The molecular formula is the simplest way to characterize a molecular compound. It specifies the actual number of atoms of each element contained in the molecule. A molecular formula is represented by the chemical symbol of each constituent element. If a molecule contains more than one atom for a particular element, the quantity is shown as subscript after the chemical symbol. Otherwise, the number of neutrons (atomic mass) that an atom is composed can differ. This different type of atoms are known as isotopes. The number of nuclei is represented as superscripted prefix previous to the chemical element. Generally it is not added when the isotope that characterizes the element is the most occurrence in nature, e.g., \(C_4H_{11}O^2D\).
Front a molecule, defined as conjunct of atoms helding together by chemical
bonds, we can simplify it taking only the information about the atoms. The rcdk
package provides a parser to translate molecules to molecular formlulas, the
get.mol2formula function.
library(rcdk)
## Loading required package: rcdklibs
## Loading required package: rJava
sp <- get.smiles.parser()
molecule <- parse.smiles('N')[[1]]
convert.implicit.to.explicit(molecule)
formula <- get.mol2formula(molecule,charge=0)
Note that the above formula object is a CDKFormula-class. This class
contains some attributes that defines a molecular formula. For example,
the mass, the charge, the isotopes, the character representation of the
molecular formula and the IMolecularFormula jobjRef object.
The molecular mass, charge and string representation for this formula are given by
formula@mass
## [1] 17.02655
formula@charge
## [1] 0
formula@string
## [1] "H3N"
The isotopes for this formula. It is formed from three attributes. isoto (the
symbol expression of the isotope), number (number of atoms for this isotope)
and mass (exact mass of this isotope).
formula@isotopes
## isoto number mass
## [1,] "N" "1" "14.003074"
## [2,] "H" "3" "1.007825032"
Depending of the circumstances, you may want to change the charge of the molecular formula.
formula <- set.charge.formula(formula, charge=1)
Other way to create a cdkFormula is from the symbol expression. Thus,
setting the characters of the elemental formula, the function get.formula
parses it to an object of cdkFormula-class.
formula <- get.formula('NH4', charge = 1)
formula
## cdkFormula: [H4N]+ , mass = 18.03383 , charge = 1
Mass spectrometry is an essential and reliable technique to determine the
molecular mass of compounds. Conversely, one can use the measured mass
to identify the compound via its elemental formula. One of the limitations
of the method is the precision and accuracy of the instrumentation. As
a result, rather than specify exact masses, we specify tolerances or ranges
of possible mass, resulting in multiple candidate formulae for a given mass
window. The generate.formula function returns a list of formulae which have
a given mass (within an error window)
mfSet <- generate.formula(18.03383, window=1,
elements=list(c("C",0,50),c("H",0,50),c("N",0,50)),
validation=FALSE)
mfSet
## [[1]]
## cdkFormula: H4N , mass = 18.03437 , charge = 0
##
## [[2]]
## cdkFormula: CH6 , mass = 18.04695 , charge = 0
##
## [[3]]
## cdkFormula: H18 , mass = 18.14085 , charge = 0
It is important to know if an elemental formula is valid. The method isvalid.formula
provides this function. Two constraints can be applied, the
nitrogen rule and the RDBE rule (Ring Double Bond Equivalent).
formula <- get.formula('NH4', charge = 0)
isvalid.formula(formula,rule=c("nitrogen","RDBE"))
## [1] FALSE
We can observe that the ammonium is only valid if it is defined with charge of +1.
formula <- get.formula('NH4', charge = 1)
isvalid.formula(formula,rule=c("nitrogen","RDBE"))
## [1] TRUE
The generate.formula method can perform these validation tests during formula generation by setting validation=TRUE. However, this can significantly slow down the process of genersating formulae, especially with larger mass windows. When the default of FALSE is used, nonsensical formulae may be generated, and it's up to the user to filter them out.
In contrast, the generate.formula.iter method employs the Round Robin formula generation algorithm, which is significantly faster than the default method. In contrast to generate/formula, this method returns an iterator which allows you to process large formula sets without excessive memory usage.
mit <- generate.formula.iter(100, charge=0, window=0.1,
elements=list(c("C",0,50), c("H",0,50), c("N",0,50)))
hit <- itertools::ihasNext(mit)
while (itertools::hasNext(hit))
print(iterators::nextElem(hit))
## [1] "[12]C8[1]H4"
## [1] "[12]C7[1]H2[14]N"
## [1] "[12]C6[14]N2"
## [1] "[12]C4[1]H10[14]N3"
## [1] "[12]C3[1]H8[14]N4"
## [1] "[12]C2[1]H6[14]N5"
## [1] "[12]C[1]H4[14]N6"
## [1] "[1]H2[14]N7"
Note that by default, this function will not check for validity of the generated formulae.
Due to the measurement errors in medium resolution spectrometry, a given
error window can result in a massive number of candidate formulae. The
isotope pattern of ions obtained experimentally can be compared with the
theoretical ones. The best match is reflected as the most probable elemental
formula. rcdk provides the function get.isotope.pattern which predicts
the theoretical isotope pattern given a formula.
formula <- get.formula('CHCl3', charge = 0)
isotopes <- get.isotopes.pattern(formula,minAbund=0.1)
isotopes
## mass abund
## [1,] 117.9144 1.0000000
## [2,] 119.9114 0.9598733
## [3,] 121.9085 0.3071189
In this example we generate a formula for a possible compound with a charge (\(z \approx 0\)) containing the standard elements C, H, and Cl. The isotope pattern can be visually inspected, as shown below.
plot(isotopes, type="h", xlab="m/z", ylab="Intensity")