You have to evaluate the Hessian to estimate standard error for a parameter
fit = optim(start.theta, fn = function, #start.theta initial value of paramter
hessian = TRUE, method = "L-BFGS-B", #hessian True to calculate Hessian matrix
lower = c(),
upper = c(),
control = list(trace = 1, fnscale = -1)) #fnscale= -1 to maximize the function
theta.hat = fit$par #parameter estimate
sd.hat = sqrt(diag(solve(fit$hessian/(n-1)))) #se estimate
# you could use also optimHess to evaluate the Hessian
solved How can I estimate standard error in maximum likelihood destinati in [closed]