How to draw the curves in an energy diagram in R? - r

Question

I wrote following R script:
#energy diagram
x <- c(0.1, 0.3, 0.5, 0.7, 0.9 ) #chosen randomly, reaction axis
y <- c(-5.057920, -5.057859, -5.057887,-5.057674, -5.057919 ) #energy of the educt, intermediate, transtition states and product
plot(x,y, type="p",
xlim=c(0,1),
ylim=c(-5.058,-5.0575),
xlab="reaction axis",
ylab=expression(paste(E[el] ," / ",10^6," ",kJ/mol)),
xaxt="n" #hide x-axis
)
#h- and v-lines, so i can draw curves by hand
abline(v=seq(0,1,0.1),h=seq(-5.0600,-5.0500,0.00005),col="black",lty=1,lwd=1)
abline(h=c(-5.057920, -5.057859, -5.057887,-5.057674), col="blue", lty=1,lwd=0.7)
Is it possible to draw a curve through the points that would look like a energy diagram. An example of an energy diagram is here:

Answer 1

A lot could be done to streamline / vectorize this code, but for a smallish diagram this works pretty well:
# get that data
x <- c(0.1, 0.3, 0.5, 0.7, 0.9 ) # reaction axis
y <- c(-5.057920, -5.057859, -5.057887,-5.057674, -5.057919 ) # energies
I'm going to make a little Bezier curve to connect each point to the next---this way we can make sure the smooth line passes through the data, not just close to it. I'll give each point a single 'control point' to define the slope. By using the same y-values for a point and it's control point, the slope at the point will be 0. I'll call the offset between the point and the control point delta. We'll start with one point-pair:
library(Hmisc)
delta = 0.15
bezx = c(0.1, 0.1 + delta, 0.3 - delta, 0.3)
bezy = rep(y[1:2], each = 2)
plot(bezx, bezy, type = 'b', col = "gray80")
lines(bezier(bezx, bezy), lwd = 2, col = "firebrick4")
Here I plotted the points and control points in gray, and the smooth line in red so we can see what's going on.
It looks promising, let's turn it into a function that we can apply to each pair of points:
bezf = function(x1, x2, y1, y2, delta = 0.15) {
bezier(x = c(x1, x1 + delta, x2 - delta, x2), y = c(y1, y1, y2, y2))
}
You can play with the delta parameter, I think 0.1 looks pretty good.
plot(x, y, xlab = "Reaction coordinate", ylab = "E", axes = F)
box(bty = "L")
axis(side = 2)
for(i in 1:(length(x) - 1)) {
lines(bezf(x1 = x[i], x2 = x[i + 1], y1 = y[i], y2 = y[i + 1], delta = 0.1))
}
You can of course tweak the plot, add labels, and ablines as in your original. (Use my for loop with the lines command to draw only the smoothed lines.) I left the points on to show that we are passing through them, not just getting close.
I prefer plotting in ggplot2, if you do too you'll need to extract the data into a data.frame:
bezlist = list()
for (i in 1:(length(x) - 1)) {
bezlist[[i]] = bezf(x1 = x[i], x2 = x[i + 1], y1 = y[i], y2 = y[i + 1], delta = 0.1)
}
xx = unlist(lapply(bezlist, FUN = '[', 'y'))
yy = unlist(lapply(bezlist, FUN = '[', 'y'))
bezdat = data.frame(react = xx, E = yy)
library(ggplot2)
ggplot(bezdat, aes(x = react, y = E)) +
geom_line() +
labs(x = "Reaction coordinate")

Answer 2

You could use a spline fit. Define some points along the energy diagram, and then fit to them using a spline function. The more points that you provide, the better that your fit will be. You can check out the smooth.splines function in the stats package for one implementation of the spline fit.