I’ve witnessed some Atheists get quite flustered and occasionally angered when other people pray for them. Although I tarried in this mindset for a short period I now value the act of prayer and meditation. It is a conscious act to extend positive energy to another being or set of beings.
I don’t believe in an interventionist God. But I know darling that you do – Nick Cave (Into my arms)
This is as good a place to start to describe my viewpoint on prayer. We are not products of the environment we exist in but we are influenced in many ways by it. I grew up in a staunchly Catholic family and school system but I was encouraged not to limit my viewpoint to those taught by religious leaders, or held by the society of the time. The most profound influence however was reading The Varieties of Scientific Experience: A Personal View of the Search for God (2006) by Dr Carl Sagan based on his Gifford Lecture under the theme The Search For Who We Are.
Dr Carl Sagan is known to have said that there is no scientific evidence that God exists but he also acknowledged that neither has evidence that God doesn’t exist been provided.
In over twenty years of training in the martial arts, specifically Aikido, the most valuable notion I have discovered is the untapped power of the sentient mind.
In general terms, how often have you felt your mind disturbed and looked up to see someone watching you. Just as in combat when we sense an opponent’s attack before they physically move, so can we sense another sentient mind’s attention on our mind.
The sentient mind is a powerful instrument and should not be underestimated
It is the act of prayer or meditation that adds value, not the actor’s faith in some hirsute gentleman or any other vision of a divine entity. So I encourage all sentient beings especially Atheists to practice the art of prayer or meditation.
A Fettered Mind 
“I like spring, however it is also young. I like summer, but it is too proud. So I like finest of all autumn, simply because its leaves are slightly yellow, its tone mellower, its colours richer, and it is tinged just a little with sorrow and a premonition of death. Its golden richness speaks not from the innocence of spring, nor from the power of summer time, but with the mellowness and kindly wisdom of approaching age. It knows the limitations of life and is content. From a information of those limitations and its richness of encounter emerges a symphony of colours, richer than all, its green speaking of life and strength, its orange speaking of golden content material and its purple of resignation and death”