalize);
 475     }
 476     xvgrclose(fp);
 477
 478     if ((fftcode = gmx_fft_init_1d_real(&fft, nframes/2,
 479                                         GMX_FFT_FLAG_NONE)) != 0)
 480     {
 481         gmx_fatal(FARGS, "gmx_fft_init_1d_real returned %d", fftcode);
 482     }
 483     if ((fftcode = gmx_fft_1d_real(fft, GMX_FFT_REAL_TO_COMPLEX,
 484                                    (void *)dos[MVACF], (void *)dos[DOS])) != 0)
 485     {
 486         gmx_fatal(FARGS, "gmx_fft_1d_real returned %d", fftcode);
 487     }
 488
 489     /* First compute the DoS */
 490     /* Magic factor of 8 included now. */
 491     bfac = 8*dt*beta/2;
 492     dos2 = 0;
 493     snew(nu, nframes/4);
 494     for (j = 0; (j < nframes/4); j++)
 495     {
 496         nu[j] = 2*j/(t1-t0);
 497         dos2 += gmx::square(dos[DOS][2*j]) + gmx::square(dos[DOS][2*j+1]);
 498         if (bAbsolute)
 499         {
 500             dos[DOS][j] = bfac*std::hypot(dos[DOS][2*j], dos[DOS][2*j+1]);
 501         }
 502         else
 503         {
 504             dos[DOS][j] = bfac*dos[DOS][2*j];
 505         }
 506     }
 507     /* Normalize it */
 508     dostot = evaluate_integral(nframes/4, nu, dos[DOS], NULL, nframes/4, &stddev);
 509     if (bNormalizeDos)
 510     {
 511         for (j = 0; (j < nframes/4); j++)
 512         {
 513             dos[DOS][j] *= 3*Natom/dostot;
 514         }
 515     }
 516
 517     /* Now analyze it */
 518     DoS0 = dos[DOS][0];
 519
 520     /* Note this eqn. is incorrect in Pascal2011a! */
 521     Delta = ((2*DoS0/(9*Natom))*std::sqrt(M_PI*BOLTZ*Temp*Natom/tmass)*
 522              std::pow((Natom/V), 1.0/3.0)*std::pow(6.0/M_PI, 2.0/3.0));
 523     f     = calc_fluidicity(Delta, toler);
 524     y     = calc_y(f, Delta, toler);
 525     z     = calc_compress(y);
 526     Sig   = BOLTZ*(5.0/2.0+std::log(2*M_PI*BOLTZ*Temp/(gmx::square(PLANCK))*V/(f*Natom)));
 527     Shs   = Sig+calc_Shs(f, y);
 528     rho   = (tmass*AMU)/(V*NANO*NANO*NANO);
 529     sigHS = std::cbrt(6*y*V/(M_PI*Natom));
 530
 531     fprintf(fplog, "System = \"%s\"\n", *top.name);
 532     fprintf(fplog, "Nmol = %d\n", Nmol);
 533     fprintf(fplog, "Natom = %d\n", Natom);
 534     fprintf(fplog, "dt = %g ps\n", dt);
 535     fprintf(fplog, "tmass = %g amu\n", tmass);
 536     fprintf(fplog, "V = %g nm^3\n", V);
 537     fprintf(fplog, "rho = %g g/l\n", rho);
 538     fprintf(fplog, "T = %g K\n", Temp);
 539     fprintf(fplog, "beta = %g mol/kJ\n", beta);
 540
 541     fprintf(fplog, "\nDoS parameters\n");
 542     fprintf(fplog, "Delta = %g\n", Delta);
 543     fprintf(fplog, "fluidicity = %g\n", f);
 544     fprintf(fplog, "hard sphere packing fraction = %g\n", y);
 545     fprintf(fplog, "hard sphere compressibility = %g\n", z);
 546     fprintf(fplog, "ideal gas entropy = %g\n", Sig);
 547     fprintf(fplog, "hard sphere entropy = %g\n", Shs);
 548     fprintf(fplog, "sigma_HS = %g nm\n", sigHS);
 549     fprintf(fplog, "DoS0 = %g\n", DoS0);
 550     fprintf(fplog, "Dos2 = %g\n", dos2);
 551     fprintf(fplog, "DoSTot = %g\n", dostot);
 552
 553     /* Now compute solid (2) and diffusive (3) components */
 554     fp = xvgropen(opt2fn("-dos", NFILE, fnm), "Density of states",
 555                   bRecip ? "E (cm\\S-1\\N)" : "\\f{12}n\\f{4} (1/ps)",
 556                   "\\f{4}S(\\f{12}n\\f{4})", oenv);
 557     xvgr_legend(fp, asize(DoSlegend), DoSlegend, oenv);
 558     recip_fac = bRecip ? (1e7/SPEED_OF_LIGHT) : 1.0;
 559     for (j = 0; (j < nframes/4); j++)
 560     {
 561         dos[DOS_DIFF][j]  = DoS0/(1+gmx::square(DoS0*M_PI*nu[j]/(6*f*Natom)));
 562         dos[DOS_SOLID][j] = dos[DOS][j]-dos[DOS_DIFF][j];
 563         fprintf(fp, "%10g  %10g  %10g  %10g\n",
 564                 recip_fac*nu[j],
 565                 dos[DOS][j]/recip_fac,
 566                 dos[DOS_SOLID][j]/recip_fac,
 567                 dos[DOS_DIFF][j]/recip_fac);
 568     }
 569     xvgrclose(fp);
 570
 571     /* Finally analyze the results! */
 572     wCdiff = 0.5;
 573     wSdiff = Shs/(3*BOLTZ); /* Is this correct? */
 574     wEdiff = 0.5;
 575     wAdiff = wEdiff-wSdiff;
 576     for (j = 0; (j < nframes/4); j++)
 577     {
 578         dos[DOS_CP][j] = (dos[DOS_DIFF][j]*wCdiff +
 579                           dos[DOS_SOLID][j]*wCsolid(nu[j], beta));
 580         dos[DOS_S][j]  = (dos[DOS_DIFF][j]*wSdiff +
 581                           dos[DOS_SOLID][j]*wSsolid(nu[j], beta));
 582         dos[DOS_A][j]  = (dos[DOS_DIFF][j]*wAdiff +
 583                           dos[DOS_SOLID][j]*wAsolid(nu[j], beta));
 584         dos[DOS_E][j]  = (dos[DOS_DIFF][j]*wEdiff +
 585                           dos[DOS_SOLID][j]*wEsolid(nu[j], beta));
 586     }
 587     DiffCoeff = evaluate_integral(nframes/2, tt, dos[VACF], NULL, nframes/2, &stddev);
 588     DiffCoeff = 1000*DiffCoeff/3.0;
 589     fprintf(fplog, "Diffusion coefficient from VACF %g 10^-5 cm^2/s\n",
 590             DiffCoeff);
 591     fprintf(fplog, "Diffusion coefficient from DoS %g 10^-5 cm^2/s\n",
 592             1000*DoS0/(12*tmass*beta));
 593
 594     cP = BOLTZ * evaluate_integral(nframes/4, nu, dos[DOS_CP], NULL,
 595                                    nframes/4, &stddev);
 596     fprintf(fplog, "Heat capacity %g J/mol K\n", 1000*cP/Nmol);
 597     fprintf(fplog, "\nArrivederci!\n");
 598     gmx_fio_fclose(fplog);
 599
 600     do_view(oenv, ftp2fn(efXVG, NFILE, fnm), "-nxy");
 601
 602     return 0;
 603 }