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_dim_cutoff

float

float

15

Ewald breakup distance.

LR_tol

float

float

3e-4

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

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. Examples of valid include:

“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>
  </simulationcell>

LR_dim_cutoff¶

When using periodic boundary conditions direct calculation of the Coulomb energy is not well behaved. As a result, QMCPACK uses an optimized Ewald summation technique to compute the Coulomb interaction. [NC95]

In the Ewald 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. controls where the short-ranged term ends and the long-ranged term begins. The real-space cutoff, reciprocal-space cutoff, and are related via:

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

where \(r_{c}\) is the Wigner-Seitz 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.

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

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.

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

attrib element:

Parent elements

particleset, group

Attribute:

Name

Datatype

Values

Default

Description

name

String

Any

None

Name of attrib

datatype

String

IntArray, realArray, posArray, stringArray

None

Type of data in attrib

size\(^o\)

String

Any

None

Size of data in attrib

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.

Required name 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]).

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>

NC95: Vincent Natoli and David M. Ceperley. An optimized method for treating long-range potentials. Journal of Computational Physics, 117(1):171 – 178, 1995. URL: http://www.sciencedirect.com/science/article/pii/S0021999185710546, doi:http://dx.doi.org/10.1006/jcph.1995.1054.