Finding the right partner at a venture fund to submit your executive summary to can significantly increase your odds of being asked in for a meeting.  Assuming that you don’t have an existing relationship or a mutual contact with any of the partners, the key is to find someone that shares common interests with you.  Common interests can be related to your business or to your personal life. 

First try to find which partner would identify with your business. There is typically some degree of specialization within a venture fund - each partner focuses on sectors that reflect their experience from their career before becoming a VC and from the boards they sit on as a VC.  If there is a partner who focuses on your sector or industry you should try to get your executive summary to them; their expertise is likely to help them more rapidly understand your vision, increasing the odds that they will want to learn more.

Whether you find a partner at the fund with sector expertise or not, you should try to find common ground on a personal level to warm up the relationship.  In your introductory email, your first direct email to the partner, you should let the partner know what you have in common.  This could include: growing up in the same town, having studied at the same place, belonging to the same country club, having a mutual friend, going to the same industry conferences or sharing the same hobbies (e.g., a sport). 

While information about the partner's background and interests may not be readily available, you should be able to find a good bit of info by scouring certain websites, such as LinkedIn and ZoomInfo.

In some instances the partner that focuses on your sector may not be the person who you have common interests with.  In this case you should copy both people on one email that introduces the company and highlights the common ground that you have with one of the partners.  If you send separate emails, the person who has common ground with you may forget to tell the sector specialist that you are more interesting than average - information that could significantly increase your traction with the sector expert (who is likely to take his partner's favoritism into account).

It's a surprisingly small world.  Even if you don’t have an existing relationship or mutual contact with any of the partners, there are good odds that you have something in common with at least on partner at each firm.  Take the time to find your common ground - it will pave the path of least resistance.