A professional executive portrait should reflect your expertise, your ambition, but most importantly your personality, energy, and your executive presence.
We should be able to feel who you are as a person, a leader, a manager, a coworker, etc.
That's what makes us unique and irreplaceable (not like knowledge or degrees) and that the intangible part of personal branding
The purpose of a professional headshot at the top of your Linkedin profile is yes, to have your profile more visited than without a professional photo: a profile including a photo receive 21x more profile views and up to 36x more messages.
But it is also to share a consistent message with the written content of your profile as well as start to convey your energy before you even meet and speak during an interview ! It should create a positive 'emotional' reaction with the person that views the professional portrait and make that person wants to meet you and speaks with you.
For that, your expression should then be genuine and comfortable. That's what people 'intentionally' mean when they describe someone as 'photogenic' on photos / looking confident on photos: the level of comfort on a picture.
During a professional portrait shoot, I very often tell my clients: "Do not overthink too much about what you should or should not do." And I guide them all the way.
>> IF YOU ARE A SMILEY PERSON NATURALLY: YES LET THAT BIG SMILE OUT.
Otherwise you will most probably not like your professional photos or even recognize yourself on them. A smile will never take away your sense of professionalism & your expertise.
>> IF YOU ARE NOT A SMILEY PERSON NATURALLY or you don't like your teeth, it is totally fine too as long as you feel COM-FOR-TABLE (.. aka the magic 'photogenic' ingredient). Through many other tricks your photographer should be able to make someone at ease to enjoy the experience and end up with a broad spectrum of smiles that all convey a beautiful warm positive comfortable approachable energy.
So to conclude:
There are absolutely NO RULES for a smile or not smile on your professional photos.
The only rule is to FEEL YOURSELF, not forcing anything and look comfortable (a big part of your professional photographer's job 😉) to leave viewers a CONVINCING first impression through your professional headshot.