The phrase "at the neglect of" is correct and usable in written English.
It can be used to indicate that something is being done while ignoring or overlooking another important aspect or consideration.
Example: "He pursued his career ambitions at the neglect of his health and personal relationships."
Alternatives: "to the detriment of" or "at the expense of".
Later, when John returned, the man said he was embittered at the neglect of his children.
This week Peter Kilfoyle, a junior minister at Westminster, resigned in protest at the neglect of traditional Labour areas.
But not at the neglect of an industrial base which has continued to be eroded in the past few years by manufacturing recession and an overvalued currency.
It is critical of emphasis on single diseases and points out that this is being done at the neglect of basic health care systems.
Forty-two andhors artistsisignedgned an open letter denouncing the choice and protesting at the neglect of Tolstoy, still alive and writing - nothing if not idealistically - on his estate at Yasnaya Polyana.
She has shown some irritation at the neglect of her later work, commenting in an interview that some people "think [The Grass is Singing is] the best thing I ever wrote, which is really annoying".
Looking at literature, the neglect of this dislocation is thankfully rarely reported.
While opinions differ within the movement as to the wisdom of US-Iran diplomacy at this time, the neglect of human rights fuels pre-existing suspicions about the objectives of American diplomacy.
The leading approximation is deficient at short times due to the neglect of the memory terms.
The neglect of Christ at Christmastime and the helplessness to which God submitted in becoming a human infant are stock themes of Christian holiday preaching.
The neglect of students at both ends of the spectrum systematically ignores our mission as educators and hurts children.
