<p>You went to a foreign university that typically ranks around #100 (within the UK not the world). You got a degree in something only tangentially related to chemistry. You don’t seem to have substantial research experience. In this U.S., this is a formula for getting summarily rejected, especially due to the lack of research.</p>
<p>There has to be confluence of high numbers (GPA/GRE), research experience <em>that results in letters</em>, and a well-matched advisor who is taking students that year. Top students from top American programs regularly get rejected by schools like Caltech and UCSF. Your Cambridge acceptance doesn’t invalidate your American rejections – a UK PhD isn’t the same as an American PhD as others have pointed out and UCR isn’t “widely regarded as easy to get into”.</p>