potfit wiki - interactions

adp

anonymous@undisclosed.example.com (Anonymous) — Mon, 22 Jan 2018 16:48:09 +0000

Angular Dependent Potentials ---------- The angular dependent potentials were developed for the Fe-Ni system. It is a generalization of the EAM model for the simulation of the covalent component of bonding. The angular dependent potential (ADP) for $$E_{\text{total}}=\frac{1}{2}\sum_{i,j(j\neq i)}^N\Phi_{ij}(r_{ij})+\sum_iF_i(n_i)+\frac{1}{2}\sum_{i,\alpha}(\mu_i^\alpha)^2+\frac{1}{2}\sum_{i,\alpha,\beta}(\lambda_i^{\alpha\beta})^2-\frac{1}{6}\sum_i\nu_i^2$$$i$$j$$\alpha,\beta=1,2,3$$$\mu_i^\…

angular_coulomb_potentials

anonymous@undisclosed.example.com (Anonymous) — Sat, 06 Jan 2018 10:18:49 +0000

Angular Coulomb Potentials ---------- Info: This page is incomplete and may contain invalid/wrong information! The angular coulomb potentials are a combination of the regular coulomb potentials and a angular dependent term similar to MEAM: $$ V=V_{Coulomb}+\frac{1}{2}\sum f_{ij}(r_{ij})f_{ik}(r_{ik})g_i(\cos(\theta_{ijk})) $$ Number of potential functions $N$$N(N+2)$$\phi_{ij}$$f_{ij}$$g_i$$N$$N(N+1)/2$$N(N+1)/2$$N$$N(N+2)$$N$$\phi_{00}, \ldots, \phi_{0N}, \phi_{11}, \ldots, \phi_{1N}, \l…

angular_pair_potentials

anonymous@undisclosed.example.com (Anonymous) — Sat, 06 Jan 2018 10:04:54 +0000

Angular Pair Potentials ---------- The angular pair potentials are a combination of the regular pair potentials and a angular dependent term similar to MEAM: $$ V=\frac{1}{2}\sum\phi_{ij}(r_{ij})+\frac{1}{2}\sum f_{ij}(r_{ij})f_{ik}(r_{ik})g_i(\cos(\theta_{ijk})) $$ With this approach it is possible to fit potentials such as this one here. Or it can be used to consider non-bonded angular interactions as DL_POLY does for the three-body terms (see 'tbp' interaction, p. 174 in the $f_{ij} = 1$…

coulomb

anonymous@undisclosed.example.com (Anonymous) — Mon, 19 Mar 2018 15:29:22 +0000

Coulomb Interactions ---------- Electrostatics can be enabled with the coulomb option. A charge $q$, which has to be given in the potential file, is assigned to each atom type. The coulomb interaction of a set of $N$ ions is calculated as $$E_\text{total}^\text{Coul} = \frac{1}{2} \sum_{i\neq j} E(r_{ij}) \qquad \text{with} \qquad E(r_{ij}) \sim \frac{q_{i}q_{j}}{r_{ij}}.$$ There are three modifications required for a proper numerical calculation.$$E_\text{total}^\text{Coul} = \frac{1}{2} \s…

dipole

anonymous@undisclosed.example.com (Anonymous) — Wed, 10 Jan 2018 16:27:08 +0000

Dipole Interactions ---------- To enable the calculation of electric dipole moments, potfit has to be compiled with the dipole option. The dipole $\vec P_{i,n}$ of atom $i$ in iteration step $n$ is then calculated self-consistently by the use of the Tangney-Scandolo potential model$$\vec P_{i,n} = \vec P_{i,\text{NF}} + \vec P_{i,\text{IND}}$$$$\vec P_{i,\text{NF}} = \alpha \sum\limits_{j \neq i} \frac{q_j \vec r_{ij}}{r_{ij}^3} f_{ij}$$$$\vec P_{i,\text{IND}} = \alpha \vec E (\vec P_{j,n-1}…

eam_elstat

anonymous@undisclosed.example.com (Anonymous) — Mon, 25 Oct 2021 16:32:34 +0000

EAM + electrostatic potential ---------- Info: This page is incomplete and may contain invalid/wrong information! The EAM + electrostatic potential is a combination of the regular EAM model with an additional coulomb term. $$ E_{tot}=E_{EAM} + \frac{1}{2} \sum_{i\neq j} E(r_{ij}) \quad \text{with} \quad E(r_{ij}) \sim \frac{q_{i}q_{j}}{r_{ij}} $$ Number of potential functions $N$$N(N+5)/2$$\Phi_{ij}$$\rho_j$$F_i$$N$$N(N+1)/2$$N$$N$$N(N+5)/2$$\Phi_{00}, \ldots, \Phi_{0N}, \Phi_{11}, \ldots…

eam

anonymous@undisclosed.example.com (Anonymous) — Thu, 22 Nov 2018 16:19:37 +0000

Embedded Atom Method (EAM) Potentials ---------- The energy in potentials of the Embedded Atom type consists of two parts, a pair potential term specified by the function $\Phi(r)$ representing the electrostatic core-core repulsion, and a cohesive term specified by the function $F(n)$$\rho(r)$$F_i(n)$$\rho_j(r)$$j$$\Phi_{ij}(r)$$i$$j$$$E_\text{total}=\frac{1}{2}\sum_{i

main

anonymous@undisclosed.example.com (Anonymous) — Mon, 24 Sep 2018 15:48:11 +0000

Interactions ---------- potfit supports various short and long range effective potentials. These potentials are defined either by tabulated functions or analytic parameters and are read from a potential file. The supported potentials can be found in the table below.

meam

anonymous@undisclosed.example.com (Anonymous) — Thu, 27 Sep 2018 06:00:34 +0000

MEAM Potentials ---------- The energy in potentials of the Modified Embedded Atom type behaves like the EAM type and consists of two parts, a pair potential term specified by the function $\Phi\left(r\right)$ representing the electrostatic core-core repulsion, and a cohesive term specified by the function $F\left(n\right)$$\rho\left(r\right)$$f\left(r\right)$$g\left(\cos\theta\right)$$F_i\left(n\right)$$g_i\left(\cos\theta\right)$$\rho_j\left(r\right)$$\Phi_{ij}\left(r\right)$$f_{ij}\left(r\…

pair_potentials

anonymous@undisclosed.example.com (Anonymous) — Mon, 24 Sep 2018 15:49:03 +0000

Pair Potentials ---------- The most simple interaction that can be used are pair potentials. They are assumed to be isotropic, i.e. they only depend on the pair distance $r_{ij}=|\boldsymbol{r}_j-\boldsymbol{r}_i|$ of the two atoms $i$ and $j$. The potential energy for a system described by pair interactions is given as $$ E_\text{total} = \frac{1}{2} \sum_{i\neq j}V_2(\boldsymbol{r}_i,\boldsymbol{r}_j) = \sum_{i

sidebar

anonymous@undisclosed.example.com (Anonymous) — Sat, 23 Feb 2019 08:46:18 +0000

Main page ---------- Download Publications Contact About potfit User Guide * Compiling potfit * Options * Running potfit * Parameters * Configuration files * Potential models * Potential files * Interactions * Pair potentials * Angular pair potentials * Angular Coulomb potentials * EAM * Two band EAM * MEAM * ADP * Coulomb (pair) * Dipole (pair) * EAM + electrostatics * Stillinger-Weber * Tersoff * modified Tersoff * Algorithms * …

stiweb

anonymous@undisclosed.example.com (Anonymous) — Sat, 06 Jan 2018 09:39:09 +0000

Stillinger-Weber Potentials ---------- The Stillinger-Weber potential is available when potfit is compiled with the stiweb flag, which also implies the apot flag for analytic potentials. Basic Theory The total potential energy is defined as $$E_{\text{total}}=\sum_{i

tbeam

anonymous@undisclosed.example.com (Anonymous) — Mon, 22 Jan 2018 16:47:23 +0000

Two band EAM Potentials ---------- Basic Theory The two band EAM potentials are an extension to the regular EAM potentials. Instead of single transfer and embedding functions, different functions to model two bands are used. Usually they are reffered to as d- and s-band contributions.$$E_\text{total}=\frac{1}{2}\sum_{i

tersoff

anonymous@undisclosed.example.com (Anonymous) — Sat, 06 Jan 2018 09:39:09 +0000

Tersoff Potentials ---------- The Tersoff potential is available when potfit is compiled with the tersoff flag, which also implies the apot flag for analytic potentials. Basic Theory The total potential energy is defined as $$E_{\text{total}}= \frac{1}{2}\sum_{i,j}f_c(r_{ij})\left(A_{ij}e^{-\lambda_{ij}r_{ij}}+b_{ij}B_{ij} e^{-\mu_{ij}r_{ij}}\right)$$ where $$b_{ij} = \chi_{ij}\left(1+\gamma_{ij}^{n_i}\zeta_{ij}^{n_i}\right)^{-\frac{1}{2n_i}},$$ $$\zeta_{ij} = \sum_{k\neq i,j}f_c(r_{ik}…

tersoffmod

anonymous@undisclosed.example.com (Anonymous) — Sat, 06 Jan 2018 09:39:09 +0000

modified Tersoff Potential ---------- The modified Tersoff potential is available when potfit is compiled with the tersoffmod flag, which also implies the apot flag for analytic potentials. Basic Theory The total potential energy is defined as$$E_{\text{total}}= \frac{1}{2}\sum_{i,j}f_c(r_{ij})\left(A_{ij}e^{-\lambda_{ij}r_{ij}}+b_{ij}B_{ij} e^{-\mu_{ij}r_{ij}}\right)$$$$b_{ij} = \left(1+\zeta_{ij}^{\eta}\right)^{-\delta},$$$$\zeta_{ij} = \sum_{k\neq i,j}f_c(r_{ik})g(\theta_{ijk})\exp[\alph…