Unable to focus after separation with wife, have suicidal thoughts

Yes, you're quite right. If suicidal thoughts have become a part of your daily life, seeking professional help is a priority.
You have gone through a traumatic experience with your partner and it seems to have affected you greatly. I would strongly suggest reaching out to a counselor/ mental health professional and making your well-being a priority at the moment.

Your relationship with your wife and the turn your marriage has taken can be due to various reasons. Also it is unclear on whether you are separated from her or are legally divorced.
If there is a possibility of addressing your wife's issues to get her to give another shot to your marriage then I would suggest you make that effort and address her issues and find out what went wrong for her in the marriage.

However, if you have broken it off for good and are facing hardships in dealing with the breakup, I would recommend seeking help, again. And also having one member of your family, whom you trust or a friend who is close to you, spend more time with you, allowing you to vent and talk about everything, serving as a support system will be hugely helpful, in addition to the professional help.
I'm glad you've taken a step and reached out for help on this platform. Your experience has bee quite traumatic and you've made a healthy choice by seeking help.