Question on hydrogen bond lifetime calculation

[horlust]

Hello everyone,

I am playing with the hydrogen bond lifetime function. I have molecules of sugar in the simulation box and around 600 molecules of water. I tried to calculate the hydrogen bond lifetime of only the bonds between the sugar oxygens and water, for example:

ids = [238, 239, 240, 243, 244, 245]

for id_val in ids:
    hbonds_oxygen_water = HBA(universe=u,
                              between=['resname SOL', f'resname B00 and id {id_val}'],
                              d_a_cutoff=3.0,
                              d_h_a_angle_cutoff=120
                             )
    sorbitol_hydrogen_donors_sel = f"resname B00 and id {id_val}"
    sorbitol_hydrogens_sel = hbonds_oxygen_water.guess_hydrogens("resname B00")
    sorbitol_acceptors_sel = hbonds_oxygen_water.guess_acceptors("resname B00")
    
    water_hydrogens_sel = "resname SOL and name HW1 HW2"
    water_acceptors_sel = "resname SOL and name OW"
    water_hydrogen_donors_sel = "resname SOL and name OW"
    
    hbonds_oxygen_water.hydrogens_sel = f"({sorbitol_hydrogens_sel}) or ({water_hydrogens_sel})"
    hbonds_oxygen_water.acceptors_sel = f"({sorbitol_acceptors_sel}) or ({water_acceptors_sel})"
    hbonds_oxygen_water.donors_sel = f"({sorbitol_hydrogen_donors_sel}) or ({water_hydrogen_donors_sel})"
    
    hbonds_oxygen_water.run(verbose=True)
    
    hbonds_sorbitol_water_per_frame = hbonds_oxygen_water.count_by_time()
    
    average_hb_count_sorbitol_water = np.mean(hbonds_sorbitol_water_per_frame)
    print(f"Average number of hydrogen bonds with water (ID {id_val}): {average_hb_count_sorbitol_water}")
    print(f"Total number of hydrogen bonds with water (ID {id_val}): {np.sum(hbonds_sorbitol_water_per_frame)}")
    
    tau_max = 40
    window_step = 1
    
    tau_frames, hbond_lifetime_sorbitol_water = hbonds_oxygen_water.lifetime(
        tau_max=tau_max,
        window_step=window_step
    )
    
    params_water, fit_t_water, fit_ac_water = fit_biexponential(tau_frames, hbond_lifetime_sorbitol_water)
    tau_times = tau_frames * u.trajectory.dt
    
    A, tau1, B, tau2 = params_water

    time_constant = A * tau1 + B * tau2
    print(f"Relevant lifetime for ID {id_val}: {time_constant:.2f} ps")

I do something similar for the intramolecular hydrogen bonds related to these oxygens. However, sometimes I get too high values in this case; for example, 179458,59 ps, which is bigger than the simulation time (5 ns). I wanted to know if I'm doing something wrong? What is the physical meaning of such a value?

The function I'm using is:

def fit_biexponential(tau_timeseries, ac_timeseries):
    """Fit a biexponential function to a hydrogen bond time autocorrelation function
    Return the two time constants
    """
    from scipy.optimize import curve_fit

    def model(t, A, tau1, B, tau2):
        """Fit data to a biexponential function.
        """
        return A * np.exp(-t / tau1) + B * np.exp(-t / tau2)

    params, params_covariance = curve_fit(model, tau_timeseries, ac_timeseries, [1, 0.5, 1, 2], maxfev=100000)

    fit_t = np.linspace(tau_timeseries[0], tau_timeseries[-1], 1000)
    fit_ac = model(fit_t, *params)

    return params, fit_t, fit_ac

And the code for intramolecular hydrogen bonds is pretty much the same, only changing:

for id_val in ids:
    hbonds_oxygen_intra = HBA(universe=u,
                              between=['resname B00', f'resname B00'],
                              d_a_cutoff=3.0,
                              d_h_a_angle_cutoff=120
                             )
    
    sorbitol_hydrogen_donors_sel = f"resname B00 and id {id_val}"
    sorbitol_hydrogens_sel = hbonds_oxygen_intra.guess_hydrogens("resname B00")
    sorbitol_acceptors_sel = hbonds_oxygen_intra.guess_acceptors("resname B00")
    
    hbonds_oxygen_intra.hydrogens_sel = f"({sorbitol_hydrogens_sel})"
    hbonds_oxygen_intra.acceptors_sel = f"({sorbitol_acceptors_sel})"
    hbonds_oxygen_intra.donors_sel = f"({sorbitol_hydrogen_donors_sel})"

    hbonds_oxygen_intra.run(verbose=True)

Thank you very much: :-)