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200
Data/F2_jast.dat
Normal file
200
Data/F2_jast.dat
Normal file
@ -0,0 +1,200 @@
|
|||||||
|
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||||||
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200
Data/F2_jastopt.dat
Normal file
200
Data/F2_jastopt.dat
Normal file
@ -0,0 +1,200 @@
|
|||||||
|
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||||||
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200
Data/F2_mu00.dat
Normal file
200
Data/F2_mu00.dat
Normal file
@ -0,0 +1,200 @@
|
|||||||
|
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|
||||||
|
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|
200
Data/F2_mu02.dat
Normal file
200
Data/F2_mu02.dat
Normal file
@ -0,0 +1,200 @@
|
|||||||
|
-0.999824692934025E+00
|
||||||
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200
Data/F2_mu05.dat
Normal file
200
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Normal file
@ -0,0 +1,200 @@
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200
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200
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Normal file
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200
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200
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Normal file
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200
Data/F2_mu50.dat
Normal file
200
Data/F2_mu50.dat
Normal file
@ -0,0 +1,200 @@
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||||||
|
-0.122370948600498E-01
|
||||||
|
0.122383617904124E-01
|
@ -5055,9 +5055,6 @@ loadfonts()
|
|||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
#+begin_example
|
#+begin_example
|
||||||
|
|
||||||
RStudio Community is a great place to get help:
|
|
||||||
https://community.rstudio.com/c/tidyverse
|
|
||||||
|
|
||||||
Registering fonts with R
|
Registering fonts with R
|
||||||
|
|
||||||
More than one version of regular/bold/italic found for Cannam Codec Fixed. Skipping setup for this font.
|
More than one version of regular/bold/italic found for Cannam Codec Fixed. Skipping setup for this font.
|
||||||
@ -5239,328 +5236,7 @@ summary(raw_data)
|
|||||||
NA's :1139 NA's :408
|
NA's :1139 NA's :408
|
||||||
#+end_example
|
#+end_example
|
||||||
|
|
||||||
*** Overlap with Jastrow optimized wf
|
*** Figure energy H2O
|
||||||
Parameters of the Jastrow:
|
|
||||||
a r_{12} / (1 + b r_{12})
|
|
||||||
p r_{12}^2 / (1 + p r_{12}^2)
|
|
||||||
a = 1/2 b = 1/2(sqrt(pi)) = 0.886226925453
|
|
||||||
p_H = 0.3467 p_O = 1.1485 (energy minimization)
|
|
||||||
|
|
||||||
#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
|
|
||||||
p <- ggplot(data = data.frame(x = 0), mapping = aes(x = x))
|
|
||||||
fun.0 <- function(x) (1.1485 * x^2) / (1 + 1.1485* x^2)
|
|
||||||
fun.1 <- function(x) (0.3467 * x^2) / (1 + 0.3467* x^2)
|
|
||||||
fun.2 <- function(x) (0.5 * x) / (1 + 0.5*sqrt(pi) * x)
|
|
||||||
p <- p + stat_function(fun = fun.0) + xlim(0,5)
|
|
||||||
p <- p + stat_function(fun = fun.1) + xlim(0,5)
|
|
||||||
p <- p + stat_function(fun = fun.2) + xlim(0,5)
|
|
||||||
p
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+RESULTS:
|
|
||||||
[[file:/tmp/babel-0OtcKh/figurePGHfN9.png]]
|
|
||||||
|
|
||||||
#+begin_src R :results output :session *R* :exports both
|
|
||||||
normalize <- function(x) {x / sqrt(sum(x^2))}
|
|
||||||
FCI <- normalize(scan("fci.dat"))
|
|
||||||
d = data.frame(FCI)
|
|
||||||
d$mu_0 <- normalize(scan("mu00.dat"))
|
|
||||||
d$mu_025 <- normalize(scan("mu25.dat"))
|
|
||||||
d$mu_05 <- normalize(scan("mu05.dat"))
|
|
||||||
d$mu_1 <- normalize(scan("mu10.dat"))
|
|
||||||
d$mu_2 <- normalize(scan("mu20.dat"))
|
|
||||||
d$mu_5 <- normalize(scan("mu50.dat"))
|
|
||||||
d$mu_inf<- normalize(scan("diag.dat"))
|
|
||||||
d$jast <- normalize(scan("jast.dat"))
|
|
||||||
overlap <- function(x) {x <- abs(crossprod(x,jast)[1]) }
|
|
||||||
ov <- apply(d,2,overlap)
|
|
||||||
ov
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+RESULTS:
|
|
||||||
#+begin_example
|
|
||||||
|
|
||||||
Read 200 items
|
|
||||||
|
|
||||||
Read 200 items
|
|
||||||
|
|
||||||
Read 200 items
|
|
||||||
|
|
||||||
Read 200 items
|
|
||||||
|
|
||||||
Read 200 items
|
|
||||||
|
|
||||||
Read 200 items
|
|
||||||
|
|
||||||
Read 200 items
|
|
||||||
|
|
||||||
Read 200 items
|
|
||||||
|
|
||||||
Read 200 items
|
|
||||||
|
|
||||||
Named num [1:9] 0.991 0.988 0.989 0.992 0.994 ...
|
|
||||||
- attr(*, "names")= chr [1:9] "FCI" "mu_0" "mu_025" "mu_05" ...
|
|
||||||
#+end_example
|
|
||||||
|
|
||||||
#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
|
|
||||||
ov <- subset(ov, names(ov) != "jast" & names(ov) != "FCI")
|
|
||||||
mu <- c(0., 0.25, 0.5, 1., 2., 5., 1.e6)
|
|
||||||
X <- mu/(mu+1.)
|
|
||||||
mu <- as.character(mu)
|
|
||||||
mu[7] <- TeX("$\\infty$")
|
|
||||||
p <- ggplot(data.frame(ov, X), aes(y=ov, x=X))
|
|
||||||
p <- p + geom_point()
|
|
||||||
p <- p + scale_x_continuous(name=TeX("$\\mu$"), breaks=X, labels=mu)
|
|
||||||
p <- p + scale_y_continuous(name = TeX("Overlap") )
|
|
||||||
p <- p + theme(text = element_text(size = 20, family="Times"), legend.position = c(.15, .15))
|
|
||||||
p
|
|
||||||
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+RESULTS:
|
|
||||||
[[file:/tmp/babel-0OtcKh/figure6cb0ql.png]]
|
|
||||||
|
|
||||||
*** Optimal mu
|
|
||||||
**** Table
|
|
||||||
Find the optimal $\mu$ in cc-pVDZ for each molecule and atom, making
|
|
||||||
a spline interpolation of the total energy wrt $\mu$.
|
|
||||||
|
|
||||||
#+begin_src R :results output :exports both :session *R*
|
|
||||||
rows <- list()
|
|
||||||
j <- 0
|
|
||||||
for (mol in levels(ref$"Molecule") )
|
|
||||||
{
|
|
||||||
data <- subset(raw_data, (Method == "DMC" & Basis == "cc-pVDZ" & Molecule == mol & Mu != "opt"))
|
|
||||||
data$"Mu" <- as.numeric(data$"Mu")
|
|
||||||
vdz <- data["Mu"]
|
|
||||||
vdz$"X" <- data$"Mu"/(data$"Mu"+1.)
|
|
||||||
vdz$"E" <- data$"TotalEnergy"
|
|
||||||
vdz$"E.lo" <- data$"TotalEnergy" - data$"TotalEnergyErr"
|
|
||||||
vdz$"E.hi" <- data$"TotalEnergy" + data$"TotalEnergyErr"
|
|
||||||
vdz$"Basis" <- "VDZ-BFD"
|
|
||||||
vdz$"X"[7] <- 1.
|
|
||||||
vdz$"Mu"[7] <- TeX("$\\infty$")
|
|
||||||
vdz.spline_int <- as.data.frame(spline(vdz$"X", vdz$"E", n=101))
|
|
||||||
vdz.spline_int_lo <- as.data.frame(spline(vdz$"X", vdz$"E.lo", n=101))
|
|
||||||
vdz.spline_int_hi <- as.data.frame(spline(vdz$"X", vdz$"E.hi", n=101))
|
|
||||||
Emin = min(vdz.spline_int)
|
|
||||||
i <- which(vdz.spline_int$y == Emin)
|
|
||||||
x <- vdz.spline_int$x[i]
|
|
||||||
Eerr <- (vdz.spline_int_hi$y - vdz.spline_int_lo$y)[i]
|
|
||||||
mu <- x / (1-x)
|
|
||||||
dat <- data.frame("Molecule"=mol, "Mu"=mu, "TotalEnergy"=Emin, "TotalEnergyErr"=Eerr)
|
|
||||||
j <- j + 1
|
|
||||||
rows[[j]] <- dat
|
|
||||||
}
|
|
||||||
mu_opt = do.call(rbind, rows)
|
|
||||||
mu_opt
|
|
||||||
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+RESULTS:
|
|
||||||
#+begin_example
|
|
||||||
|
|
||||||
Molecule Mu TotalEnergy TotalEnergyErr
|
|
||||||
1 Be 22.076923 -1.0104925 5.769640e-06
|
|
||||||
2 BeH 3.918033 -1.5804522 -3.092773e-05
|
|
||||||
3 C 6.500000 -5.4320500 1.999488e-04
|
|
||||||
4 C2H2 5.976744 -12.4977890 1.631542e-03
|
|
||||||
5 C2H4 5.976744 -13.7496692 3.475880e-03
|
|
||||||
6 C2H6 5.976744 -14.9862763 3.649831e-03
|
|
||||||
7 CH 6.142857 -6.0641447 4.604460e-04
|
|
||||||
8 CH2_1A1 6.500000 -6.7168723 9.408143e-04
|
|
||||||
9 CH2_3B1 6.500000 -6.7315386 8.420592e-04
|
|
||||||
10 CH3 5.250000 -7.4161384 4.575831e-04
|
|
||||||
11 CH3Cl 6.692308 -22.5123351 4.313597e-03
|
|
||||||
12 CH4 5.818182 -8.0950439 6.943745e-04
|
|
||||||
13 Cl Inf -14.9623070 5.120000e-04
|
|
||||||
14 Cl2 6.317073 -30.0149662 4.286545e-03
|
|
||||||
15 ClF Inf -39.2471030 2.942000e-03
|
|
||||||
16 ClO 6.317073 -30.9553639 3.379987e-03
|
|
||||||
17 CN 6.142857 -15.5135815 1.475441e-03
|
|
||||||
18 CO 6.317073 -21.7422093 1.746556e-03
|
|
||||||
19 CO2 Inf -37.8388280 3.554000e-03
|
|
||||||
20 CS 8.090909 -15.8227883 2.261302e-03
|
|
||||||
21 F 6.692308 -24.1947898 7.291550e-04
|
|
||||||
22 F2 10.538462 -48.4486772 1.191581e-02
|
|
||||||
23 H 2.000000 -0.5000220 3.200000e-05
|
|
||||||
24 H2CO 6.317073 -22.9170478 3.280498e-03
|
|
||||||
25 H2O 6.142857 -17.2591198 1.451158e-03
|
|
||||||
26 H2O2 19.000000 -33.2358899 -4.071474e-03
|
|
||||||
27 H2S 6.317073 -11.4106220 4.174444e-04
|
|
||||||
28 H3COH Inf -24.1332880 2.934000e-03
|
|
||||||
29 H3CSH 6.142857 -18.2991121 4.432337e-03
|
|
||||||
30 HCl 6.692308 -15.6303653 1.821596e-03
|
|
||||||
31 HCN 6.142857 -16.2206750 1.801664e-03
|
|
||||||
32 HCO 5.976744 -22.2672833 3.238134e-03
|
|
||||||
33 HF 6.142857 -24.9103839 1.130866e-03
|
|
||||||
34 HOCl 8.677419 -31.6179815 2.879019e-03
|
|
||||||
35 Li 22.076923 -0.1963761 3.904561e-05
|
|
||||||
36 Li2 22.076923 -0.4317381 1.040406e-04
|
|
||||||
37 LiF 6.317073 -24.6087084 1.505761e-03
|
|
||||||
38 LiH 6.142857 -0.7887410 3.993582e-05
|
|
||||||
39 N 6.500000 -9.7986241 2.993923e-04
|
|
||||||
40 N2 6.142857 -19.9524462 1.089443e-03
|
|
||||||
41 N2H4 5.976744 -22.2697720 4.213610e-03
|
|
||||||
42 Na 26.272727 -0.1822304 1.180745e-04
|
|
||||||
43 Na2 22.076923 -0.3915674 2.174183e-04
|
|
||||||
44 NaCl 19.000000 -15.3131353 9.113055e-03
|
|
||||||
45 NH 6.142857 -10.4264783 7.713270e-04
|
|
||||||
46 NH2 6.142857 -11.0809754 1.375113e-03
|
|
||||||
47 NH3 5.818182 -11.7605110 3.663185e-04
|
|
||||||
48 NO 6.142857 -25.9343787 2.038331e-03
|
|
||||||
49 O 6.317073 -15.9016039 5.110339e-04
|
|
||||||
50 O2 8.090909 -31.9863532 -1.189911e-03
|
|
||||||
51 OH 6.500000 -16.5656422 1.038452e-03
|
|
||||||
52 P 6.317073 -6.4727574 3.574169e-04
|
|
||||||
53 P2 6.317073 -13.1211638 2.071087e-03
|
|
||||||
54 PH2 Inf -7.7124550 8.060000e-04
|
|
||||||
55 PH3 Inf -8.3503240 1.756000e-03
|
|
||||||
56 S Inf -10.1249220 3.820000e-04
|
|
||||||
57 S2 16.647059 -20.4112519 -1.963031e-03
|
|
||||||
58 Si Inf -3.7651370 1.260000e-04
|
|
||||||
59 Si2 10.538462 -7.6463418 1.778160e-04
|
|
||||||
60 Si2H6 8.677419 -11.3730775 3.703778e-04
|
|
||||||
61 SiH2_1A1 17.750000 -5.0122525 5.573410e-04
|
|
||||||
62 SiH2_3B1 19.000000 -4.9762802 -8.064654e-04
|
|
||||||
63 SiH3 22.076923 -5.6262336 -6.690674e-03
|
|
||||||
64 SiH4 6.142857 -6.2776229 9.405144e-04
|
|
||||||
65 SiO 7.571429 -19.9632204 2.175365e-03
|
|
||||||
66 SO Inf -26.2122290 4.822000e-03
|
|
||||||
67 SO2 6.500000 -42.2992438 6.376208e-03
|
|
||||||
#+end_example
|
|
||||||
|
|
||||||
**** Atoms
|
|
||||||
Average percentage of the difference E_{DMC}(KS) - E_{DMC}(FCI) for all
|
|
||||||
atoms.
|
|
||||||
|
|
||||||
#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
|
|
||||||
atoms = c("Be", "C", "Cl", "F", "N", "O", "P", "S", "Si")
|
|
||||||
mid <- rep(0.,7)
|
|
||||||
hi <- rep(0.,7)
|
|
||||||
lo <- rep(0.,7)
|
|
||||||
x <- rep(0.,7)
|
|
||||||
|
|
||||||
for (atom in atoms) {
|
|
||||||
data <- subset(raw_data, (Method == "DMC" & Basis == "cc-pVDZ" & Molecule == atom))
|
|
||||||
vdz = data["Mu"]
|
|
||||||
data$"Mu" <- as.numeric(data$"Mu")
|
|
||||||
vdz$"X" = data$"Mu"/(data$"Mu"+1.)
|
|
||||||
vdz$"E" = data$"TotalEnergy"
|
|
||||||
vdz$"E.lo" = data$"TotalEnergy" - data$"TotalEnergyErr"
|
|
||||||
vdz$"E.hi" = data$"TotalEnergy" + data$"TotalEnergyErr"
|
|
||||||
vdz$"Basis" = "VDZ-BFD"
|
|
||||||
vdz$"X"[7] <- 1.
|
|
||||||
vdz$"Mu"[7] <- TeX("$\\infty$")
|
|
||||||
# vdz.spline_int <- as.data.frame(spline(vdz$"X", vdz$"E", n=101))
|
|
||||||
# vdz.spline_int_lo <- as.data.frame(spline(vdz$"X", vdz$"E.lo", n=101))
|
|
||||||
# vdz.spline_int_hi <- as.data.frame(spline(vdz$"X", vdz$"E.hi", n=101))
|
|
||||||
|
|
||||||
# vdz.spline_int_lo$y <- (vdz.spline_int_lo$y - vdz.spline_int$y[101])/(vdz.spline_int$y[1]-vdz.spline_int$y[101])
|
|
||||||
# vdz.spline_int_hi$y <- (vdz.spline_int_hi$y - vdz.spline_int$y[101])/(vdz.spline_int$y[1]-vdz.spline_int$y[101])
|
|
||||||
# vdz.spline_int$y <- (vdz.spline_int$y - vdz.spline_int$y[101])/(vdz.spline_int$y[1]-vdz.spline_int$y[101])
|
|
||||||
|
|
||||||
# mid <- mid + vdz.spline_int$y
|
|
||||||
# hi <- hi + vdz.spline_int_hi$y
|
|
||||||
# lo <- lo + vdz.spline_int_lo$y
|
|
||||||
# x <- vdz.spline_int$x
|
|
||||||
|
|
||||||
mid <- mid + (vdz$"E" - vdz$"E"[7])/(vdz$"E"[1] - vdz$"E"[7])
|
|
||||||
hi <- hi + (vdz$"E.hi" - vdz$"E"[7])/(vdz$"E"[1] - vdz$"E"[7])
|
|
||||||
lo <- lo + (vdz$"E.lo" - vdz$"E"[7])/(vdz$"E"[1] - vdz$"E"[7])
|
|
||||||
x <- vdz$"X"
|
|
||||||
}
|
|
||||||
|
|
||||||
out = data.frame(mid)
|
|
||||||
out$mid <- mid / length(atoms)
|
|
||||||
out$hi <- hi / length(atoms)
|
|
||||||
out$lo <- lo / length(atoms)
|
|
||||||
out$x <- x
|
|
||||||
|
|
||||||
breaks <- vdz$"X"
|
|
||||||
labels <- vdz$"Mu"
|
|
||||||
labels[7] <- TeX("$\\infty$")
|
|
||||||
|
|
||||||
p <- ggplot(out, aes(x=x, y=mid, ymin=lo, ymax=hi) )
|
|
||||||
p <- p + geom_point()
|
|
||||||
p <- p + geom_ribbon(alpha=0.5)
|
|
||||||
p <- p + scale_x_continuous(name=TeX("$\\mu$"), breaks=breaks, labels=labels)
|
|
||||||
p <- p + scale_y_continuous(name = TeX("\\frac{E_{DMC} - E_{DMC}(FCI)}{E_{DMC}(KS) - E_{DMC}(FCI)}"), breaks=seq(0.,1.,0.2))
|
|
||||||
p <- p + theme(text = element_text(size = 20, family="Times"), legend.position = c(.15, .15))
|
|
||||||
p
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+RESULTS:
|
|
||||||
[[file:/tmp/babel-8WVd9w/figureBMs1Mr.png]]
|
|
||||||
|
|
||||||
**** Molecules
|
|
||||||
|
|
||||||
#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
|
|
||||||
molecules <- c("BeH", "C2H2", "C2H4", "C2H6", "CH", "CH2_1A1", "CH2_3B1", "CH3", "CH3Cl", "CH4", "CN", "CO", "CO2", "CS", "Cl2", "ClF", "ClO", "F2", "H2CO", "H2O", "H2O2", "H2S", "H3COH", "H3CSH", "HCN", "HCO", "HCl", "HF", "HOCl", "Li2", "LiF", "LiH", "N2", "N2H4", "NH", "NH2", "NH3", "NO", "Na2", "NaCl", "O2", "OH", "P2", "PH2", "PH3", "S2", "SO", "SO2", "Si2", "Si2H6", "SiH2_1A1", "SiH2_3B1", "SiH3", "SiH4", "SiO")
|
|
||||||
molecules <- c("H2O")
|
|
||||||
mid <- rep(0.,101)
|
|
||||||
hi <- rep(0.,101)
|
|
||||||
lo <- rep(0.,101)
|
|
||||||
x <- rep(0.,101)
|
|
||||||
|
|
||||||
#mid <- rep(0.,7)
|
|
||||||
#hi <- rep(0.,7)
|
|
||||||
#lo <- rep(0.,7)
|
|
||||||
#x <- rep(0.,7)
|
|
||||||
|
|
||||||
for (molecule in molecules) {
|
|
||||||
data <- subset(raw_data, (Method == "DMC" & Basis == "cc-pVDZ" & Molecule == molecule & Mu != "opt"))
|
|
||||||
vdz = data["Mu"]
|
|
||||||
data$"Mu" <- na.omit(as.numeric(data$"Mu"))
|
|
||||||
vdz$"X" = data$"Mu"/(data$"Mu"+1.)
|
|
||||||
vdz$"E" = data$"TotalEnergy"
|
|
||||||
vdz$"E.lo" = data$"TotalEnergy" - data$"TotalEnergyErr"
|
|
||||||
vdz$"E.hi" = data$"TotalEnergy" + data$"TotalEnergyErr"
|
|
||||||
vdz$"Basis" = "VDZ-BFD"
|
|
||||||
vdz$"X"[7] <- 1.
|
|
||||||
vdz$"Mu"[7] <- TeX("$\\infty$")
|
|
||||||
vdz.spline_int <- as.data.frame(spline(vdz$"X", vdz$"E", n=101))
|
|
||||||
vdz.spline_int_lo <- as.data.frame(spline(vdz$"X", vdz$"E.lo", n=101))
|
|
||||||
vdz.spline_int_hi <- as.data.frame(spline(vdz$"X", vdz$"E.hi", n=101))
|
|
||||||
|
|
||||||
vdz.spline_int_lo$y <- (vdz.spline_int_lo$y - vdz.spline_int$y[101])/(vdz.spline_int$y[1]-vdz.spline_int$y[101])
|
|
||||||
vdz.spline_int_hi$y <- (vdz.spline_int_hi$y - vdz.spline_int$y[101])/(vdz.spline_int$y[1]-vdz.spline_int$y[101])
|
|
||||||
vdz.spline_int$y <- (vdz.spline_int$y - vdz.spline_int$y[101])/(vdz.spline_int$y[1]-vdz.spline_int$y[101])
|
|
||||||
|
|
||||||
mid <- mid + vdz.spline_int$y
|
|
||||||
hi <- hi + vdz.spline_int_hi$y
|
|
||||||
lo <- lo + vdz.spline_int_lo$y
|
|
||||||
x <- vdz.spline_int$x
|
|
||||||
|
|
||||||
# mid <- mid + (vdz$"E" - vdz$"E"[7])/(vdz$"E"[1] - vdz$"E"[7])
|
|
||||||
# hi <- hi + (vdz$"E.hi" - vdz$"E"[7])/(vdz$"E"[1] - vdz$"E"[7])
|
|
||||||
# lo <- lo + (vdz$"E.lo" - vdz$"E"[7])/(vdz$"E"[1] - vdz$"E"[7])
|
|
||||||
# x <- vdz$"X"
|
|
||||||
}
|
|
||||||
|
|
||||||
out = data.frame(mid)
|
|
||||||
out$mid <- mid / length(molecules)
|
|
||||||
out$hi <- hi / length(molecules)
|
|
||||||
out$lo <- lo / length(molecules)
|
|
||||||
out$x <- x
|
|
||||||
|
|
||||||
breaks <- vdz$"X"
|
|
||||||
labels <- vdz$"Mu"
|
|
||||||
labels[7] <- TeX("$\\infty$")
|
|
||||||
|
|
||||||
p <- ggplot(out, aes(x=x, y=mid, ymin=lo, ymax=hi) )
|
|
||||||
p <- p + geom_line()
|
|
||||||
p <- p + geom_ribbon(alpha=0.5)
|
|
||||||
p <- p + scale_x_continuous(name=TeX("$\\mu$"), breaks=breaks, labels=labels)
|
|
||||||
p <- p + scale_y_continuous(name = TeX("\\frac{E_{DMC} - E_{DMC}(FCI)}{E_{DMC}(KS) - E_{DMC}(FCI)}"))
|
|
||||||
p <- p + theme(text = element_text(size = 20, family="Times"), legend.position = c(.15, .15))
|
|
||||||
p
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+RESULTS:
|
|
||||||
[[file:/tmp/babel-8WVd9w/figureRuNz9o.png]]
|
|
||||||
|
|
||||||
*** Figure H2O R
|
|
||||||
#+begin_src R :var data=tab1 :results output :session *R* :exports both
|
#+begin_src R :var data=tab1 :results output :session *R* :exports both
|
||||||
str(data)
|
str(data)
|
||||||
data$X
|
data$X
|
||||||
@ -5609,14 +5285,14 @@ labels <- data$"X..mu"
|
|||||||
labels[9] <- ""
|
labels[9] <- ""
|
||||||
labels[11] <- TeX("$\\infty$")
|
labels[11] <- TeX("$\\infty$")
|
||||||
|
|
||||||
spline_int1 <- as.data.frame(spline(d$X, d$E))
|
#vdz.spline_int <- as.data.frame(spline(d$X, d$E))
|
||||||
|
|
||||||
p <- ggplot(d, aes(x=X, y=E, ymin=E.lo, ymax=E.hi, fill=Basis ))
|
p <- ggplot(d, aes(x=X, y=E, ymin=E.lo, ymax=E.hi, fill=Basis ))
|
||||||
p <- p + geom_point()
|
p <- p + geom_smooth(span=.5, se=FALSE, color='darkgrey')
|
||||||
p <- p + geom_ribbon(alpha=0.5)
|
p <- p + geom_ribbon(alpha=0.5)
|
||||||
#p <- p + geom_smooth(span=.7, se=FALSE)
|
p <- p + geom_point()
|
||||||
#p <- p + geom_line(data = vdz.spline_int, aes(x = x, y = y))
|
#p <- p + geom_line(data = vdz.spline_int, aes(x = x, y = y))
|
||||||
p <- p + scale_x_continuous(name=TeX("$\\mu$"), breaks=breaks, labels=labels)
|
p <- p + scale_x_continuous(name=TeX("$\\mu$ (bohr$^{-1}$)"), breaks=breaks, labels=labels)
|
||||||
p <- p + scale_y_continuous(name = TeX("Energy (a.u.)"), breaks=seq(-17.266,-17.252,0.002))
|
p <- p + scale_y_continuous(name = TeX("Energy (a.u.)"), breaks=seq(-17.266,-17.252,0.002))
|
||||||
p <- p + theme(text = element_text(size = 20, family="Times"), legend.position = c(.15, .15))
|
p <- p + theme(text = element_text(size = 20, family="Times"), legend.position = c(.15, .15))
|
||||||
p
|
p
|
||||||
@ -5624,7 +5300,7 @@ p
|
|||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
[[file:/tmp/babel-cHKMq8/figureXKea51.png]]
|
[[file:/tmp/babel-RBQjE9/figurelVzAZK.png]]
|
||||||
|
|
||||||
#+begin_src R :results output :session *R* :exports both
|
#+begin_src R :results output :session *R* :exports both
|
||||||
pdf("../Manuscript/h2o-dmc.pdf", family="Times", width=8, height=5)
|
pdf("../Manuscript/h2o-dmc.pdf", family="Times", width=8, height=5)
|
||||||
@ -5637,6 +5313,482 @@ dev.off()
|
|||||||
: null device
|
: null device
|
||||||
: 1
|
: 1
|
||||||
|
|
||||||
|
*** Figure energy F2
|
||||||
|
#+begin_src R :var data=tab1 :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
|
||||||
|
data <- subset(raw_data, (Method == "DMC" & Basis == "cc-pVDZ" & Molecule == "F2" & Mu != "opt"))
|
||||||
|
vdz = data["Mu"]
|
||||||
|
vdz$"Mu" <- as.numeric(levels(factor(data$"Mu")))
|
||||||
|
vdz$"X" = vdz$"Mu"/(vdz$"Mu"+1.)
|
||||||
|
vdz$"E" = data$"TotalEnergy"
|
||||||
|
vdz$"E.lo" = data$"TotalEnergy" - data$"TotalEnergyErr"
|
||||||
|
vdz$"E.hi" = data$"TotalEnergy" + data$"TotalEnergyErr"
|
||||||
|
vdz$"Basis" = "VDZ-BFD"
|
||||||
|
vdz$"X"[7] <- 1.
|
||||||
|
vdz$"Mu"[7] <- TeX("$\\infty$")
|
||||||
|
vdz.spline_int <- as.data.frame(spline(vdz$"X", vdz$"E", n=101))
|
||||||
|
|
||||||
|
breaks <- vdz$"X"
|
||||||
|
labels <- vdz$"Mu"
|
||||||
|
labels[7] <- TeX("$\\infty$")
|
||||||
|
d <- vdz
|
||||||
|
|
||||||
|
p <- ggplot(d, aes(x=X, y=E, ymin=E.lo, ymax=E.hi, fill="red"))
|
||||||
|
p <- p + geom_smooth(span=.75, se=FALSE, color='darkgrey', show.legend=FALSE )
|
||||||
|
p <- p + geom_ribbon(alpha=0.5, show.legend = FALSE)
|
||||||
|
p <- p + geom_point(show.legend=FALSE )
|
||||||
|
p <- p + scale_x_continuous(name=TeX("$\\mu$ (bohr$^{-1}$)"), breaks=breaks, labels=labels)
|
||||||
|
p <- p + scale_y_continuous(name = TeX("Energy (a.u.)"), breaks=seq(-48.45,-48.42,0.005))
|
||||||
|
p <- p + theme(text = element_text(size = 20, family="Times"))
|
||||||
|
p
|
||||||
|
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:/tmp/babel-RBQjE9/figurewct2z7.png]]
|
||||||
|
|
||||||
|
#+begin_src R :results output :session *R* :exports both
|
||||||
|
pdf("../Manuscript/f2-dmc.pdf", family="Times", width=8, height=5)
|
||||||
|
p
|
||||||
|
dev.off()
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
:
|
||||||
|
: `geom_smooth()` using method = 'loess' and formula 'y ~ x'
|
||||||
|
:
|
||||||
|
: png
|
||||||
|
: 2
|
||||||
|
|
||||||
|
*** Overlap with Jastrow optimized wf
|
||||||
|
**** H2O
|
||||||
|
Parameters of the Jastrow:
|
||||||
|
a r_{12} / (1 + b r_{12})
|
||||||
|
p r_{12}^2 / (1 + p r_{12}^2)
|
||||||
|
a = 1/2 b = 1/2(sqrt(pi)) = 0.886226925453
|
||||||
|
p_H = 0.3467 p_O = 1.1485 (energy minimization)
|
||||||
|
|
||||||
|
#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
|
||||||
|
p <- ggplot(data = data.frame(x = 0), mapping = aes(x = x))
|
||||||
|
fun.0 <- function(x) ((1.1485 * x) / (1 + 1.1485* x))**2
|
||||||
|
fun.1 <- function(x) ((0.3467 * x) / (1 + 0.3467* x))**2
|
||||||
|
fun.2 <- function(x) (0.5 * x) / (1 + 0.5*sqrt(pi) * x)
|
||||||
|
p <- p + stat_function(fun = fun.0) + xlim(0,5)
|
||||||
|
p <- p + stat_function(fun = fun.1) + xlim(0,5)
|
||||||
|
p <- p + stat_function(fun = fun.2) + xlim(0,5)
|
||||||
|
p
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:/tmp/babel-RBQjE9/figureuAYjXv.png]]
|
||||||
|
|
||||||
|
#+begin_src R :results output :session *R* :exports both
|
||||||
|
normalize <- function(x) {x / sqrt(sum(x^2))}
|
||||||
|
FCI <- normalize(scan("fci.dat"))
|
||||||
|
dH2O <- data.frame(FCI)
|
||||||
|
dH2O$mu_0 <- normalize(scan("mu00.dat"))
|
||||||
|
dH2O$mu_025 <- normalize(scan("mu25.dat"))
|
||||||
|
dH2O$mu_05 <- normalize(scan("mu05.dat"))
|
||||||
|
dH2O$mu_1 <- normalize(scan("mu10.dat"))
|
||||||
|
dH2O$mu_2 <- normalize(scan("mu20.dat"))
|
||||||
|
dH2O$mu_5 <- normalize(scan("mu50.dat"))
|
||||||
|
dH2O$mu_inf<- normalize(scan("diag.dat"))
|
||||||
|
dH2O$jast <- normalize(scan("jast.dat"))
|
||||||
|
overlap <- function(x) {x <- abs(crossprod(x,dH2O$jast)[1]) }
|
||||||
|
H2O <- apply(dH2O,2,overlap)
|
||||||
|
H2O
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
#+begin_example
|
||||||
|
FCI mu_0 mu_025 mu_05 mu_1 mu_2 mu_5 mu_inf
|
||||||
|
0.9908628 0.9875157 0.9885532 0.9918674 0.9943390 0.9926737 0.9906157 0.9899355
|
||||||
|
jast
|
||||||
|
1.0000000
|
||||||
|
#+end_example
|
||||||
|
|
||||||
|
**** F2
|
||||||
|
Parameters of the Jastrow:
|
||||||
|
a r_{12} / (1 + b r_{12})
|
||||||
|
p r_{12}^2 / (1 + p r_{12}^2)
|
||||||
|
a = 1/2 b = 1/2(sqrt(pi)) = 0.886226925453
|
||||||
|
p_F = 1.1900 (energy minimization)
|
||||||
|
|
||||||
|
#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
|
||||||
|
p <- ggplot(data = data.frame(x = 0), mapping = aes(x = x))
|
||||||
|
fun.0 <- function(x) ((1.1900 * x) / (1 + 1.1900* x))**2
|
||||||
|
fun.2 <- function(x) (0.5 * x) / (1 + 0.8862 * x)
|
||||||
|
p <- p + stat_function(fun = fun.0) + xlim(0,5)
|
||||||
|
p <- p + stat_function(fun = fun.2) + xlim(0,5)
|
||||||
|
p
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:/tmp/babel-RBQjE9/figureFQ9sdT.png]]
|
||||||
|
|
||||||
|
#+begin_src R :results output :session *R* :exports both
|
||||||
|
normalize <- function(x) {x / sqrt(sum(x^2))}
|
||||||
|
FCI <- normalize(scan("F2_fci.dat"))
|
||||||
|
dF2 = data.frame(FCI)
|
||||||
|
dF2$mu_0 <- normalize(scan("F2_mu00.dat"))
|
||||||
|
dF2$mu_025 <- normalize(scan("F2_mu02.dat"))
|
||||||
|
dF2$mu_05 <- normalize(scan("F2_mu05.dat"))
|
||||||
|
dF2$mu_1 <- normalize(scan("F2_mu10.dat"))
|
||||||
|
dF2$mu_2 <- normalize(scan("F2_mu20.dat"))
|
||||||
|
dF2$mu_5 <- normalize(scan("F2_mu50.dat"))
|
||||||
|
dF2$mu_inf<- normalize(scan("F2_diag.dat"))
|
||||||
|
dF2$jast <- normalize(scan("F2_jast.dat"))
|
||||||
|
overlap <- function(x) {x <- abs(crossprod(x,dF2$jast)[1]) }
|
||||||
|
F2 <- apply(dF2,2,overlap)
|
||||||
|
F2
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
#+begin_example
|
||||||
|
|
||||||
|
FCI mu_0 mu_025 mu_05 mu_1 mu_2 mu_5 mu_inf
|
||||||
|
0.9973656 0.9684951 0.9719259 0.9821996 0.9934597 0.9972475 0.9978171 0.9973656
|
||||||
|
jast
|
||||||
|
1.0000000
|
||||||
|
#+end_example
|
||||||
|
|
||||||
|
**** F2 optimal
|
||||||
|
Parameters of the Jastrow:
|
||||||
|
a r_{12} / (1 + b r_{12})
|
||||||
|
p r_{12}^2 / (1 + p r_{12}^2)
|
||||||
|
a = 1/2 b = 1.3557
|
||||||
|
p_F = 0.8081 (energy minimization)
|
||||||
|
|
||||||
|
#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
|
||||||
|
p <- ggplot(data = data.frame(x = 0), mapping = aes(x = x))
|
||||||
|
fun.0 <- function(x) ((0.8081 * x) / (1 + 0.8081* x))**2
|
||||||
|
fun.2 <- function(x) (0.5 * x) / (1 + 1.3557 * x)
|
||||||
|
p <- p + stat_function(fun = fun.0) + xlim(0,5)
|
||||||
|
p <- p + stat_function(fun = fun.2) + xlim(0,5)
|
||||||
|
p
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:/tmp/babel-RBQjE9/figure8Oip7n.png]]
|
||||||
|
|
||||||
|
#+begin_src R :results output :session *R* :exports both
|
||||||
|
normalize <- function(x) {x / sqrt(sum(x^2))}
|
||||||
|
FCI <- normalize(scan("F2_fci.dat"))
|
||||||
|
dF2 = data.frame(FCI)
|
||||||
|
dF2$mu_0 <- normalize(scan("F2_mu00.dat"))
|
||||||
|
dF2$mu_025 <- normalize(scan("F2_mu02.dat"))
|
||||||
|
dF2$mu_05 <- normalize(scan("F2_mu05.dat"))
|
||||||
|
dF2$mu_1 <- normalize(scan("F2_mu10.dat"))
|
||||||
|
dF2$mu_2 <- normalize(scan("F2_mu20.dat"))
|
||||||
|
dF2$mu_5 <- normalize(scan("F2_mu50.dat"))
|
||||||
|
dF2$mu_inf<- normalize(scan("F2_diag.dat"))
|
||||||
|
dF2$jast <- normalize(scan("F2_jastopt.dat"))
|
||||||
|
overlap <- function(x) {x <- abs(crossprod(x,dF2$jast)[1]) }
|
||||||
|
F2opt <- apply(dF2,2,overlap)
|
||||||
|
F2opt
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
#+begin_example
|
||||||
|
|
||||||
|
FCI mu_0 mu_025 mu_05 mu_1 mu_2 mu_5 mu_inf
|
||||||
|
0.9985079 0.9684980 0.9722671 0.9834621 0.9953808 0.9987209 0.9989324 0.9985079
|
||||||
|
jast
|
||||||
|
1.0000000
|
||||||
|
#+end_example
|
||||||
|
|
||||||
|
**** Plot
|
||||||
|
|
||||||
|
#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
|
||||||
|
Mu <- c(0., 0.25, 0.5, 1., 2., 5., Inf)
|
||||||
|
X <- Mu/(Mu+1.)
|
||||||
|
X[7] <- 1.
|
||||||
|
H2O_FCI <- H2O["FCI"]
|
||||||
|
F2_FCI <- F2["FCI"]
|
||||||
|
H2O <- subset(H2O, names(H2O) != "jast" & names(H2O) != "FCI")
|
||||||
|
F2 <- subset(F2 , names(F2 ) != "jast" & names(F2 ) != "FCI")
|
||||||
|
F2opt <- subset(F2opt , names(F2opt) != "jast" & names(F2opt) != "FCI")
|
||||||
|
ov = data.frame(Mu, X, H2O, F2, F2opt)
|
||||||
|
print(ov)
|
||||||
|
Mu <- as.character(Mu)
|
||||||
|
Mu[7] <- TeX("$\\infty$")
|
||||||
|
|
||||||
|
H2O.spline_int <- as.data.frame(spline(ov$"X", ov$"H2O", n=101))
|
||||||
|
F2.spline_int <- as.data.frame(spline(ov$"X", ov$"F2", n=101))
|
||||||
|
F2opt.spline_int <- as.data.frame(spline(ov$"X", ov$"F2opt", n=101))
|
||||||
|
|
||||||
|
p <- ggplot()
|
||||||
|
p <- p + geom_point(aes(x=X,y=F2), color='red')
|
||||||
|
p <- p + geom_point(aes(x=X,y=H2O), color='blue')
|
||||||
|
#p <- p + geom_point(aes(x=X,y=F2opt), color='green')
|
||||||
|
p <- p + geom_line(data = F2.spline_int, aes(x=x, y=y, colour='a'))
|
||||||
|
p <- p + geom_line(data = H2O.spline_int, aes(x=x, y=y, colour='b'))
|
||||||
|
#p <- p + geom_line(data = F2opt.spline_int, aes(x=x, y=y, colour='c'))
|
||||||
|
p <- p + scale_x_continuous(name=TeX("$\\mu$ (bohr$^{-1}$)"), breaks=X, labels=mu)
|
||||||
|
p <- p + scale_y_continuous(name = TeX("Overlap") )
|
||||||
|
p <- p + scale_colour_manual(name = 'Molecule', guide='legend',
|
||||||
|
values =c('c'='green', 'b'='blue','a'='red'),
|
||||||
|
labels = c(expression(F[2]), expression(H[2]*O), expression(F[2]*opt) ))
|
||||||
|
p <- p + theme(text = element_text(size = 20, family="Times"), legend.position = c(.85, .15))
|
||||||
|
p
|
||||||
|
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:/tmp/babel-RBQjE9/figureTA79X4.png]]
|
||||||
|
|
||||||
|
#+begin_src R :results output :session *R* :exports both
|
||||||
|
pdf("../Manuscript/overlap.pdf", family="Times", width=8, height=5)
|
||||||
|
p
|
||||||
|
dev.off()
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
:
|
||||||
|
: png
|
||||||
|
: 2
|
||||||
|
|
||||||
|
*** Optimal mu
|
||||||
|
**** Table
|
||||||
|
Find the optimal $\mu$ in cc-pVDZ for each molecule and atom, making
|
||||||
|
a spline interpolation of the total energy wrt $\mu$.
|
||||||
|
|
||||||
|
#+begin_src R :results output :exports both :session *R*
|
||||||
|
rows <- list()
|
||||||
|
j <- 0
|
||||||
|
for (mol in levels(ref$"Molecule") )
|
||||||
|
{
|
||||||
|
data <- subset(raw_data, (Method == "DMC" & Basis == "cc-pVDZ" & Molecule == mol & Mu != "opt"))
|
||||||
|
data$"Mu" <- as.numeric(levels(factor(data$"Mu")))
|
||||||
|
vdz <- data["Mu"]
|
||||||
|
vdz$"X" <- data$"Mu"/(data$"Mu"+1.)
|
||||||
|
vdz$"E" <- data$"TotalEnergy"
|
||||||
|
vdz$"E.lo" <- data$"TotalEnergy" - data$"TotalEnergyErr"
|
||||||
|
vdz$"E.hi" <- data$"TotalEnergy" + data$"TotalEnergyErr"
|
||||||
|
vdz$"Basis" <- "VDZ-BFD"
|
||||||
|
vdz$"X"[7] <- 1.
|
||||||
|
vdz$"Mu"[7] <- TeX("$\\infty$")
|
||||||
|
vdz.spline_int <- as.data.frame(spline(vdz$"X", vdz$"E", n=101))
|
||||||
|
vdz.spline_int_lo <- as.data.frame(spline(vdz$"X", vdz$"E.lo", n=101))
|
||||||
|
vdz.spline_int_hi <- as.data.frame(spline(vdz$"X", vdz$"E.hi", n=101))
|
||||||
|
Emin = min(vdz.spline_int)
|
||||||
|
i <- which(vdz.spline_int$y == Emin)
|
||||||
|
x <- vdz.spline_int$x[i]
|
||||||
|
Eerr <- (vdz.spline_int_hi$y - vdz.spline_int_lo$y)[i]
|
||||||
|
mu <- x / (1-x)
|
||||||
|
dat <- data.frame("Molecule"=mol, "Mu"=mu, "TotalEnergy"=Emin, "TotalEnergyErr"=Eerr)
|
||||||
|
j <- j + 1
|
||||||
|
rows[[j]] <- dat
|
||||||
|
}
|
||||||
|
mu_opt = do.call(rbind, rows)
|
||||||
|
mu_opt
|
||||||
|
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
#+begin_example
|
||||||
|
|
||||||
|
Molecule Mu TotalEnergy TotalEnergyErr
|
||||||
|
1 Be 0.9607843 -1.0079615 2.171751e-05
|
||||||
|
2 BeH 0.5625000 -1.5805129 4.067433e-04
|
||||||
|
3 C 2.8461538 -5.4320134 2.060275e-04
|
||||||
|
4 C2H2 2.1250000 -12.4978013 1.693933e-03
|
||||||
|
5 C2H4 2.0303030 -13.7496646 3.523327e-03
|
||||||
|
6 C2H6 2.0303030 -14.9862616 3.724381e-03
|
||||||
|
7 CH 2.1250000 -6.0641416 4.574267e-04
|
||||||
|
8 CH2_1A1 3.3478261 -6.7168950 1.009825e-03
|
||||||
|
9 CH2_3B1 3.1666667 -6.7315434 8.764920e-04
|
||||||
|
10 CH3 1.2727273 -7.4162327 5.305483e-04
|
||||||
|
11 CH3Cl 3.5454545 -22.5123924 4.245374e-03
|
||||||
|
12 CH4 1.7777778 -8.0950231 7.121452e-04
|
||||||
|
13 Cl Inf -14.9623070 5.120000e-04
|
||||||
|
14 Cl2 2.5714286 -30.0152826 4.435378e-03
|
||||||
|
15 ClF Inf -39.2471030 2.942000e-03
|
||||||
|
16 ClO 2.7037037 -30.9557213 3.402424e-03
|
||||||
|
17 CN 2.3333333 -15.5136342 1.488321e-03
|
||||||
|
18 CO 2.4482759 -21.7422903 1.696224e-03
|
||||||
|
19 CO2 Inf -37.8388280 3.554000e-03
|
||||||
|
20 CS 3.7619048 -15.8228210 2.003188e-03
|
||||||
|
21 F 3.1666667 -24.1949312 7.391838e-04
|
||||||
|
22 F2 4.8823529 -48.4453257 4.050079e-03
|
||||||
|
23 H 0.0000000 -0.5000220 3.200000e-05
|
||||||
|
24 H2CO 2.7037037 -22.9171510 3.311087e-03
|
||||||
|
25 H2O 2.2258065 -17.2591426 1.461246e-03
|
||||||
|
26 H2O2 13.2857143 -33.2120183 4.669473e-03
|
||||||
|
27 H2S 2.4482759 -11.4106147 3.903350e-04
|
||||||
|
28 H3COH Inf -24.1332880 2.934000e-03
|
||||||
|
29 H3CSH 2.4482759 -18.2993308 4.557326e-03
|
||||||
|
30 HCl 3.3478261 -15.6303714 1.893189e-03
|
||||||
|
31 HCN 2.3333333 -16.2207533 1.825787e-03
|
||||||
|
32 HCO 2.0303030 -22.2673034 3.309921e-03
|
||||||
|
33 HF 2.3333333 -24.9104643 1.191760e-03
|
||||||
|
34 HOCl 4.5555556 -31.6166964 4.824703e-03
|
||||||
|
35 Li 1.0000000 -0.1963480 2.000000e-05
|
||||||
|
36 Li2 0.7241379 -0.4314662 3.585501e-05
|
||||||
|
37 LiF 2.5714286 -24.6088303 1.550810e-03
|
||||||
|
38 LiH 2.4482759 -0.7887656 3.052112e-05
|
||||||
|
39 N 3.0000000 -9.7986421 3.121059e-04
|
||||||
|
40 N2 2.1250000 -19.9524868 1.048942e-03
|
||||||
|
41 N2H4 2.1250000 -22.2699022 4.249663e-03
|
||||||
|
42 Na 0.6129032 -0.1821443 2.754961e-05
|
||||||
|
43 Na2 0.0000000 -0.3910930 1.660000e-04
|
||||||
|
44 NaCl 1.1276596 -15.3111605 5.178434e-03
|
||||||
|
45 NH 2.3333333 -10.4264840 7.976368e-04
|
||||||
|
46 NH2 2.1250000 -11.0809890 1.362137e-03
|
||||||
|
47 NH3 1.8571429 -11.7605192 3.873223e-04
|
||||||
|
48 NO 2.3333333 -25.9345356 2.074537e-03
|
||||||
|
49 O 2.7037037 -15.9017110 5.380787e-04
|
||||||
|
50 O2 4.2631579 -31.9858778 2.794643e-03
|
||||||
|
51 OH 2.8461538 -16.5657615 1.069651e-03
|
||||||
|
52 P 2.5714286 -6.4727490 3.693525e-04
|
||||||
|
53 P2 2.8461538 -13.1215885 2.097094e-03
|
||||||
|
54 PH2 Inf -7.7124550 8.060000e-04
|
||||||
|
55 PH3 Inf -8.3503240 1.756000e-03
|
||||||
|
56 S Inf -10.1249220 3.820000e-04
|
||||||
|
57 S2 6.6923077 -20.4034043 3.266119e-03
|
||||||
|
58 Si Inf -3.7651370 1.260000e-04
|
||||||
|
59 Si2 4.0000000 -7.6457238 9.502980e-04
|
||||||
|
60 Si2H6 3.5454545 -11.3730818 3.867320e-03
|
||||||
|
61 SiH2_1A1 6.1428571 -5.0079101 8.651101e-04
|
||||||
|
62 SiH2_3B1 7.3333333 -4.9746405 7.553165e-04
|
||||||
|
63 SiH3 Inf -5.6243160 1.250000e-03
|
||||||
|
64 SiH4 2.5714286 -6.2776913 9.957806e-04
|
||||||
|
65 SiO 3.7619048 -19.9634155 1.961388e-03
|
||||||
|
66 SO Inf -26.2122290 4.822000e-03
|
||||||
|
67 SO2 3.0000000 -42.2998957 6.613564e-03
|
||||||
|
#+end_example
|
||||||
|
|
||||||
|
**** Atoms
|
||||||
|
Average percentage of the difference E_{DMC}(KS) - E_{DMC}(FCI) for all
|
||||||
|
atoms.
|
||||||
|
|
||||||
|
#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
|
||||||
|
atoms = c("Be", "C", "Cl", "F", "N", "O", "P", "S", "Si")
|
||||||
|
mid <- rep(0.,7)
|
||||||
|
hi <- rep(0.,7)
|
||||||
|
lo <- rep(0.,7)
|
||||||
|
x <- rep(0.,7)
|
||||||
|
|
||||||
|
for (atom in atoms) {
|
||||||
|
data <- subset(raw_data, (Method == "DMC" & Basis == "cc-pVDZ" & Molecule == atom))
|
||||||
|
vdz = data["Mu"]
|
||||||
|
data$"Mu" <- as.numeric(levels(factor(data$"Mu")))
|
||||||
|
vdz$"X" = data$"Mu"/(data$"Mu"+1.)
|
||||||
|
vdz$"E" = data$"TotalEnergy"
|
||||||
|
vdz$"E.lo" = data$"TotalEnergy" - data$"TotalEnergyErr"
|
||||||
|
vdz$"E.hi" = data$"TotalEnergy" + data$"TotalEnergyErr"
|
||||||
|
vdz$"Basis" = "VDZ-BFD"
|
||||||
|
vdz$"X"[7] <- 1.
|
||||||
|
vdz$"Mu"[7] <- TeX("$\\infty$")
|
||||||
|
# vdz.spline_int <- as.data.frame(spline(vdz$"X", vdz$"E", n=101))
|
||||||
|
# vdz.spline_int_lo <- as.data.frame(spline(vdz$"X", vdz$"E.lo", n=101))
|
||||||
|
# vdz.spline_int_hi <- as.data.frame(spline(vdz$"X", vdz$"E.hi", n=101))
|
||||||
|
|
||||||
|
# vdz.spline_int_lo$y <- (vdz.spline_int_lo$y - vdz.spline_int$y[101])/(vdz.spline_int$y[1]-vdz.spline_int$y[101])
|
||||||
|
# vdz.spline_int_hi$y <- (vdz.spline_int_hi$y - vdz.spline_int$y[101])/(vdz.spline_int$y[1]-vdz.spline_int$y[101])
|
||||||
|
# vdz.spline_int$y <- (vdz.spline_int$y - vdz.spline_int$y[101])/(vdz.spline_int$y[1]-vdz.spline_int$y[101])
|
||||||
|
|
||||||
|
# mid <- mid + vdz.spline_int$y
|
||||||
|
# hi <- hi + vdz.spline_int_hi$y
|
||||||
|
# lo <- lo + vdz.spline_int_lo$y
|
||||||
|
# x <- vdz.spline_int$x
|
||||||
|
|
||||||
|
mid <- mid + (vdz$"E" - vdz$"E"[7])/(vdz$"E"[1] - vdz$"E"[7])
|
||||||
|
hi <- hi + (vdz$"E.hi" - vdz$"E"[7])/(vdz$"E"[1] - vdz$"E"[7])
|
||||||
|
lo <- lo + (vdz$"E.lo" - vdz$"E"[7])/(vdz$"E"[1] - vdz$"E"[7])
|
||||||
|
x <- vdz$"X"
|
||||||
|
}
|
||||||
|
|
||||||
|
out = data.frame(mid)
|
||||||
|
out$mid <- mid / length(atoms)
|
||||||
|
out$hi <- hi / length(atoms)
|
||||||
|
out$lo <- lo / length(atoms)
|
||||||
|
out$x <- x
|
||||||
|
|
||||||
|
breaks <- vdz$"X"
|
||||||
|
labels <- vdz$"Mu"
|
||||||
|
labels[7] <- TeX("$\\infty$")
|
||||||
|
|
||||||
|
p <- ggplot(out, aes(x=x, y=mid, ymin=lo, ymax=hi) )
|
||||||
|
p <- p + geom_point()
|
||||||
|
p <- p + geom_ribbon(alpha=0.5)
|
||||||
|
p <- p + scale_x_continuous(name=TeX("$\\mu$"), breaks=breaks, labels=labels)
|
||||||
|
p <- p + scale_y_continuous(name = TeX("\\frac{E_{DMC} - E_{DMC}(FCI)}{E_{DMC}(KS) - E_{DMC}(FCI)}"), breaks=seq(0.,1.,0.2))
|
||||||
|
p <- p + theme(text = element_text(size = 20, family="Times"), legend.position = c(.15, .15))
|
||||||
|
p
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:/tmp/babel-RBQjE9/figuremq7fNJ.png]]
|
||||||
|
|
||||||
|
**** Molecules
|
||||||
|
|
||||||
|
#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
|
||||||
|
molecules <- c("BeH", "C2H2", "C2H4", "C2H6", "CH", "CH2_1A1", "CH2_3B1", "CH3", "CH3Cl", "CH4", "CN", "CO", "CO2", "CS", "Cl2", "ClF", "ClO", "F2", "H2CO", "H2O", "H2O2", "H2S", "H3COH", "H3CSH", "HCN", "HCO", "HCl", "HF", "HOCl", "Li2", "LiF", "LiH", "N2", "N2H4", "NH", "NH2", "NH3", "NO", "Na2", "NaCl", "O2", "OH", "P2", "PH2", "PH3", "S2", "SO", "SO2", "Si2", "Si2H6", "SiH2_1A1", "SiH2_3B1", "SiH3", "SiH4", "SiO")
|
||||||
|
molecules <- c("H2O")
|
||||||
|
molecules <- c("CH2_1A1")
|
||||||
|
molecules <- c("F2")
|
||||||
|
mid <- rep(0.,101)
|
||||||
|
hi <- rep(0.,101)
|
||||||
|
lo <- rep(0.,101)
|
||||||
|
x <- rep(0.,101)
|
||||||
|
|
||||||
|
#mid <- rep(0.,7)
|
||||||
|
#hi <- rep(0.,7)
|
||||||
|
#lo <- rep(0.,7)
|
||||||
|
#x <- rep(0.,7)
|
||||||
|
|
||||||
|
for (molecule in molecules) {
|
||||||
|
data <- subset(raw_data, (Method == "DMC" & Basis == "cc-pVDZ" & Molecule == molecule & Mu != "opt"))
|
||||||
|
vdz = data["Mu"]
|
||||||
|
vdz$"Mu" <- as.numeric(levels(factor(data$"Mu")))
|
||||||
|
vdz$"X" = vdz$"Mu"/(vdz$"Mu"+1.)
|
||||||
|
vdz$"E" = data$"TotalEnergy"
|
||||||
|
vdz$"E.lo" = data$"TotalEnergy" - data$"TotalEnergyErr"
|
||||||
|
vdz$"E.hi" = data$"TotalEnergy" + data$"TotalEnergyErr"
|
||||||
|
vdz$"Basis" = "VDZ-BFD"
|
||||||
|
vdz$"X"[7] <- 1.
|
||||||
|
vdz$"Mu"[7] <- TeX("$\\infty$")
|
||||||
|
vdz.spline_int <- as.data.frame(spline(vdz$"X", vdz$"E", n=101))
|
||||||
|
vdz.spline_int_lo <- as.data.frame(spline(vdz$"X", vdz$"E.lo", n=101))
|
||||||
|
vdz.spline_int_hi <- as.data.frame(spline(vdz$"X", vdz$"E.hi", n=101))
|
||||||
|
|
||||||
|
vdz.spline_int_lo$y <- (vdz.spline_int_lo$y - vdz.spline_int$y[101])/(vdz.spline_int$y[1]-vdz.spline_int$y[101])
|
||||||
|
vdz.spline_int_hi$y <- (vdz.spline_int_hi$y - vdz.spline_int$y[101])/(vdz.spline_int$y[1]-vdz.spline_int$y[101])
|
||||||
|
vdz.spline_int$y <- (vdz.spline_int$y - vdz.spline_int$y[101])/(vdz.spline_int$y[1]-vdz.spline_int$y[101])
|
||||||
|
|
||||||
|
mid <- mid + vdz.spline_int$y
|
||||||
|
hi <- hi + vdz.spline_int_hi$y
|
||||||
|
lo <- lo + vdz.spline_int_lo$y
|
||||||
|
x <- vdz.spline_int$x
|
||||||
|
|
||||||
|
# mid <- mid + (vdz$"E" - vdz$"E"[7])/(vdz$"E"[1] - vdz$"E"[7])
|
||||||
|
# hi <- hi + (vdz$"E.hi" - vdz$"E"[7])/(vdz$"E"[1] - vdz$"E"[7])
|
||||||
|
# lo <- lo + (vdz$"E.lo" - vdz$"E"[7])/(vdz$"E"[1] - vdz$"E"[7])
|
||||||
|
# x <- vdz$"X"
|
||||||
|
}
|
||||||
|
|
||||||
|
out = data.frame(mid)
|
||||||
|
out$mid <- mid / length(molecules)
|
||||||
|
out$hi <- hi / length(molecules)
|
||||||
|
out$lo <- lo / length(molecules)
|
||||||
|
out$x <- x
|
||||||
|
|
||||||
|
breaks <- vdz$"X"
|
||||||
|
labels <- vdz$"Mu"
|
||||||
|
labels[7] <- TeX("$\\infty$")
|
||||||
|
|
||||||
|
p <- ggplot(out, aes(x=x, y=mid, ymin=lo, ymax=hi) )
|
||||||
|
p <- p + geom_line()
|
||||||
|
p <- p + geom_ribbon(alpha=0.5)
|
||||||
|
p <- p + scale_x_continuous(name=TeX("$\\mu$"), breaks=breaks, labels=labels)
|
||||||
|
p <- p + scale_y_continuous(name = TeX("\\frac{E_{DMC} - E_{DMC}(FCI)}{E_{DMC}(KS) - E_{DMC}(FCI)}"))
|
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|
p <- p + theme(text = element_text(size = 20, family="Times"), legend.position = c(.15, .15))
|
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|
p
|
||||||
|
#+end_src
|
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|
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|
#+RESULTS:
|
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|
[[file:/tmp/babel-RBQjE9/figureD9kKIs.png]]
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|
|
||||||
*** Figure MAD R DZ
|
*** Figure MAD R DZ
|
||||||
#+begin_src R :results output :session *R* :exports both
|
#+begin_src R :results output :session *R* :exports both
|
||||||
data <- data.frame(ref["Molecule"])
|
data <- data.frame(ref["Molecule"])
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|
BIN
Manuscript/f2-dmc.pdf
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Manuscript/f2-dmc.pdf
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Manuscript/overlap.pdf
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Manuscript/overlap.pdf
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@ -142,14 +142,14 @@ factor.\cite{Giner_2016,Dash_2018,Dash_2019}
|
|||||||
\begin{enumerate}
|
\begin{enumerate}
|
||||||
\item Total energies and nodal quality:
|
\item Total energies and nodal quality:
|
||||||
\begin{itemize}
|
\begin{itemize}
|
||||||
\item Factual stuffs: KS occupied orbitals closer to NOs than HF
|
\item Facts: KS occupied orbitals closer to NOs than HF
|
||||||
\item Even if exact functional, complete basis set, still approximated nodes for KS
|
\item Even if exact functional, complete basis set, still approximated nodes for KS
|
||||||
\item KS -> exponentially fast convergence (as HF) with basis because of non divergence of effective KS potential (citer le papier de Gill)
|
\item KS -> exponentially fast convergence (as HF) with basis because of non divergence of effective KS potential (citer le papier de Gill)
|
||||||
\item With correlation consistent basis set, FCI nodes (which include correlation) are better than KS
|
\item With correlation consistent basis set, FCI nodes (which include correlation) are better than KS
|
||||||
\item With FCI, good limit at CBS ==> exact energy
|
\item With FCI, good limit at CBS ==> exact energy
|
||||||
\item But slow convergence with basis set because of divergence of the e-e interaction not well represented in atom centered basis set
|
\item But slow convergence with basis set because of divergence of the e-e interaction not well represented in atom centered basis set
|
||||||
\item Exponential increase of number of Slater determinants
|
\item Exponential increase of number of Slater determinants
|
||||||
\item Cite papierS RS-DFT: there exists an hybrid scheme combining fast convergence wr to basis set (non divergent basis set) and short expansion in SCI (cite papier Ferté)
|
\item Cite papiers RS-DFT: there exists an hybrid scheme combining fast convergence wr to basis set (non divergent basis set) and short expansion in SCI (cite papier Ferté)
|
||||||
\item Question: does such a scheme provide better nodal quality ?
|
\item Question: does such a scheme provide better nodal quality ?
|
||||||
\item In RSDFT we cannot optimize energy with $\mu$ , but in FNDMC
|
\item In RSDFT we cannot optimize energy with $\mu$ , but in FNDMC
|
||||||
\item Factual stuffs: with optimal $\mu$, lower FNDMC energy than HF/KS/FCI
|
\item Factual stuffs: with optimal $\mu$, lower FNDMC energy than HF/KS/FCI
|
||||||
@ -166,6 +166,9 @@ factor.\cite{Giner_2016,Dash_2018,Dash_2019}
|
|||||||
\item basis set dependent: $\mu \rightarrow \infty$ when $\mathcal{B}\rightarrow \text{CBS}$
|
\item basis set dependent: $\mu \rightarrow \infty$ when $\mathcal{B}\rightarrow \text{CBS}$
|
||||||
\item large wave functions
|
\item large wave functions
|
||||||
\end{itemize}
|
\end{itemize}
|
||||||
|
\begin{itemize}
|
||||||
|
\item plot $N_{det}$ en fonction de $\mu$
|
||||||
|
\end{itemize}
|
||||||
\end{itemize}
|
\end{itemize}
|
||||||
\end{enumerate}
|
\end{enumerate}
|
||||||
|
|
||||||
@ -398,10 +401,18 @@ implemented.\cite{GinPraFerAssSavTou-JCP-18}
|
|||||||
\begin{figure}[h]
|
\begin{figure}[h]
|
||||||
\centering
|
\centering
|
||||||
\includegraphics[width=\columnwidth]{h2o-dmc.pdf}
|
\includegraphics[width=\columnwidth]{h2o-dmc.pdf}
|
||||||
\caption{Fixed-node energies of the water molecule with variable
|
\caption{Fixed-node energies of the water molecule for different
|
||||||
values of $\mu$.}
|
values of $\mu$.}
|
||||||
\label{fig:h2o-dmc}
|
\label{fig:h2o-dmc}
|
||||||
\end{figure}
|
\end{figure}
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=\columnwidth]{f2-dmc.pdf}
|
||||||
|
\caption{Fixed-node energies of difluorine for different
|
||||||
|
values of $\mu$.}
|
||||||
|
\label{fig:f2-dmc}
|
||||||
|
\end{figure}
|
||||||
The water molecule was taken at the equilibrium
|
The water molecule was taken at the equilibrium
|
||||||
geometry,\cite{Caffarel_2016} and RSDFT-CIPSI wave functions were
|
geometry,\cite{Caffarel_2016} and RSDFT-CIPSI wave functions were
|
||||||
generated with BFD pseudopotentials and the corresponding double-zeta
|
generated with BFD pseudopotentials and the corresponding double-zeta
|
||||||
@ -433,6 +444,13 @@ in the CBS limit we expect the minimum of the FN-DMC energy to be
|
|||||||
obtained for the FCI wave function, at $\mu=\infty$.
|
obtained for the FCI wave function, at $\mu=\infty$.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=\columnwidth]{overlap.pdf}
|
||||||
|
\caption{Overlap of the RSDFT-CIPSI wave functions with the
|
||||||
|
wave function reoptimized in the presence of a Jastrow factor.}
|
||||||
|
\label{fig:overlap}
|
||||||
|
\end{figure}
|
||||||
\section{Computational details}
|
\section{Computational details}
|
||||||
\label{sec:comp-details}
|
\label{sec:comp-details}
|
||||||
|
|
||||||
|
Loading…
Reference in New Issue
Block a user