It is a good idea, however, to start an honest conversation with them and become interested in their posts. Rather than spamming them with your requests and links, try for example: “I found this Tweet you did interesting and I’d like to know more about it.”
Through sincere conversations, you are more likely to get better reactions from your Tweets. It is a good idea, also, to follow people and connect with people who work at the recognized companies that you think will benefit you; however the people you follow may not necessarily be the company VPs. Chances are people who have over 10,000 followers receive messages frequently and you less likely to get a response from them. However, if you are able to find people who work at the company you want to get connected with that may have between 100-and 1,000 followers, you are more likely to get a response.