diff --git a/doc/doc2/Eqs/pair_mgpt.jpg b/doc/doc2/Eqs/pair_mgpt.jpg new file mode 100644 index 0000000000..2bede7f90f Binary files /dev/null and b/doc/doc2/Eqs/pair_mgpt.jpg differ diff --git a/doc/doc2/Eqs/pair_mgpt.tex b/doc/doc2/Eqs/pair_mgpt.tex new file mode 100644 index 0000000000..9c314df916 --- /dev/null +++ b/doc/doc2/Eqs/pair_mgpt.tex @@ -0,0 +1,12 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E_{\rm tot}({\bf R}_1 \ldots {\bf R}_N) = NE_{\rm vol}(\Omega ) + + \frac{1}{2} \sum _{i,j} \mbox{}^\prime \ v_2(ij;\Omega ) + + \frac{1}{6} \sum _{i,j,k} \mbox{}^\prime \ v_3(ijk;\Omega ) + + \frac{1}{24} \sum _{i,j,k,l} \mbox{}^\prime \ v_4(ijkl;\Omega ) +$$ + +\end{document} diff --git a/doc/doc2/Eqs/pair_smtbq1.jpg b/doc/doc2/Eqs/pair_smtbq1.jpg new file mode 100644 index 0000000000..6bfb07b778 Binary files /dev/null and b/doc/doc2/Eqs/pair_smtbq1.jpg differ diff --git a/doc/doc2/Eqs/pair_smtbq1.tex b/doc/doc2/Eqs/pair_smtbq1.tex new file mode 100755 index 0000000000..21ae0e9a49 --- /dev/null +++ b/doc/doc2/Eqs/pair_smtbq1.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +E_{tot} & = & E_{ES} + E_{OO} + E_{MO} \\ +E_{ES} & = & \sum_i{\Big[ \chi_{i}^{0}Q_i + \frac{1}{2}J_{i}^{0}Q_{i}^{2} + + \frac{1}{2} \sum_{j\neq i}{ J_{ij}(r_{ij})f_{cut}^{R_{coul}}(r_{ij})Q_i Q_j } \Big] } \\ +E_{OO} & = & \sum_{i,j}^{i,j = O}{\Bigg[Cexp( -\frac{r_{ij}}{\rho} ) - Df_{cut}^{r_1^{OO}r_2^{OO}}(r_{ij}) exp(Br_{ij})\Bigg]} \\ +E_{MO} & = & \sum_i{E_{cov}^{i} + \sum_{j\neq i}{ Af_{cut}^{r_{c1}r_{c2}}(r_{ij})exp\Big[-p(\frac{r_{ij}}{r_0} -1) \Big] } } \\ +\end{eqnarray*} + +\end{document} \ No newline at end of file diff --git a/doc/doc2/Eqs/pair_smtbq2.jpg b/doc/doc2/Eqs/pair_smtbq2.jpg new file mode 100644 index 0000000000..0e20248788 Binary files /dev/null and b/doc/doc2/Eqs/pair_smtbq2.jpg differ diff --git a/doc/doc2/Eqs/pair_smtbq2.tex b/doc/doc2/Eqs/pair_smtbq2.tex new file mode 100755 index 0000000000..8524c2586c --- /dev/null +++ b/doc/doc2/Eqs/pair_smtbq2.tex @@ -0,0 +1,12 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +E_{cov}^{i(i=M,O)} & = & - \Bigg\{\eta_i(\mu \xi^{0})^2 f_{cut}^{r_{c1}r_{c2}}(r_{ij}) +\Bigg( \sum_{j(j=O,M)}{ exp[ -2q(\frac{r_{ij}}{r_0} - 1)] } \Bigg) +\delta Q_i \Big( 2\frac{n_0}{\eta_i} - \delta Q_i \Big) \Bigg\}^{1/2} \\ +\delta Q_i & = & | Q_i^{F} | - | Q_i | +\end{eqnarray*} + +\end{document} \ No newline at end of file diff --git a/doc/doc2/Eqs/pair_smtbq3.jpg b/doc/doc2/Eqs/pair_smtbq3.jpg new file mode 100644 index 0000000000..1d60459165 Binary files /dev/null and b/doc/doc2/Eqs/pair_smtbq3.jpg differ diff --git a/doc/doc2/Eqs/pair_smtbq3.tex b/doc/doc2/Eqs/pair_smtbq3.tex new file mode 100755 index 0000000000..5bc6e465d1 --- /dev/null +++ b/doc/doc2/Eqs/pair_smtbq3.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\xi^0 & = & \frac{\xi_O}{m} = \frac{\xi_C}{n} \\ +\frac{\beta_O}{\sqrt{m}} & = & \frac{\beta_C}{\sqrt{n}} = \xi^0 \frac{\sqrt{m}+\sqrt{n}}{2}\\ +\end{eqnarray*} + +\end{document} \ No newline at end of file diff --git a/doc/doc2/Eqs/pair_vashishta.jpg b/doc/doc2/Eqs/pair_vashishta.jpg new file mode 100644 index 0000000000..ca5f118a87 Binary files /dev/null and b/doc/doc2/Eqs/pair_vashishta.jpg differ diff --git a/doc/doc2/Eqs/pair_vashishta.tex b/doc/doc2/Eqs/pair_vashishta.tex new file mode 100644 index 0000000000..b65056a254 --- /dev/null +++ b/doc/doc2/Eqs/pair_vashishta.tex @@ -0,0 +1,22 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + U & = & \sum_i^N \sum_{j > i}^N U_{ij}^{(2)} (r_{ij}) + + \sum_i^N \sum_{j \neq i}^N \sum_{k > j, k \neq i}^N + U_{ijk}^{(3)} (r_{ij}, r_{ik}, \theta_{ijk}) + \\ + U_{ij}^{(2)} (r) & = & \frac{H_{ij}}{r^{\eta_{ij}}} + + \frac{Z_i Z_j}{r}\exp(-r/\lambda_{1,ij}) + - \frac{D_{ij}}{r^4}\exp(-r/\lambda_{4,ij}) + - \frac{W_{ij}}{r^6}, r < r_{c,{ij}} + \\ + U_{ijk}^{(3)}(r_{ij},r_{ik},\theta_{ijk}) & = & B_{ijk} + \frac{\left[ \cos \theta_{ijk} - \cos \theta_{0ijk} \right]^2} + {1+C_{ijk}\left[ \cos \theta_{ijk} - \cos \theta_{0ijk} \right]^2} \times \\ +& & \exp \left( \frac{\gamma_{ij}}{r_{ij} - r_{0,ij}} \right) + \exp \left( \frac{\gamma_{ik}}{r_{ik} - r_{0,ik}} \right), r_{ij} < r_{0,ij}, r_{ik} < r_{0,ik} +\end{eqnarray*} + +\end{document} diff --git a/doc/doc2/Eqs/polymorphic1.tex b/doc/doc2/Eqs/polymorphic1.tex new file mode 100644 index 0000000000..b4b925ccf8 --- /dev/null +++ b/doc/doc2/Eqs/polymorphic1.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +E=\frac{1}{2}\sum_{i=1}^{i=N}\sum_{j=1}^{j=N}\left[\left(1-\delta_{ij}\right)\cdot U_{IJ}\left(r_{ij}\right)-\left(1-\eta_{ij}\right)\cdot F_{IJ}\left(r_{ij}\right)\cdot V_{IJ}\left(r_{ij}\right)\right] +$$ + +\end{document} diff --git a/doc/doc2/Eqs/polymorphic2.tex b/doc/doc2/Eqs/polymorphic2.tex new file mode 100644 index 0000000000..80b1c93821 --- /dev/null +++ b/doc/doc2/Eqs/polymorphic2.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +X_{ij}=\sum_{k=i_1,k\neq i,j}^{i_N}W_{IK}\left(r_{ik}\right)\cdot G_{JIK}\left(\theta_{jik}\right)\cdot P_{IK}\left(\Delta r_{jik}\right) +\label{X_eq2} +$$ + +\end{document} diff --git a/doc/doc2/Eqs/polymorphic3.tex b/doc/doc2/Eqs/polymorphic3.tex new file mode 100644 index 0000000000..71db8d81b0 --- /dev/null +++ b/doc/doc2/Eqs/polymorphic3.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +\Delta r_{jik}=r_{ij}-\xi_{IJ}\cdot r_{ik} +\label{Dr_eq3} +$$ + +\end{document} diff --git a/doc/doc2/Eqs/polymorphic4.tex b/doc/doc2/Eqs/polymorphic4.tex new file mode 100644 index 0000000000..b792df82a0 --- /dev/null +++ b/doc/doc2/Eqs/polymorphic4.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\left\{\begin{array}{l} +\eta_{ij}=\delta_{ij},\xi_{IJ}=0 \\ +U_{IJ}\left(r\right)=A_{IJ}\cdot\epsilon_{IJ}\cdot \left(\frac{\sigma_{IJ}}{r}\right)^q\cdot \left[B_{IJ}\cdot \left(\frac{\sigma_{IJ}}{r}\right)^{p-q}-1\right]\cdot exp\left(\frac{\sigma_{IJ}}{r-a_{IJ}\cdot \sigma_{IJ}}\right) \\ +V_{IJ}\left(r\right)=\sqrt{\lambda_{IJ}\cdot \epsilon_{IJ}}\cdot exp\left(\frac{\gamma_{IJ}\cdot \sigma_{IJ}}{r-a_{IJ}\cdot \sigma_{IJ}}\right) \\ +F_{IJ}\left(X\right)=-X \\ +P_{IJ}\left(\Delta r\right)=1 \\ +W_{IJ}\left(r\right)=\sqrt{\lambda_{IJ}\cdot \epsilon_{IJ}}\cdot exp\left(\frac{\gamma_{IJ}\cdot \sigma_{IJ}}{r-a_{IJ}\cdot \sigma_{IJ}}\right) \\ +G_{JIK}\left(\theta\right)=\left(cos\theta+\frac{1}{3}\right)^2 +\end{array}\right. +\end{eqnarray*} + +\end{document} diff --git a/doc/doc2/Eqs/polymorphic5.tex b/doc/doc2/Eqs/polymorphic5.tex new file mode 100644 index 0000000000..a5451b98d6 --- /dev/null +++ b/doc/doc2/Eqs/polymorphic5.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\left\{\begin{array}{l} +\eta_{ij}=\delta_{ij},\xi_{IJ}=1 \\ +U_{IJ}\left(r\right)=\frac{D_{e,IJ}}{S_{IJ}-1}\cdot exp\left[-\beta_{IJ}\sqrt{2S_{IJ}\left(r-r_{e,IJ}\right)}\right]\cdot f_{c,IJ}\left(r\right) \\ +V_{IJ}\left(r\right)=\frac{S_{IJ}\cdot D_{e,IJ}}{S_{IJ}-1}\cdot exp\left[-\beta_{IJ}\sqrt{\frac{2}{S_{IJ}}\left(r-r_{e,IJ}\right)}\right]\cdot f_{c,IJ}\left(r\right) \\ +F_{IJ}\left(X\right)=\left(1+X\right)^{-\frac{1}{2}} \\ +P_{IJ}\left(\Delta r\right)=exp\left(2\mu_{IK}\cdot \Delta r\right) \\ +W_{IJ}\left(r\right)=f_{c,IK}\left(r\right) \\ +G_{JIK}\left(\theta\right)=\gamma_{IK}\left[1+\frac{c_{IK}^2}{d_{IK}^2}-\frac{c_{IK}^2}{d_{IK}^2+\left(h_{IK}+cos\theta\right)^2}\right] +\end{array}\right. +\end{eqnarray*} + +\end{document} diff --git a/doc/doc2/Eqs/polymorphic6.tex b/doc/doc2/Eqs/polymorphic6.tex new file mode 100644 index 0000000000..c8f9f2f25b --- /dev/null +++ b/doc/doc2/Eqs/polymorphic6.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +f_{c,IJ}=\left\{\begin{array}{lr} +1, & r\leq r_{s,IJ} \\ +\frac{1}{2}+\frac{1}{2} cos \left[\frac{\pi \left(r-r_{s,IJ}\right)}{r_{c,IJ}-r_{s,IJ}}\right], & r_{s,IJ}