Specifying the system to be simulated

Specifying the Simulation Cell

The simulationcell block specifies the geometry of the cell, how the boundary conditions should be handled, and how ewald summation should be broken up.

simulationcell Element:

Parent elements:

qmcsystem

Child elements:

None

Attribute:

parameter name

datatype

values

default

description

lattice

9 floats

any float

Must be specified

Specification of lattice vectors.

bconds

string

“p” or “n”

“n n n “

Boundary conditions for each axis.

vacuum

float

\(\geq 1.0\)

1.0

Vacuum scale.

LR_handler

string

string

“opt_breakup”

Ewald breakup method.

LR_dim_cutoff

float

float

15

Ewald breakup distance.

LR_tol

float

float

3e-4

Tolerance in Ha for Ewald ion-ion energy per atom.

ewald_grid

int

int

1001

The number of linear grid points used for short-range part of the Ewald potential.

An example of a block is given below:

<simulationcell>
    <parameter name="lattice">
      3.8       0.0       0.0
      0.0       3.8       0.0
      0.0       0.0       3.8
    </parameter>
    <parameter name="bconds">
       p p p
    </parameter>
    <parameter name="LR_dim_cutoff"> 20 </parameter>
  </simulationcell>

Here, a cubic cell 3.8 bohr on a side will be used. This simulation will use periodic boundary conditions, and the maximum \(k\) vector will be \(20/r_{wigner-seitz}\) of the cell.

Lattice

The cell is specified using 3 lattice vectors.

Boundary conditions

QMCPACK offers the capability to use a mixture of open and periodic boundary conditions. The parameter expects a single string of three characters separated by spaces, e.g. “p p p” for purely periodic boundary conditions. These characters control the behavior of the \(x\), \(y\), and \(z\), axes, respectively. Non periodic directions must be placed after the periodic ones. The only supported combinations are:

“p p p” Periodic boundary conditions. Corresponds to a 3D crystal.

“p p n” Slab geometry. Corresponds to a 2D crystal.

“p n n” Wire geometry. Corresponds to a 1D crystal.

“n n n” Open boundary conditions. Corresponds to an isolated molecule in a vacuum.

Vacuum

The vacuum option allows adding a vacuum region in slab or wire boundary conditions (bconds= p p n or bconds= p n n, respectively). The main use is to save memory with spline or plane-wave basis trial wavefunctions, because no basis functions are required inside the vacuum region. For example, a large vacuum region can be added above and below a graphene sheet without having to generate the trial wavefunction in such a large box or to have as many splines as would otherwise be required. Note that the trial wavefunction must still be generated in a large enough box to sufficiently reduce periodic interactions in the underlying electronic structure calculation.

With the vacuum option, the box used for Ewald summation increases along the axis labeled by a factor of vacuum. Note that all the particles remain in the original box without altering their positions. i.e. Bond lengths are not changed by this option. The default value is 1, no change to the specified axes.

An example of a simulationcell block using is given below. The size of the box along the z-axis increases from 12 to 18 by the vacuum scale of 1.5.

<simulationcell>
    <parameter name="lattice">
      3.8       0.0       0.0
      0.0       3.8       0.0
      0.0       0.0      12.0
    </parameter>
    <parameter name="bconds">
       p p n
    </parameter>
    <parameter name="vacuum"> 1.5 </parameter>
    <parameter name="LR_dim_cutoff"> 20 </parameter>
    <parameter name="LR_handler"> ewald </parameter>
    <parameter name="ewald_grid"> 1001 </parameter>
  </simulationcell>

LR_handler

When using periodic boundary conditions direct calculation of the Coulomb energy is conditionally convergent. As a result, QMCPACK uses an optimized short-range/long-range breakup technique to compute the Coulomb interaction in a rapidly convergent lattice sum. [NC95]

In this summation, the energy is broken into short- and long-ranged terms. The short-ranged term is computed directly in real space, while the long-ranged term is computed in reciprocal space.

\[v(r) = 1/r = v^{sr}(r) + v^{lr}(r)\]

LR_handler determines the functional form of \(v^{sr}\) and \(v^{lr}\). For example, the Ewald forms are

\[v^{sr}(r) = \text{erfc}(\alpha r)/r\]

\[v^{lr}(r) = \text{erf}(\alpha r)/r\]

Implemented choices for 3D systems are: ewald, opt_breakup, and opt_breakup_original. The choice for a 2D system is ewald_strict2d. The choice for a quasi-2D (e.g. slab) system is ewald_quasi2d.

LR_dim_cutoff

QMCPACK chooses the short-range part to terminate at the image radius of the simulation cell. This way only one real-space cell needs to be considered using the minimum image convention. LR_dim_cutoff controls the number of terms to include in the long-range sum. The real-space cutoff \(r_{c}\) and reciprocal-space cutoff \(k_{c}\) are related by

\[\mathrm{LR\_dim\_cutoff} = r_{c} \times k_{c}\]

where \(r_{c}\) is the Wigner-Seitz (simulation cell image) radius, and \(k_{c}\) is the length of the maximum \(k\)-vector used in the long-ranged term. Larger values of increase the accuracy of the evaluation. A value of 15 tends to be conservative for the opt_breakup handler in 3D.

ewald_grid

The short-range part of the Ewald/optimized potential \(v^{sr}(r)\) is put on a linear grid. ewald_grid controls the number of grid points on this 1D grid.

Specifying the particle set

The particleset blocks specify the particles in the QMC simulations: their types, attributes (mass, charge, valence), and positions.

Input specification

particleset element:

Parent elements

simulation

Child elements

group, attrib

Attribute:

Name

Datatype

Values

Default

Description

name/id

Text

Any

e

Name of particle set

size\(^o\)

Integer

Any

0

Number of particles in set

random\(^o\)

Text

Yes/no

No

Randomize starting positions

randomsrc/randomsrc\(^o\)

Text

particleset.name

None

Particle set to randomize

spinor\(^o\)

Text

Yes/no

No

particleset treated as spinor

Detailed attribute description

Required particleset attributes

name/id

Unique name for the particle set. Default is “e” for electrons. “i” or “ion0” is typically used for ions. For special cases where an empty particle set is needed, the special name “empty” can be used to bypass the zero-size error check.

Optional particleset attributes

size

Number of particles in set.
random

Randomize starting positions of particles. Each component of each particle’s position is randomized independently in the range of the simulation cell in that component’s direction.
randomsrc/random_source

Specify source particle set around which to randomize the initial positions of this particle set.
spinor

Sets an internal flag that the particleset (usually for electrons) is a spinor object. This is used in the wavefunction builders and QMC drivers to determiane if spin sampling will be used

Group element:

Parent elements

particleset

Child elements

parameter, attrib

Attribute:

Name

Datatype

Values

Default

Description

name

Text

Any

e

Name of particle set

size\(^o\)

Integer

Any

0

Number of particles in set

mass\(^o\)

Real

Any

1

Mass of particles in set

unit\(^o\)

Text

au/amu

au

Units for mass of particles

Parameters:

Name

Datatype

Values

Default

Description

charge

Real

Any

0

Charge of particles in set

valence

Real

Any

0

Valence charge of particles in set

atomicnumber

Integer

Any

0

Atomic number of particles in set

Required group attributes

name/id

Unique name for the particle set group. Typically, element symbols are used for ions and “u” or “d” for spin-up and spin-down electron groups, respectively.

Optional group attributes

mass

Mass of particles in set.
unit

Units for mass of particles in set (au[\(m_e\) = 1] or amu[\(\frac{1}{12}m_{\rm ^{12}C}\) = 1]).

attrib element:

Parent elements

particleset, group

Attribute:

Name

Datatype

Values

Default

Description

name

String

ionid, Any

None

Name of attrib

datatype

String

IntArray, realArray, posArray, stringArray

None

Type of data in attrib

condition

Integer

0, 1

0

Select coordinates

size\(^o\)

String

Any

None

Size of data in attrib

condition

When datatype is posArray, set 0 for cartesian coordinates or set 1 for fractional coordinates.

Example use cases

Particleset elements for ions and electrons randomizing electron start positions.

<particleset name="i" size="2">
  <group name="Li">
    <parameter name="charge">3.000000</parameter>
    <parameter name="valence">3.000000</parameter>
    <parameter name="atomicnumber">3.000000</parameter>
  </group>
  <group name="H">
    <parameter name="charge">1.000000</parameter>
    <parameter name="valence">1.000000</parameter>
    <parameter name="atomicnumber">1.000000</parameter>
  </group>
  <attrib name="position" datatype="posArray" condition="1">
  0.0   0.0   0.0
  0.5   0.5   0.5
  </attrib>
  <attrib name="ionid" datatype="stringArray">
     Li H
  </attrib>
</particleset>
<particleset name="e" random="yes" randomsrc="i">
  <group name="u" size="2">
    <parameter name="charge">-1</parameter>
  </group>
  <group name="d" size="2">
    <parameter name="charge">-1</parameter>
  </group>
</particleset>

Particleset elements for ions and electrons specifying electron start positions.

<particleset name="e">
  <group name="u" size="4">
    <parameter name="charge">-1</parameter>
    <attrib name="position" datatype="posArray">
  2.9151687332e-01 -6.5123272502e-01 -1.2188463918e-01
  5.8423636048e-01  4.2730406357e-01 -4.5964306231e-03
  3.5228575807e-01 -3.5027014639e-01  5.2644808295e-01
     -5.1686250912e-01 -1.6648002292e+00  6.5837023441e-01
    </attrib>
  </group>
  <group name="d" size="4">
    <parameter name="charge">-1</parameter>
    <attrib name="position" datatype="posArray">
  3.1443445436e-01  6.5068682609e-01 -4.0983449009e-02
     -3.8686061749e-01 -9.3744432997e-02 -6.0456005388e-01
  2.4978241724e-02 -3.2862514649e-02 -7.2266047173e-01
     -4.0352404772e-01  1.1927734805e+00  5.5610824921e-01
    </attrib>
  </group>
</particleset>
<particleset name="ion0" size="3">
  <group name="O">
    <parameter name="charge">6</parameter>
    <parameter name="valence">4</parameter>
    <parameter name="atomicnumber">8</parameter>
  </group>
  <group name="H">
    <parameter name="charge">1</parameter>
    <parameter name="valence">1</parameter>
    <parameter name="atomicnumber">1</parameter>
  </group>
  <attrib name="position" datatype="posArray">
    0.0000000000e+00  0.0000000000e+00  0.0000000000e+00
    0.0000000000e+00 -1.4308249289e+00  1.1078707576e+00
    0.0000000000e+00  1.4308249289e+00  1.1078707576e+00
  </attrib>
  <attrib name="ionid" datatype="stringArray">
    O H H
  </attrib>
</particleset>

Particleset elements for ions specifying positions by ion type.

<particleset name="ion0">
  <group name="O" size="1">
    <parameter name="charge">6</parameter>
    <parameter name="valence">4</parameter>
    <parameter name="atomicnumber">8</parameter>
    <attrib name="position" datatype="posArray">
      0.0000000000e+00  0.0000000000e+00  0.0000000000e+00
    </attrib>
  </group>
  <group name="H" size="2">
    <parameter name="charge">1</parameter>
    <parameter name="valence">1</parameter>
    <parameter name="atomicnumber">1</parameter>
    <attrib name="position" datatype="posArray">
      0.0000000000e+00 -1.4308249289e+00  1.1078707576e+00
      0.0000000000e+00  1.4308249289e+00  1.1078707576e+00
    </attrib>
  </group>
</particleset>