MCP 1 Chapter 3 Molecular Dynamics

Questions about the lecture 'From Molecular to Continuum Physics 1' of the RWTH Aachen Chapter 3 Molecular Dynamics

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This flashcard set delves into advanced molecular dynamics (MD) techniques at the university level, focusing on key concepts like NPT and NVT ensembles, pressure and temperature control methods, and their implementation in tools like GROMACS. It covers essential topics such as the Parrinello-Rahman and Berendsen algorithms, their characteristics, and activation procedures. Researchers and students in computational chemistry and molecular physics will find this set particularly useful for understanding and applying these methods in their simulations.

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What to use in case of pairwise interactions via potential phi(r) for P?

[isothermal-isobaric NPT ensembles.MD]

P = rho*k_b*T – 1/Vd * < Sum_i=1^N Sum_j>i r_ij dphi/dr >

What is the virial theorem?

[isothermal-isobaric NPT ensembles.MD, 2]

1. Link conecpt of mac pressure and mic dynamics

2. PV = N*k_B*T + 1/3 * < Sum_i=1^N r_i*f_i >

What is the idea?

[time evolution algorithm.isothermal-isobaric NPT ensembles.MD]

Coordinate scaling with ad hoc modulation of coordinates

What are the characteristics?

[berendsen.time evolution algorithm.isothermal-isobaric NPT ensembles.MD, 4]

1. Mimics pressure coupling with first-order kinetics relaxation with pressure towards P^ref

2. Rescale each particle’s coordinates and box vectors

3. Correct system pressure

4. Repeat periodically

How to rescale?

[berendsen.time evolution algorithm.isothermal-isobaric NPT ensembles.MD, 3]

1. Use time-dependent matrix

2. mye_ij = d_ij – n*dt/tao_p *b_ij {P_ij^Ref – P_ij(t)}

3. With b_ij the isothermal compressibility

How to correct system pressure?

[berendsen.time evolution algorithm.isothermal-isobaric NPT ensembles.MD]

dP/dt = P^ref-P/tao_p

How to active in GROMACS?

[berendsen.time evolution algorithm.isothermal-isobaric NPT ensembles.MD, 5]

1. pcoupl = berendsen

2. pcoupltype = isotropic

3. ref-p = 0.79

4. tau-p = 0.5

5. compressibility = 2e-4

What are the effects?

[berendsen.time evolution algorithm.isothermal-isobaric NPT ensembles.MD, 2]

1. Yields correct average pressure

2. Not yield exact isobaric ensemble

What is the idea?

[equations of motions.isothermal-isobaric NPT ensembles.MD]

Extended ensemble with new variables added to 6N phase space

Which methods exist?

[equations of motions.isothermal-isobaric NPT ensembles.MD, 3]

1. Andersen

2. Parrinello-Rahman

3. MTTK

What are the characteristics?

[parrinello-rahman.equations of motions.isothermal-isobaric NPT ensembles.MD, 5]

1. Extended by new DoF and terms

2. DoF represent box vectors represented by matrix h

3. h obeys equation of motion

4. Equation of motions changes

5. Micocanonical sampling yields isobaric distribution

How does h obeys the equation of motion?

[parrinello-rahman.equations of motions.isothermal-isobaric NPT ensembles.MD, 2]

1. d²h/dt² = VW^-1(h^T)^-1(P-P^ref)

2. With (W^-1)_ij = 4pi²*b_ij / 3tao_p*max(h_ij)

How does the equation of motion changes?

[parrinello-rahman.equations of motions.isothermal-isobaric NPT ensembles.MD, 2]

1. d²r_i/dt² = f_i/m_i – M dr_i/dt

2. With M = h^-1[h dh^T/dt + dh/dt h^T](h^T)^-1

How to active in GROMACS?

[parrinello-rahman.equations of motions.isothermal-isobaric NPT ensembles.MD, 5]

1. pcoupl = parrinello-rahman

2. pcoupltype = isotropic

3. ref-p = 0.79

4. tau-p = 0.5

5. compressibility = 2e-4

What are the effects?

[parrinello-rahman.equations of motions.isothermal-isobaric NPT ensembles.MD, 2]

1. Yields true ensemble

2. Not reversible due to usage of old pressure // Missing high precision

What are the steps?

[equilibration procedure.isothermal-isobaric NPT ensembles.MD, 2]

1. Initial heating

2. Employ barostat algorithm to find correct density

How to react if pressure far from equilibrium?

[equilibration procedure.isothermal-isobaric NPT ensembles.MD, 3]

1. Increase time constant

2. OR use weak-coupling scheme

3. After target pressure reached switch back

What to do?

[temperature and pressure.equilibration procedure.isothermal-isobaric NPT ensembles.MD, 3]

1. Use same type of algorithm

2. Berendsen thermostat + Berendsen barostat

3. Nose-Hoover thermostat + Parrinello-Rahman barostat

What are the characteristics?

[berendsen.temperature and pressure.equilibration procedure.isothermal-isobaric NPT ensembles.MD, 2]

1. Weak coupling

2. Does not yield exact NPT ensemble

What are the characteristics?

[nose-hoover parrinello-rahman.temperature and pressure.equilibration procedure.isothermal-isobaric NPT ensembles.MD, 2]

1. Extended ensemble approach

2. Yields exact NPT ensemble

What are the characteristics of experiments in the past? [3]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. System subjected to measurements

2. Results in numeric form compared with...

3. Theory is a model of the system as a set of mathematical equations

What are the characteristics of experiments nowadays using computers? [5]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Following a recipe

2. More complexity

3. Large amount of degrees of freedom

4. Simulation condition close to experimental one

5. Thought experiments possible

What is the definition of molecular dynamics (MD)? [4]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Computer simulation of a set of atoms time evolution due to motion

2. Numerically integration of motion equations with time discretization Dt

3. N material points move deterministically

4. m_i* d²r_1/dt² = f_i wuth r_i position vector and f_i force vector

What are the limitations of molecular dynamics (MD)? [4]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Accuracy improved by increased numerical precision or smaller Dt

2. Classical laws of motion

3. Realism of forces // Force-filed problem

4. Time and size

What can be done with molecular dynamics (MD)?

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

Measure thermodynamic properties

What are the components of a physical system model? [2]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Potential function U(r_1,… ,r_n) representing potential energy

2. Forces f_i are gradients of the potential -Grad_r_i(U)

What are the notes for a physical system model? [3]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Conservation law o the total energy E=K+U

2. For simulated system N is negligible small compared to amount in matter

3. Use PBC to mimic as replicating a small box (program) in all directions

What is the definition of the Lennard-Jones pair potential for the potential function? [3]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Interaction Sum_i Sum_j>i phi(|r_i-r_j|)

2. phi(r) = 4*eps*[(sigma/r)^12 – [sigma/r]^6]

3. Describes correctly e.g. for liquid Argon

What is a practical extension of the Lennard-Jones pair potential for the potential function? [3]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Short-range interaction potential saves resources

2. Lennard-Jones has infinite range

3. Cutoff radius is practical with R_c=3sigma

What has to be done if the short-range interaction potential is applied to the Lennard-Jones pair potential for the potential function? [4]

Tastatur-Befehle:

= drehen,

= vor-/rückwärts,

= scrollen

1. Constant additive correction for quantities

2. Treat system as a uniform continuum beyond cutoff

3. phi_ij^LRC = ½*4pi*p*int_Rc^inf(dr_ij*r_ij²*phi(r_ij)) = 8pi*p*eps*sigma³*[1/9(sigma/Rc)^9 – 1/3(sigma/Rc)^3]

4. P_ij^LRC = = ½*4pi*p²*int_Rc^inf(dr_ij*r_ij²*r_ij*F_ij) = 16/3*pi*p²*eps*sigma³*[2/3(sigma/Rc)^9 – (sigma/Rc)^3] with p=N/V the number density

What is the meaning of the abbreviation GROMACS?

Groningen machine for chemical simulations

What is GROMACS for?

Molecular dynamics package for simulations of proteins, lipids and nucleic acids

What are the characteristics of GROMACS? [3]

1. Used at universities and research centers across the world

2. Fast and most popular MD SW available

3. Open source

Which file type exist in GROMACS? [3]

1. Topology 2. coordinate and 3. simulation parameter

What is the question answered by a topology file in GROMACS?

How Is the system to be run? // Force-filed parameters

What is the question answered by a coordinate file in GROMACS?

Where is the system to be run? // Coordinates of atoms

What is the question answered by a simulation parameter file in GROMACS?

What do you want to run? // Time step and cutoffs

How to indicate comments in a topology file in GROMACS?

With a semicolon ;

What are the categories of a topology file in GROMACS? [6]

1. [defaults]

2. [atomtypes]

3. [moleculetype]

4. [atoms]

5. [system]

6. [molecules]

What are the sub categories of [defaults] of a topology file in GROMACS? [2]

1. nb-function

2. combination rule

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What are the dimensions in the phase space used for?

For complete dynamical evolution via (Newtonian) equations of motion

What are the characteristics of constant energy in a physical system model? [5]

1. For N material points and 3N degrees of freedom

2. No external force and though isolated system

3. Internal forces -Grad_xi*U(x₁,…,x_N) are conservative forces

4. Total energy conserved by (Newtonian) equations of motion

5. Applied MD samples a mic ensemble

What are the characteristics of the sample mic ensemble by MD? [2]

1. Trajectory lies on a hypersurface in phase space

2 .Not all position, momentum combinations are allowed/visited

What is the definition of real systems?

“Natural systems or systems prepared in laboratory for measurements”

Are real systems compatible with mic ensembles?

No, real systems are open systems (Exchange mass and energy with outside)

What holds for canonical (NVT) ensembles for MD? [3]

1. Constant temperature T

2. Energy is no more conserved along trajectory

3. Points in phase space, if correspond to state with total energy E then visited with Boltzmann probability p(E) = e^{-E(x1,…,xN,p1,…,pN)/kB*T} / int dx₁…dx_Ndxp₁…dp_N e^{-E(x1,…,xN,p1,…,pN)/kB*T}

What has to be done for canonical (NVT) ensembles for MD to ensure correctness? [2]

1. Modify time evolution algorithm

2. Modify equations of motions

What is the idea of modifying the time evolution algorithm for canonical (NVT) ensembles in MD?

Velocity scaling with ad hoc modulation of velocities

What are the types of modifying the time evolution algorithm for canonical (NVT) ensembles in MD? [4]

1. Isokinetic

2. Berendsen

3. Andersen

4. Velocity rescaling

What are the characteristics of the isokinetic way of modifying the time evolution algorithm for canonical (NVT) ensembles in MD? [4]

1. Naive

2. Measure instantaneous temperature T

3. Rescale by lambda = sqrt(T_ref/T)

4. Repeat periodically

What are the characteristics of the Berendsen way of modifying the time evolution algorithm for canonical (NVT) ensembles in MD? [4]

1. Mimics weak coupling with external heat bath

2. Measure instantaneous temperature T

3. Rescale by lambda

4. Repeat periodically

How to activate the Berendsen way of modifying the time evolution algorithm for canonical (NVT) ensembles in MD in GROMACS? [4]

1. tcoupl = berendsen

2. ref-t = 85.0

3. tau-t = 5.0

4. tc-grps = System

What are the characteristics of the Andersen way of modifying the time evolution algorithm for canonical (NVT) ensembles in MD? [4]

1. Mimics collisions with hotter/colder particles

2. Randomly select particle

3. Exchange actual by Maxwell-Boltzmann distribution velocity

4. Repeat periodically

What are the types of modifying the equations of motion for canonical (NVT) ensembles in MD? [2]

1. Nose-Hoover

2. MTTK

What are the characteristics of the Nose-Hoover way of modifying the equations of motion for canonical (NVT) ensembles in MD? [3]

1. Extended by thermal reservoir and friction term

2. H_NH

3. Equation of motion changes

How to activate the Nose-Hoover way of modifying the equations of motion for canonical (NVT) ensembles in MD in GROMACS? [4]

1. tcoupl = nose-hoover

2. ref-t = 85.0

3. tau-t = 5.0

4. tc-grps = System

How to display temperature time evolution in GROMACS?

‘gmx energy -f md.edr -p T.xvg -xvg none’

How to influence energy conservation in GROMACS? [3]

1. Numerical precision

2. Cut-off distance

3. Time step

How to influence energy conservation with numerical precision in GROMACS? [2]

1. gmx_mpi vs gmx_mpi_d

2. Use with ‘module switch gromacs gromacs/5.1.2dp’

Does numerical precision works to improve energy conservation in GROMACS?

No significantly effect

How to influence energy conservation with cut-off distance in GROMACS?

rvdw = 1.0, 1.2, 1.4 nm

Does cut-off distance works to improve energy conservation in GROMACS?

Yes, noise reduced

How to influence energy conservation with time step in GROMACS? [3]

1. dt=0.01 vs 0.001

2. nsteps=25000 vs 250000

3. nstxtcout=100 vs 1000

Does time step works to improve energy conservation in GROMACS?

Yes, noise reduced, but other improvements necessary

What are the characteristics?

[isothermal-isobaric NPT ensembles.MD, 4]

1. Constant pressure

2. Volume thus density is no more constant along trajectory

3. Fluctuations in pressure are connected with volume

4. Work with constant temperature // Mimic experimental conditions

On what is the measurement of pressure in MD based on?

[isothermal-isobaric NPT ensembles.MD, 3]

1. Clausius virial function W

2. W(r₁,…,r_N) = < Sum_i=1^N r_i*f_i^TOT >

3. PV = N*k_B*T + 1/d * < Sum_i=1^N r_i*f_i >

What to use in case of pairwise interactions via potential phi(r) for P?

[isothermal-isobaric NPT ensembles.MD]

P = rho*k_b*T – 1/Vd * < Sum_i=1^N Sum_j>i r_ij dphi/dr >

What is the virial theorem?

[isothermal-isobaric NPT ensembles.MD, 2]

1. Link conecpt of mac pressure and mic dynamics

2. PV = N*k_B*T + 1/3 * < Sum_i=1^N r_i*f_i >

What is the idea?

[time evolution algorithm.isothermal-isobaric NPT ensembles.MD]

Coordinate scaling with ad hoc modulation of coordinates

What are the characteristics?

[berendsen.time evolution algorithm.isothermal-isobaric NPT ensembles.MD, 4]

1. Mimics pressure coupling with first-order kinetics relaxation with pressure towards P^ref

2. Rescale each particle’s coordinates and box vectors

3. Correct system pressure

4. Repeat periodically

How to rescale?

[berendsen.time evolution algorithm.isothermal-isobaric NPT ensembles.MD, 3]

1. Use time-dependent matrix

2. mye_ij = d_ij – n*dt/tao_p *b_ij {P_ij^Ref – P_ij(t)}

3. With b_ij the isothermal compressibility

How to correct system pressure?

[berendsen.time evolution algorithm.isothermal-isobaric NPT ensembles.MD]

dP/dt = P^ref-P/tao_p

How to active in GROMACS?

[berendsen.time evolution algorithm.isothermal-isobaric NPT ensembles.MD, 5]

1. pcoupl = berendsen

2. pcoupltype = isotropic

3. ref-p = 0.79

4. tau-p = 0.5

5. compressibility = 2e-4

What are the effects?

[berendsen.time evolution algorithm.isothermal-isobaric NPT ensembles.MD, 2]

1. Yields correct average pressure

2. Not yield exact isobaric ensemble

What is the idea?

[equations of motions.isothermal-isobaric NPT ensembles.MD]

Extended ensemble with new variables added to 6N phase space

Which methods exist?

[equations of motions.isothermal-isobaric NPT ensembles.MD, 3]

1. Andersen

2. Parrinello-Rahman

3. MTTK

What are the characteristics?

[parrinello-rahman.equations of motions.isothermal-isobaric NPT ensembles.MD, 5]

1. Extended by new DoF and terms

2. DoF represent box vectors represented by matrix h

3. h obeys equation of motion

4. Equation of motions changes

5. Micocanonical sampling yields isobaric distribution

How does h obeys the equation of motion?

[parrinello-rahman.equations of motions.isothermal-isobaric NPT ensembles.MD, 2]

1. d²h/dt² = VW^-1(h^T)^-1(P-P^ref)

2. With (W^-1)_ij = 4pi²*b_ij / 3tao_p*max(h_ij)

How does the equation of motion changes?

[parrinello-rahman.equations of motions.isothermal-isobaric NPT ensembles.MD, 2]

1. d²r_i/dt² = f_i/m_i – M dr_i/dt

2. With M = h^-1[h dh^T/dt + dh/dt h^T](h^T)^-1

How to active in GROMACS?

[parrinello-rahman.equations of motions.isothermal-isobaric NPT ensembles.MD, 5]

1. pcoupl = parrinello-rahman

2. pcoupltype = isotropic

3. ref-p = 0.79

4. tau-p = 0.5

5. compressibility = 2e-4

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MCP 1 Chapter 3 Molecular Dynamics

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